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estimation of energy consumed 
by middle-aged recreational 
marathoners during a marathon 
using accelerometry-based devices
carlos Hernando1,2*, Carla Hernando3, Ignacio Martinez-navarro4,5, Eladio collado-Boira6, 
nayara panizo6 & Barbara Hernando7
As long-distance races have substantially increased in popularity over the last few years, the 
improvement of training programs has become a matter of concern to runners, coaches and health 
professionals. triaxial accelerometers have been proposed as a one of the most accurate tools to 
evaluate physical activity during free-living conditions. In this study, eighty-eight recreational 
marathon runners, aged 30–45 years, completed a marathon wearing a GENEActiv accelerometer 
on their non-dominant wrist. energy consumed by each runner during the marathon was estimated 
based on both running speed and accelerometer output data, by applying the previously established 
GENEActiv cut-points for discriminating the six relative-intensity activity levels. Since accelerometry 
allowed to perform an individualized estimation of energy consumption, higher interpersonal 
differences in the number of calories consumed by a runner were observed after applying the 
accelerometry-based approach as compared to the speed-based method. Therefore, pacing analyses 
should include information of effort intensity distribution in order to adjust race pacing appropriately 
to achieve the marathon goal time. Several biomechanical and physiological parameters (maximum 
oxygen uptake, energy cost of running and running economy) were also inferred from accelerometer 
output data, which is of great value for coaches and doctors.
Running a marathon has rapidly become one of the most popular activities nowadays as shown by the number of 
amateur participants with hundreds of marathons worldwide1,2. It is well-known that running a marathon is one 
of the most challenging endurance competitions3,4. As a result of recent research focused on improving training 
programs, which aimed to avoid soreness and prevent energy deficit during ultraendurance races5, the number 
of runners crossing the finish (ultra)marathon line has significantly raised over the past few years6,7. For example, 
a total of 3,388 runners more finished the Valencia Fundación Trinidad Alfonso EDP Marathon in 2018 as com-
pared to the 2016 edition (19,246 versus 15,858 finishers, respectively)8.
In their way towards the improvement of marathon time, recreational runners are surrounded by a wide range 
of professionals in order to achieve their objectives9,10. Consequently, many studies has been focused on develop-
ing different methodologies to evaluate factors affecting running performance, such as the pacing strategy2,11, the 
energy consumption12–14, the maximal oxygen uptake V
( O
)
2 max
15, the fraction of VO2 max

 maintained (F)15, the 
running speed16, the energy cost of running (Cr)17, and physical, biomechanical, metabolic, psychological and 
social factors18.
Among all these factors, changes of running speed over race sections have been widely studied in order to 
explain the running success of more efficient pacers – runners who are able to maintain their initial running pace 
for more kilometers2. These more efficient pacers may avoid an excessive energy consumption while running the 
first part of the marathon5.
1Sport Service, Jaume I University, Castellon, Spain. 2Department of Education and Specific Didactics, Jaume 
I University, Castellon, Spain. 3Department of Mathematics, Carlos III University of Madrid, Madrid, Spain. 
4Department of Physical Education and Sport, University of Valencia, Valencia, Spain. 5Sports Health Unit, Vithas-
Nisa 9 de Octubre Hospital, Valencia, Spain. 6Faculty of Health Sciences, Jaume I University, Castellon, Spain. 
7Department of Medicine, Jaume I University, Castellon, Spain. *email: hernando@uji.es
open
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Therefore, measuring the energy expended by an individual while performing a specific activity has recently 
been targeted by researchers. Ainsworth and colleagues published The Compendium of Physical Activities in 
1993 (which was reviewed in 2000 and 2011), allowing to directly extrapolate the energy expenditure in Metabolic 
Equivalent Task (METs), and thus in kilocalories (kcal), for running activities according to speed12,13,19.
Since the Compendium did not take into account interpersonal differences, the use of accelerometry-based 
devices has been proposed to evaluate free-living physical activities performed by an individual, in terms of dura-
tion, frequency and intensity14,20,21. Therefore, using the cut-points recommended for a specific population and/
or activity, accelerometer output data can be applied to indirectly measure the energy expended by an individual 
in METs22–24.
In this regard, our research group aimed to monitor middle-aged recreational marathoners during a marathon 
using accelerometry-based devices. For this purpose, we previously established the GENEActiv cut-points that 
dsicriminate the six relative-intensity activity levels in recreational marathoners25. This lab-based study was essen-
tial in order to delineate specific GENEActiv cut-points for a specific population who presents higher relative level 
of fitness than the standard adult population. At this point, the main goal of the current study was to apply the 
GENEActiv cut-points previously established for estimating the energy consumed by middle-aged recreational 
marathoners during a marathon race (a free-living condition). Accelerometer output data allowed us to analyze 
the effort distribution that runners followed to achieve their marathon time, by means of the time running at 
each one of the six related-intensity levels (sedentary, light, moderate, vigorous, very vigorous and extremely vig-
orous activity) during the marathon. This information may be extremely valuable for both athletes and coaches. 
Knowing the intensity, duration and energy cost of an activity is useful for designing training sessions because it 
allows to objectively quantify and monitor training load. Energy consumption was also estimated based on run-
ning speed12, and results were compared with those obtained after using accelerometer data.
Results
A detailed description of individuals included in this study is summarized in Table 1.
The accelerometer output data allowed us to analyse the effort distribution that runners followed to achieve 
their marathon time, by means of the time running at each one of the six related-intensity levels (sedentary, light, 
moderate, vigorous, very vigorous and extremely vigorous activity) during the marathon. Values established for 
delineating the six-relative intensity levels of physical activity are detailed in Table 2.
For all individuals, we estimated the energy cost of running a marathon, presenting the caloric consumption 
for each one of the 9 marathon sections as well as for the full marathon distance (Tables 3 and 4). The calories 
consumed by each runner were calculated based on both accelerometer data (Table 3), as previously described by 
our research group25, and running speed (Table 4), following the methodology proposed by Ainsworth and cols12. 
The aim of applying also the speed-based method12 in the estimation of energy consumption was to compare the 
results obtained with accelerometer devices25. Note that a gold standard method for energy quantification in long 
distance races has not been defined yet.
Except for the last race section, a higher number of calories was estimated to be consumed by a runner when 
the accelerometry-based method was applied, as compared to the caloric consumption estimated by using the 
Variable
Subjects
(N = 88)
Physiological characteristics*
age
38.68 ± 3.61
BMI
22.91 ± 1.62
Weight
69.96 ± 8.91
Heigh
174.44 ± 8.66
% body fat
14.74 ± 4.38
VO2 max (ml·kg−1·min−1)
54.41 ± 5.66
maximum METs
15.55 ± 1.62
Training indicators*
years of running
6.43 ± 2.78
sessions per week
4.90 ± 0.84
kilometers per week
63.45 ± 13.06
hours per week
7.44 ± 2.70
History as marathoner*
marathons finished
3.36 ± 3.02
marathon per year
1.10 ± 0.63
Work intensity#
high intensity
7.95%
medium intensity
30.68%
low intensity
61.36%
Levels of study#
school graduate
4.60%
high school graduate
6.90%
professional certificate
17.24%
undergraduate degree
71.26%
Table 1. Population description. Abbreviations: N, number of samples; BMI, body mass index; SD, standard 
deviation. *Values are presented as mean ± SD. #Values are presented as percentage.
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speed method (Table 4). It is worth highlighting that a greater variation of calories consumed per each individual 
was observed after using accelerometry for energy cost estimation, rather than running speed (shown by higher 
standard deviation values). The reason of this difference is due to the fact that the accelerometer-based method 
takes into account the variability across individuals in terms of energy consumption, while speed-based method 
tends to standardize values for all subjects26.
Although no significant differences between energy consumption and marathon time were observed (Fig. 1), 
correlation analysis showed that the accelerometry-based method tended to increase the number of calories con-
sumed by the runner with marathon time (ρ = 0.179, p = 0.094). However, the Ainsworth’s method seemed to 
present a negative correlation between the caloric consumption and marathon time (Fig. 1). This correlation was 
also no significant (ρ = −0.137, p = 0.202).
For a better comparison between methods, the energy consumed by runners was expressed as a relative rate in kil-
ocalories per kilogram of body mass either per minute12,26 or per kilometer17,27, and as the number of times consum-
ing his/her Basal Metabolic Rate (BMR)26,28 (Table 4). The results of this comparison denoted statistically significant 
differences in the energy estimated to be consumed by runners after applying the accelerometry- and speed-based 
method. That was observed in each one of the 9 race sections as well as in the full marathon distance (Table 4).
Accelerometer output data allowed us to know the physical effort distribution of runners during the mara-
thon, in terms of physical activity intensity. That is, we were able to identify and quantify when a runner is racing 
at each one of the six relative-intensity activity levels (sedentary, light, moderate, vigorous, very vigorous and 
extremely vigorous)25. Therefore, following the values established in Table 2, the percentage of VO2 max

 produced 
per each runner was estimated, and this allowed then to calculate the energy of cost running above standing 
(Crnet)28 (Table 5).
A negative correlation between the relative energy consumed and the marathon time was observed when 
energy consumption was expressed as kilocalories per kilogram of body mass per minute. This negative correla-
tion was enlarged when the speed-based method was applied (ρ = −0.976, p = 1.12 × 10−58), in comparison with 
the accelerometry-based method (ρ = −0.307, p = 0.004) (Fig. 2). When the relative rate of energy consumption 
was expressed per distance (kcal·kg−1·km−1), the energy expended by runners was positively correlated with the 
marathon time after using accelerometry (ρ = 0.402, p = 1.01 × 10−4). No significant correlation was observed 
between energy consumption (expressed as a relative rate per kilogram of body weight per kilometre) and time 
when speed-based method was applied (ρ = −0.200, p = 0.062).
Discussion
In this study, we aimed to estimate the energy consumed by middle-aged recreational marathoners during a 
marathon race (a free-living condition) using accelerometry-based devices25. In our opinion, the application 
of accelerometers should be useful to minimize the interpersonal differences in energy consumption caused by 
physiological and biomechanical parameters and, therefore, to perform an individualized estimation of energy 
consumption.
Up to now, the viability of accelerometers to measure VO2 in combination with other devices, such as pulsom-
eters or global positioning system (GPS) devices, has been analysed under laboratory conditions29–31. 
Accelerometers have also been used to monitor athletes and infer their physical activity level24,32,33. However, 
accelerometry-based devices had not been applied so far for estimating the energy consumed by a runner in a 
marathon race, under normal race conditions, yet. By applying the GENEActiv cut-points for discriminating the 
six relative-intensity activity levels in recreational marathoners (previously established in a lab-based study by our 
research group25), we were able to know the amount of time that a runner was running at a specific 
relative-intensity level (sedentary, light, moderate, vigorous, very vigorous and extremely vigorous activity) 
Relative-intensity levels 
of physical activity#
Reference values established for each intensity 
level by Hernando et al.25
Values used for energy consumption 
estimation
VO2

(ml·kg−1·min−1)
METs*

%VO2max
VO2

(ml·kg−1·min−1)
METs*
Sedentary
X < 10%
VO
5 45
2

<
.
METs < 1.56
8.26%
4.5
1.29
Ligth
10% ≤ X < 25%

.
≤
<
.
V
5 45
O
13 63
2
1.56 ≤ METs < 3.90
17.5%
9.54
2.73
Moderate
25% ≤ X < 45%
V
13 63
O
24 54
2
.
≤
<
.
3.9 ≤ METs < 7.01
35.0%
19.10
5.45
Vigorous
45% ≤ X < 65%
.
≤
<
.
V
24 54
O
35 44
2
7.01 ≤ METs < 10.13
55.0%
29.99
8.57
Very Vigorous
65% ≤ X < 85%
V
35 44
O
46 35
2
.
≤
<
.
10.13 ≤ METs < 13.24
75.0%
40.90
11.69
Extremely Vigorous
X ≥ 85%
VO
46 35
2

≥
.
METs ≥ 13.24
92.5%
50.44
14.41
Table 2. Values established for delineating the six-relative intensity levels of physical activity. Abbreviations: N, 
number of individuals; VO2 max, maximum oxygen consumption; VO2

, oxygen consumption; MET, metabolic 
equivalent task. Each minute of the cardiopulmonary test was classified into one of the six intensity categories of 
physical activity relative to an individual’s level of cardiorespiratory V
( O
)
2max . *1 MET = 3.5 ml·kg−1·min−1. 1 
MET = 1 kcal·h−1. #X denotes the percentage of a person’s aerobic capacity V
( O
2max)

 used to classify each one of 
the six relative-intensity categories.
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during the marathon. Accordingly, the energy consumed by the runner along the race sections and the full mar-
athon distance was estimated.
Differences in the estimation of runners’ energy consumption were observed between the speed- and 
accelerometry-based methods. These differences lie in the ability of the accelerometer output data to determine 
the physical effort distribution of each runner during the marathon, in terms of physical activity intensity34–36. 
Therefore, accelerometers are able to perform an individualized estimation of energy consumption. Note that 
several physiological and biomechanical factors that are unique to the individual have been shown to affect the 
running efficiency among runners at the same steady-state speed16,27,37. This fact pointed up that estimating the 
energy consumption of a runner based uniquely on his/her running speed might be insufficient and that it might 
be advisable to apply a correction factor for adjusting for individual differences when estimating the energy 
cost of, at least, moderate/vigorous physical activities26. The speed-based approach, proposed by Ainsworth and 
cols12, analyse the marathon pace of a runner without taking into account the runner’s effort to race at this speed. 
Fewer interpersonal differences in the number of calories consumed by a runner were then observed with the 
speed-based method as compared to the accelerometry-based approach. For example, two individuals racing 
at identical speed and having equal body mass are estimated to present the same energy cost after applying the 
Race 
section
Time spend at each relative-intensity level (minutes)
Energy consumed according to the time spend at each relative-intensity level (kcal)
S
L
M
V
VV
EV
Total
S
L
M
V
VV
EV
Total
0–5 km
0.01 ± 0.11
0.00 ± 0.00
1.17 ± 4.87
1.30 ± 4.03
9.82 ± 10.65
14.81 ± 11.53
27.10 ± 3.35
0.02 ± 0.15
0.00 ± 0.00
6.76 ± 26.60
13.94 ± 45.35
136.71  
± 148.23
244.83  
± 191.55
402.26  
± 76.44
5–10 km
0.00 ± 0.00
0.00 ± 0.00
1.42 ± 4.31
1.63 ± 4.00
8.67 ± 8.94
12.86 ± 10.32
24.58 ± 2.23
0.00 ± 0.00
0.00 ± 0.00
8.28 ± 23.95
17.16 ± 44.77
119.77  
± 123.75
214.47  
± 173.67
359.68  
± 73.47
10–15 km
0.00 ± 0.00
0.00 ± 0.00
1.25 ± 3.66
1.84 ± 4.30
8.56 ± 8.94
13.09 ± 10.24
24.74 ± 2.32
0.00 ± 0.00
0.00 ± 0.00
7.84 ± 20.59
19.07 ± 45.53
118.40  
± 126.80
216.93  
± 171.78
362.25  
± 69.49
15-HM
0.01 ± 0.11
0.00 ± 0.00
1.88 ± 4.90
2.23 ± 4.44
9.74 ± 10.07
16.16 ± 12.47
30.01 ± 2.87
0.01 ± 0.12
0.00 ± 0.00
11.62 ± 28.85
23.10 ± 48.98
135.17  
± 141.08
267.77  
± 208.66
437.67  
± 87.00
HM-25km
0.00 ± 0.00
0.01 ± 0.11
0.51 ± 2.09
1.23 ± 3.48
6.06 ± 7.41
11.72 ± 8.45
19.52 ± 1.77
0.00 ± 0.00
0.03 ± 0.29
3.02 ± 12.38
12.57 ± 37.79
84.05  
± 102.70
195.15  
± 143.59
294.83  
± 57.25
25–30 km
0.00 ± 0.00
0.01 ± 0.11
1.13 ± 2.94
1.91 ± 3.84
8.33 ± 8.41
14.11 ± 10.23
25.49 ± 2.51
0.00 ± 0.00
0.04 ± 0.33
6.85 ± 17.57
19.15 ± 38.97
115.57  
± 118.10
235.14  
± 172.56
376.75  
± 72.58
30–35 km
0.00 ± 0.00
0.06 ± 0.38
1.53 ± 4.75
1.81 ± 3.95
8.06 ± 8.74
15.06 ± 11.00
26.51 ± 3.45
0.00 ± 0.00
0.20 ± 1.40
10.00 ± 31.54
18.34 ± 40.36
110.92  
± 121.80
250.91  
± 186.13
390.38  
± 77.84
35–40 km
0.00 ± 0.00
0.09 ± 0.58
2.08 ± 5.38
1.64 ± 3.28
8.22 ± 8.66
15.11 ± 10.51
27.14 ± 3.89
0.00 ± 0.00
0.33 ± 2.21
13.50 ± 36.03
16.04 ± 31.78
114.47  
± 120.83
251.14  
± 175.75
395.48  
± 72.99
40-M
0.02 ± 0.21
0.02 ± 0.15
0.67 ± 2.22
0.39 ± 0.84
2.55 ± 3.30
6.24 ± 4.10
9.89 ± 1.76
0.03 ± 0.31
0.07 ± 0.47
4.23 ± 13.93
3.79 ± 8.19
35.79  
± 8.19
104.43  
± 70.04
148.35  
± 37.76
Marathon
0.05 ± 0.34
0.19 ± 0.92
11.6 ± 25.32
13.95 ± 27.75
69.99 ± 66.19
119.16 ± 82.86
214.98 ± 20.78
0.06 ± 0.47
0.67 ± 3.48
72.10 ± 160.10
143.17 ± 301.99
970.84  
± 938.15
1980.78  
± 1386.54
3167.63  
± 584.12
Table 3. Evaluation of effort distribution and estimation of calories consumed by runners based on 
accelerometry data. Abbreviations: S, Sedentary; L, Light; M, Moderate; V, Vigorous; VV, Very Vigorous; 
EV, Extremely Vigorous; HM, Half marathon; M, marathon; SD, standard deviation. Values are presented as 
mean ± SD.
Race 
section
Running 
speed
(m·min−1)
Absolute energy
(kcal)
Energy relative to body mass per time
(kcal·kg−1·min−1)
Energy relative to body mass per distance 
(kcal·kg−1·km−1)
Number of BMR
Accelerometry
Running
speed*
Accelerometry
Running
speed*
Adjusted
p-value¥
Accelerometry
Running
speed*
Adjusted
p-value¥
Accelerometry
Running
speed*
Adjusted
p-value¥
0–5 km
187.27 ± 23.06
402.26 ± 76.44
352.30 ± 44.85
0.214 ± 0.031
0.189 ± 0.023
6.27 × 10-12
1.154 ± 0.195
1.008 ± 0.026
1.09 × 10-11
12.82 ± 1.84
11.30 ± 1.40
6.27 × 10-12
5–10 km
205.06 ± 18.43
359.68 ± 73.47
354.24 ± 47.26
0.210 ± 0.034
0.208 ± 0.019
0.149
1.030 ± 0.176
1.012 ± 0.023
0.495
12.59 ± 2.03
12.43 ± 1.11
0.149
10–15 km
203.85 ± 18.88
362.25 ± 69.49
355.00 ± 46.26
0.211 ± 0.032
0.207 ± 0.018
0.062
1.040 ± 0.171
1.015 ± 0.025
0.169
12.63 ± 1.93
12.38 ± 1.10
0.062
15-HM
204.94 ± 18.82
437.67 ± 87.00
427.90 ± 54.89
0.210 ± 0.033
0.206 ± 0.020
0.093
1.030 ± 0.177
1.003 ± 0.020
0.358
12.57 ± 2.00
12.31 ± 1.17
0.088
HM-25km
201.49 ± 18.00
294.83 ± 57.25
273.44 ± 35.86
0.217 ± 0.030
0.202 ± 0.022
1.05 × 10-5
1.055 ± 0.164
1.001 ± 0.026
2.46 × 10-3
12.99 ± 1.78
12.10 ± 1.33
1.05 × 10-5
25–30 km
198.01 ± 19.10
376.75 ± 72.58
353.60 ± 47.10
0.213 ± 0.030
0.200 ± 0.020
7.85 × 10-5
1.080 ± 0.170
1.010 ± 0.024
3.16 × 10-4
12.73 ± 1.82
11.98 ± 1.21
7.85 × 10-5
30–35 km
191.43 ± 22.58
390.38 ± 77.84
351.74 ± 46.67
0.213 ± 0.032
0.193 ± 0.025
2.06 × 10-7
1.119 ± 0.186
1.006 ± 0.040
8.18 × 10-7
12.73 ± 1.89
11.55 ± 1.49
2.06 × 10-7
35–40 km
187.65 ± 24.50
395.48 ± 72.99
353.24 ± 46.98
0.211 ± 0.032
0.190 ± 0.026
7.21 × 10-7
1.134 ± 0.174
1.010 ± 0.039
2.37 × 10-10
12.65 ± 1.91
11.36 ± 1.56
7.21 × 10-7
40-M
229.14 ± 42.02
148.35 ± 37.76
153.73 ± 20.93
0.215 ± 0.034
0.229 ± 0.038
0.202
0.964 ± 0.210
1.000 ± 0.039
1.000
12.90 ± 2.03
13.69 ± 2.26
0.209
Marathon
198.06 ± 18.78
3167.63 ± 584.12
2951.45 ± 394.20
0.212 ± 0.030
0.198 ± 0.021
3.48 × 10-5
1.076 ± 0.163
0.999 ± 0.023
8.75 × 10-5
12.70 ± 1.77
11.86 ± 1.23
3.48 × 10-5
Table 4. Comparison between accelerometry- and speed-based approaches in the estimation of energy 
consumption. Abbreviations: BMR, Basal metabolic rate; HM, Half marathon; M, Marathon; SD, standard 
deviation; p, p-value. Values are presented as mean ± SD. Bold indicates significant results (p-value < 0.05). 
*The values are estimated based on running speed, and following the methodology proposed by Ainsworth  
et al. (2000)12. ¥P-values were corrected for multiple comparisons by applying the Benjamini-Hochberg 
procedure for decreasing the False Discovery Rate.
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speed-based method, although their physical efforts are completely different according to accelerometry data. 
Nevertheless, note that, as in the speed-based methods, accelerometry is not able to perform an absolute quantifi-
cation of the energy consumed by a runner and it is necessary, therefore, to combine different approaches, as well 
as to explore other technologies, in future work.
In this regard, accelerometer data collected for each runner was thoroughly analyzed in order to compare 
effort distribution between the fastest and the slowest runner of our dataset (Table 6). Note that the fastest runner 
was almost running at very vigorous intensity level, showing a good control of physical effort along the full mar-
athon distance. In contrast, the effort distribution of the slowest runner was far from being well-balanced2,38,39. 
In fact, the accelerometer data revealed a considerable decay of the intensity level at which the slowest runner 
performed after completing 30 km (running at a moderate intensity from an extremely vigorous level). This was a 
consequence of the high physical effort sustained by the runner from the beginning of the marathon line, which 
reveals the importance of controlling effort distribution in a marathon race. In short, our results suggest that 
future pacing analyses should include information of effort intensity distribution in order to adjust race pacing 
appropriately to achieve the marathon goal time.
Thanks to accelerometer output data, we were also able to estimate the percentage of VO2 max produced per 
each runner, and afterwards the energy of cost running above standing (Crnet)28, at each of the 9 marathon sec-
tions as well as at the full marathon distance. These physiological parameters seem to explain up to 87% of the 
long distance race performance27. In addition, the accelerometry-based approach also allowed us to extrapolate 
the running economy of each runner, which is considered an important physiological measure for long distance 
runners37,40. It is thought that a variety of biomechanical characteristics are likely to contribute to having interper-
sonal differences in the running efficiency, such as the running technique, the elastic power of the muscle-tendon 
unit, or the amount of ground contact and vertical oscillation when running41.
As results shown, the fastest runner seemed to present a better efficiency of movement than that presented 
by the slowest runner. That is, the energy demanded for a given running velocity was lower by the fastest runner 
as compared to the slowest runner. In fact, the average energy cost of marathon running was 3.31 J·kg−1·m−1 for 
the fastest runner (whose average speed was 237.05 m·min−1), while it was 4.59 J·kg−1·m−1 for the slowest runner 
Figure 1. Plot showing the linear correlation between the calories estimated to be consumed by each runner 
and the marathon time. Energy consumption was estimated by using both accelerometry (solid line) and 
running speed (dashed line). Each individual is represented by a specific point: filled circles are used when 
accelerometry was applied for energy consumption estimation, and filled triangles when speed-based method 
was used. Abbreviations: ρ, Spearman’s rank correlation coefficient; p, p-value.
Race 
section
Percentage of maximum 
oxygen consumption 
V
(% O
2 max)

Oxygen uptake relative 
to body mass per minute 
(ml·kg−1·min−1)
Energy cost of running 
above standing*
(J·kg−1·m−1)
0–5 km
82% ± 11.78
44.87 ± 6.43
4.54 ± 0.83
5–10 km
81% ± 13.05
44.07 ± 7.12
4.05 ± 0.76
10–15 km
81% ± 12.41
44.19 ± 6.77
4.09 ± 0.73
15-HM
81% ± 12.83
44.00 ± 7.00
4.04 ± 0.76
HM-25km
83% ± 11.46
45.45 ± 6.25
4.26 ± 0.72
25–30 km
82% ± 11.69
44.54 ± 6.38
4.25 ± 0.73
30–35 km
82% ± 12.11
44.55 ± 6.60
4.40 ± 0.79
35–40 km
81% ± 12.27
44.28 ± 6.70
4.44 ± 0.74
40-M
83% ± 13.06
45.15 ± 7.12
3.79 ± 0.86
Marathon
81% ± 11.38
44.43 ± 6.21
4.23 ± 0.70
Table 5. Estimation of the percentage of VO2 max

, the oxygen uptake relative to body mass per minute and the 
energy cost of running above standing based on accelerometry data. Abbreviations: HM, Half marathon; M, 
Marathon; VO2 max

, maximum oxygen consumption. *Energy cost of running above 
standing = ( 
− 
V
V
( O
O
)
2
2standing  (running speed)−1) · 20.9.
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(whose average speed was 152.88 m·min−1). Apart from physiological parameters, these differences may be also 
resulted from biomechanical efficiency, which is influenced by anthropometric parameters, kinematic character-
istics and running style37.
This suggests that the design of training sessions for the slowest runner by his coach should focus on improv-
ing his running style and muscle strength, and subsequently his performance. The useful information offered by 
accelerometers (distribution of physical effort in free-living conditions and inference of physiological parameters 
as Crnet or % VO2 max) should become more and more important as race distance increase42. Application of accel-
erometers to monitor ultratrail runners may be useful not only for adjusting race strategy, which is crucial for 
achieving performance goals2,27,43,44, but also to monitor training sessions and recovery time. Indeed, both 
long-term data collection and wrist watch-like format are valuable characteristics of accelerometers since data can 
be continuously collected for a long period of time (more than a week) without causing any physical discomfort 
to ultraendurance runners45.
However, values of all physiological parameters analyzed in this study were merely estimations based on accel-
erometer data, and were not directly measured46. It is quite difficult, if not impossible, to perform a direct meas-
urement of VO2

 on a marathon race, an extremely demanding free-living condition. This makes difficult to find a 
gold standard method for quantifying calories consumed by an individual when she/he is performing a physical 
activity. That is the reason why indirect measurement methods (such as heart-rate recording devices14,47, pedom-
eters48,49 and accelerometers14,34,36, or their combination29,30,50) are normally applied. Another limitation of our 
study is related to the protocol followed to estimate energy consumption according to the range of % VO2 max

 
delimiting each relative-intensity activity level. Estimations can present a maximum error of 10%, since the 
median value of the % VO2 max range was used for energy calculations (as shown in Table 2). Having said that, our 
results indicate that accelerometry-based method allows to both identify the individual’s levels of physical activity 
intensity during the marathon race and estimate an individualized energy consumption.
In summary, overall the results in this study lead us to believe that GENEActiv. accelerometer is an accu-
rate tool for estimating the energy consumption of middle-recreational marathoners running a marathon, an 
extremely demanding free-living physical activity. Accelerometer-derived data was useful to evaluate the effort 
intensity distribution along the race, by means of the time running at each six related-intensity levels (sedentary, 
light, moderate, vigorous, very vigorous and extremely vigorous activity), and subsequently to estimate the energy 
consumption. Therefore, accelerometers may be extremely useful for both athletes and coaches who need to 
evaluate the race strategy to achieve marathon final time, but also to monitor training sessions and assess perfor-
mance level progression needed to reach a goal. Several physiological and biomechanical parameters that can be 
inferred from accelerometer output data may also support coaches to design specific training sessions according 
to runner’s characteristics. Furthermore, the ability to perform an objective assessment of a runner’s fitness level, 
as well as energy consumption, in the context of free-living movement indicates that accelerometry-based devices 
may be of great value to sport medical professionals.
Since accelerometry-based data is thought to be valuable for monitoring runners along ultra-trail races, future 
studies determining cut-off points for quantifying energy consumption would help in the race strategy in terms 
of food and fluid intake on race day (a key factor for performance success). Note that these future studies must 
take into account that biomechanics and physiology of downhill and uphill running, as well as the energy cost of 
running, may differ.
Methods
Sample set. 
A total of 95 recreational marathon runners (80 males and 15 females) aged between 30 and 
45 years lined up at the start of the Valencia Fundación Trinidad Alfonso EDP 2016 Marathon (20th November, 
2016). From all of them, eighty-eight participants crossed the finish line (74 males and 14 females). Non-finishers 
Figure 2. Plot showing the linear correlation between the energy estimated to be consumed by each runner 
relative to his/her body mass per minute and the marathon time. Energy consumption was estimated by using 
both accelerometry (solid line) and running speed (dashed line). Each individual is represented by a specific point: 
filled circles are used when accelerometry was applied for energy consumption estimation, and filled triangles 
when speed-based method was used. Abbreviations: ρ, Spearman’s rank correlation coefficient; p, p-value.
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were discarded from further analyses. The entire process of sampling (contact approach and criteria for inclusion 
and exclusion of volunteers) has been previously described25.
ethics statement. 
All individuals included in the current study were fully informed and gave their writ-
ten consent to participate. The research was conducted according to the Declaration of Helsinki, and it was 
approved by the Research Ethics Committee of the University Jaume I of Castellon. This study is enrolled in the 
ClinicalTrails.gov database, with the code number NCT03155633 (www.clinicaltrials.gov).
Data collection and analysis. 
Four weeks before the marathon, we made an appointment with all partic-
ipants in order to collect anthropometric data, demographics, medical information, training program and com-
petition history. Indeed, all individuals completed a cardiopulmonary test. Details of data collection, processing 
and analysis have been previously described25. Population description according to data collected is also available 
in our previous work25.
All participants were weighed one hour before the start of the marathon, wearing racing clothes and flats, by 
using a Seca 770 scale (Seca Hamburg, Germany). BMI was then calculated (height·mass−2).
For this research, all the participants underwent the same testing under the same experimental conditions. 
Participants completed the Valencia Fundación Trinidad Alfonso EDP 2016 Marathon, which was held in 
November with a mean dry temperature of 15.6 °C and a mean relative humidity of 50%. The race course altitude 
varied from 1 to 27 m above sea level.
During the race, participants wore a GENEActiv accelerometer (Activinsights Ltd., Kimbolton, 
Cambridgeshire, United Kingdom). The accelerometer was worn on the non-dominant wrist as a watch. 
Accelerometers were adjusted to record acceleration data at a rate of 85.7 Hz. Devices were calibrated by the man-
ufacturer prior to use. Processing of acceleration data has been previously explained in detail25.
Data analysis. 
The marathon race was divided into 9 sections as follow: 6 sections of 5 km (0–5 km, 5–10 km, 
10–15 km, 25–30 km, 30–35 km and 35–40 km), 1 section of 6.0975 km (15–21.0975 km), 1 section of 3.9025 km 
(21.0975–25 km) and 1 section of 2.195 km (40–42.195 km). All data analyses were performed for each one of the 
nine marathon sections and for the whole marathon distance. Statistical analyses were done using the IBM SPSS 
Statistics v.23 software, and p-values lower than 0.05 were considered as statistically significant. Supplementary 
information includes raw data used in this study.
Fastest runner: Marathon time of 178 min, body mass of 69.2 kg, and BMI of 21.36 kg·m−2
Race 
section
Time running at each relative-
intensity level (min)
Energy consumption
Running 
speed 
(m·min−1)
V
% O2max
Crnet 
(J·kg−1·m−1)
S
L
M
V
VV
EV
Total
Absolute 
(kcal)
Relative to 
time
(kcal·kg−1 
·min−1)
Relative to 
distance 
(kcal·kg−1 
·km−1)
0–5 km
0
0
0
0
21
0
21.00
283.70
0.20
0.82
238.10
75.00%
3.29
5–10 km
0
0
0
0
21
0
21.00
283.70
0.20
0.82
238.10
75.00%
3.29
10–15 km
0
0
0
1
20
0
21.00
280.09
0.19
0.81
238.10
74.05%
3.25
15-HM
0
0
0
3
22
0
25.00
326.92
0.19
0.77
243.90
72.60%
3.11
HM-25km
0
0
0
0
16
0
16.00
216.15
0.20
0.80
243.91
75.00%
3.22
25–30 km
0
0
0
0
22
0
22.00
297.21
0.20
0.86
227.27
75.00%
3.45
30–35 km
0
0
0
1
21
0
22.00
293.60
0.19
0.85
227.27
74.09%
3.41
35–40 km
0
0
0
0
18
3
21.00
293.13
0.20
0.85
238.10
77.50%
3.40
40-M
0
0
0
0
7
2
9.00
127.87
0.21
0.84
243.89
78.89%
3.38
Marathon
0
0
0
5
168
5
178.00
2402.37
0.20
0.82
237.05
74.93%
3.31
Slowest runner: Marathon time of 276 min, body mass of 74.9 kg, and BMI of 23.38 kg·m−2
0–5
0
0
0
0
24
5
29.00
441.06
0.20
1.18
172.41
78.02%
4.73
5–10
0
0
0
0
17
11
28.00
446.85
0.21
1.19
178.57
81.88%
4.79
10–15
0
0
1
0
7
20
28.00
469.66
0.22
1.25
178.57
86.07%
5.04
15-HM
0
0
0
0
4
31
35.00
617.25
0.24
1.35
174.21
90.50%
5.43
HM-25
0
0
0
0
0
22
22.00
396.54
0.24
1.36
177.39
92.50%
5.45
25–30
0
0
2
4
13
12
31.00
462.89
0.20
1.24
161.29
76.61%
4.97
30–35
0
0
41
1
1
0
43.00
304.84
0.09
0.81
116.28
36.40%
3.27
35–40
0
0
43
0
1
0
44.00
307.75
0.09
0.82
113.64
35.91%
3.30
40-M
0
0
11
0
0
5
16.00
165.11
0.14
1.00
137.19
52.97%
4.04
Marathon
0
0
98
5
67
106
276.00
3611.95
0.17
1.14
152.88
67.16%
4.59
Table 6. Comparison of effort distribution according to accelerometer output data between the fastest and the 
slowest runner of our dataset. Abbreviations: S, Sedentary; L, Light; M, Moderate; V, Vigorous; VV, Very 
Vigorous; EV, Extremely Vigorous; HM, Half marathon; M, marathon; VO2 max

, maximum oxygen 
consumption; Crnet, energy cost of running above standing.
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Firstly, accelerometer-derived data was used to determine the distribution of exercise intensity of runners 
along the marathon with the aim to estimate the calories consumed per each runner. The intensity levels of phys-
ical activity were established following the cut-off points delineated by Hernando and cols25. For calculating the 
energy cost, we used the median value of the range of % VO2 max delimiting each intensity category (Table 2), 
except for the sedentary category where the standing oxygen cost (4.5 mlO2·kg−1·min−1) was applied as reference 
value28. As unit of measurement, we considered that one MET is equal to 3.5ml O2·kg−1·min−1, and one MET is 
equal to one kcal·kg−1·h−1. These equivalencies were applied in accordance with the determinations proposed by 
Ainsworth and cols12, and taking into account that all volunteers included in the study reported similar BMI 
(between 22.17 and 23.44 kg·m−2) and, therefore, differences in the percentage of fatty component among partic-
ipants were absence26,46,51.
Accelerometers were also used to estimate the percentage of VO2 max produced per each runner. Briefly, the 
time racing at a specific intensity level was multiplied by its corresponding % VO2 max (Table 2). A weighted aver-
age relative to the total time spent at each section, as well as at the full marathon distance, was then performed. 
Then, the VO2net of each runner was calculated by subtracting the VO2standing to the percentage of VO2 max esti-
mated17,28. Together with the running speed measured, the VO2net was finally used to calculate the energy of cost 
running above standing (Crnet), following the methodology proposed by di Prampero and cols17.
Next, the average running speed was used to calculate the caloric consumption of runners, following the 
methodology proposed by Ainsworth and cols12. The split-times in minutes were recorded for each one of the 
marathon sections electronically, and the average running speed of all sections and the whole marathon distance 
was calculated. Then, the running speed was associated with a specific MET value, which can be directly used to 
calculate the number of calories consumed by a runner12,19.
Finally, the relative values of energy consumption estimated by the two models were compared. As the energy 
consumption depends on the person’s body mass, the energy cost of each runner is presented as: (i) the calories 
consumed per kilogram of body weight per minute (kcal·kg−1·min−1), in order to obtain the effort intensity;12,19,26 
(ii) the calories consumed per kilogram of body weight per kilometer (kcal·kg−1·km−1), to infer the running effi-
ciency of runners;18,27 and (iii) as the number of Basal Metabolic Rate (BMR) consumed, used as an indicator of 
the effort intensity degree above the basal metabolism26,28.
The Kolgomorov-Smirnov test was used for testing data normality. Since variables were not normally dis-
tributed, all statistical analyses were performed by applying non-parametric statistical tests. The Mann-Whitney 
U test was used to compare the energy consumption values estimated by using the accelerometer-derived 
data and the relative running speed. Then, P-values were corrected for multiple comparisons by applying the 
Benjamini-Hochberg procedure for decreasing the False Discovery Rate.The Sperman’s correlation test was 
applied to analyze linear association between two continuous variables.
Data availability
All data generated or analysed during this study are included in this published article (and its Supplementary 
Information File). Any other relevant data can be obtained from the corresponding author upon reasonable 
request.
Received: 13 February 2019; Accepted: 15 January 2020;
Published: xx xx xxxx
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Acknowledgements
Current research could be carried out thanks to the collaboration of Fundación Trinidad Alfonso, Vithas-Nisa 
Hospitals group and Sociedad Deportiva Correcaminos. Authors are also grateful to all the stuff involved in 
the organization of the Valencia Fundación Trinidad Alfonso EDP 2016 Marathon, and all marathoners and 
volunteers participating in this study.
Author contributions
C.H. and B.H. contributed to conception and design of the study, article drafting, and critical revision of the 
article. C.H. and C.H. contributed to data curation, analysis and interpretation. C.H., I.M.-N., E.C.-B. and N.P. 
contributed to data collection and critical revision of the article. C.H., I.M.-N. and E.C.-B. contributed to funding 
acquisition.
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competing interests
The authors declare no competing interests.
Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/s41598-020-58492-8.
Correspondence and requests for materials should be addressed to C.H.
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Estimation of energy consumed by middle-aged recreational marathoners during a marathon using accelerometry-based devices.
Hernando, Carlos,Hernando, Carla,Martinez-Navarro, Ignacio,Collado-Boira, Eladio,Panizo, Nayara,Hernando, Barbara