opinion: MARTIN, Circuit Judge.
  A local CIO union and seven of its members, suing on behalf of all similarly situated employees, brought this action against the appellant employer, charging violations of the Fair Labor Standards Act (52 Stat. 1060, 29 U.S.C.A. §§ 201-219) in numerous respects. Approximately 300 employees or ex-employees of appellant were permitted, by order of the district court, to sign and file designations authorizing the plaintiffs to represent them.
  The appellant corporation for twenty-eight years has operated a pottery plant at Mt. Clemens, Michigan; and during the period with which we are concerned, employed some 1,000 to 1,200 individuals. The original complaint, which was filed a few days after an organizational strike had been instituted by the union at the pottery plant, charged among other things that the time clocks of the company had been so rigged or “doctored” that the figures punched on the cards failed to reflect correctly the actual time at which the card was punched. This charge was abandoned and, in lieu, the charge was made that the employer did not compute the working time of the employees, or pay them, in accordance with the time-card records. The complaint further charged that the employees were worked by the company 45 hours a week from late in October, 1938, until the action was filed. There was no proof made to support the charges of the complaint that certain employees performed homework without compensation or that certain employees earned less than thirty cents an hour. Numerous motions were made and other preliminary steps taken, resulting in the filing by plaintiffs of two bills of particulars.
  It was charged by plaintiffs that the company had credited employees with working time only from the succeeding quarter hour when an employee checked in to the preceding quarter hour when he checked out; and that under this practice the company “has deducted from the time worked, as shown on said time cards, a period of as much as 56 minutes each day.”
  Numerous new charges were made and dropped and numerous motions were made and acted upon which it is immaterial to detail.
  The district judge finally referred the cause to a special master to hear the parties, to take testimony with respect to the issues as framed by the pleadings, and to report his findings of fact and conclusions of law.
  The lengthy proceedings before the master were recorded in a typewritten transcript comprising more than 3500 pages. During the course of the procedure before the master charges not set up in the pleadings were made by the plaintiffs, including claims that office workers were not compensated in accordance with the Act, that the company had violated the child labor provisions thereof, and that company meetings were held without crediting the employees with the time spent in attendance. The master held that, in the absence of amendment of the pleadings, testimony would not be received upon such issues.
  The evidence adduced before the master consisted largely of testimony of eight union employees or former employees of the company on behalf of the plaintiffs, while the testimony offered by the pottery company was primarily that of its foremen and managerial representatives. Each side introduced expert testimony as to industrial customs and practices; and an inspector of the Wage and Hour Division of the United States Department of Labor testified for the plaintiffs.
  The special master reported that the employees involved in the case were engaged in the production of goods for commerce within the meaning of the Fair Labor Standards Act; that the plaintiffs were not estopped to maintain the action by reason of acquiescence for a long time in the practices of the company with respect to the computation of time; that the prior inspection of the plant by the Wage and Hour Division was irrelevant upon the issues in suit; and that the defense of lack of authority of the union to sue was invalid, He recognized that employees subject to the provisions of the Fair Labor Standards Act are entitled to receive full payment for the time they have worked in excess of its limited statutory period at a rate not less than time and one-half for the extra time worked.
  The master stated that, while legal questions as to what constitutes working time were involved, the principle issue is factual. He found that the pottery company employs an average of approximately 1200 persons in ten or twelve departments, of which only four, the clay shop, brushing and dipping, glost belt and decorating departments, were directly represented by the witnesses who had testified for the plaintiffs. He found further that more than 95% of the employees in the plant, who are engaged in production work, are compensated upon a piece work basis; that the rate of pay is generally based upon the output of a group or a crew, but in departments where employees work individually the rate is based upon the output of the individual; and that the pottery company operates generally on a five-day week, the departments variously operating from one to three shifts per day, with shifts in the different departments beginning at different times during the morning, although the established starting time was always on an even quarter hour. The bisque and glost kiln departments operated on a three-shift seven-day basis.
  The pottery plant covers more than eight acres of ground, the employees’ entrance being at the northeast corner immediately adjacent to which are cloak and toilet rooms for men and women. Upon entering the production part of the plant, an employee must pass and punch a time clock. There were two time clocks placed at different locations in the plant, a third one having been added shortly before the commencement of this action. In checking in and out at the clocks, the employee removes his card from the rack, places it in a slot, pushes down a hand lever, and removes the card with the time recorded on it. He then places the card in another rack. An average of 25 employees a minute can check in and out in this manner. After' punching the time clock, the employees proceed by somewhat defined aisles to their particular places of work. The distance from the time clock to the place of work varies from 130 to 325 feet in the glost kilns to 820 or 890 feet in the mold department.
  The master found further that the time clock system was first installed by the company in 1933; and that employees are not permitted fo punch their cards more than fourteen minutes prior to the time which the company designates as starting time. For computation of time worked by the employees, the time cards are removed from the racks and the time is calculated from the succeeding even quarter hour after employees ring in, to the quarter hour immediately preceding the time when they punch out. For example, an employee whose card is punched in at 6:46 A. M., punched out at 12:03 P. M., punched in at 12:50 P. M., and punched out again at 4:07 P. M., is credited with 8 hours’ working time. The resultant figure is entered on the card in the righthand column and the card is returned to the rack. In computing overtime pay under the Fair Labor Standards Act the method employed by the company is to divide the gross pay received by the employee in each work week by the number of hours credited to him, and the resultant average hourly rate is multiplied by time and half for the overtime hours. This method conforms to the system prescribed by the Wage and Hour Division of the Department of Labor.
  Because the shifts in the different departments commenced at different times in the morning, no whistle signalized the commencement of work on most shifts, but clocks belonging to the company or to employees were distributed freely throughout the plant. Whistles were blown, however, at 6:55 and 7 A. M., as the most commonly established starting time in the morning. Whistles were also blown at several other times during the day.
  The policy of the company, put into effect through the operation of the Fair Labor Standards Act, was to keep the working hours of its employees below the statutory limitation for payment of straight time as far as possible. Before the passage of the Act, the company had been officially on a forty-five hour week, but lay-offs during that period had reduced the working hours of employees to less than forty-five.
  The matter of compliance with the Act was frequently discussed at weekly meetings of foremen; and employees were informed of the policy adopted by the company and were instructed, when possible, to keep their hours below the statutory period.
  Practically all the workmen in the plant had certain preliminary duties to perform, after arriving at their respective departments and before commencing production work, such as putting on their aprons or overalls, removing their shirts, taping or greasing their arms and putting on finger cots, and preparing equipment for commencement of production work by turning on switches for lights and machinery, opening windows and assembling and sharpening tools. The nature of this work varied from department to department, and from job to job within the department.
  The "master reviewed at length the evidence introduced with respect to the working time of the employees. It was pointed out that the foremen had testified that the employees were not instructed to report for work at fourteen minutes to starting time, but rather at such time as to be in their respective departments ready for work at the even quarter hour set for the start of the shift, and that they could ring in at any time after “14 to.” They testified further that production work, was not commenced until the established starting time, except in rare instances where employees may have “jumped the gun” a minute or two, and that frequently, where a crew had to be assembled, work was not commenced until considerably after starting time. It was conceded that in order for employees to be in their departments ready for work by starting time, it was necessary for them to punch the time clocks some minutes before starting time. The time consumed by the employees in walking from time clocks to the departments was not treated by the company as working time. None of the estimates of the time consumed by employees in reaching their departments, ranging from one and one-half to three minutes, was based upon actual clocking of the time in transit.
  The testimony was conflicting concerning the extent of the personal activities of the employees prior to commencing work. Witnesses for the company testified that most of an employee’s time, after he had arrived in a department in advance of regular starting time, was spent in conversation or personal activities not connected with his work. The master stated in his report that there was practically no direct testimony by the witnesses for the plaintiffs as to their procedure when going out for lunch, returning therefrom and when leaving at the end of a shift; but that, on cross-examination, several had admitted that they did not work fourteen minutes beyond quitting time, but on the contrary frequently stopped production and cleaned up before quitting time. Such testimony was in line with that of the foremen. The time card exhibits reveal that the employees came in at a practically uniform rate during the first seven minutes that the clocks were open, and that by five minutes to 7 o’clock 95% of the employees had rung in. In three of the four departments concerning which testimony was offered, employees worked in groups; and production work could not be commenced until the entire group had arrived.
  The master found that the proof demonstrated that no practice existed of working the employees of the pottery company fourteen minutes after quitting time for lunch or at the end of a shift. More difficulty was found in passing upon the claims of the plaintiffs that all time between punched entries on the cards was working time. In appraising the evidence, both direct and. circumstantial, the master concluded that the plaintiffs had not carried the burden of proof on the issue.
  The master rationalized upon the proven facts and circumstances in arriving at this conclusion. He did so upon a consideration of pertinent authorities. He stated that a computation of overtime on the basis of a finding that the employees worked more than the time credited to them, but less than the time shown by the entries on the cards would, on the record in the case, be speculative, inasmuch as the witnesses for the plaintiffs had kept no record of their time and admitted that, apart from the time clock cards, they could not tell on any particular day when they arrived at their departments or commenced preliminary work. The time consumed in preliminary activities varied in each department and in the same department on different days.
  The master found that the evidence did not bear out that women employees were paid sub-minimum wages. He found no violation of the Wage and Hour Act in respect of deductions for tools or for the “invisible man.” The claim of employees as to “charity work” was not found on the facts to be in violation of the Act.
  The general conclusion reached by the master, based upon the evidence and applicable law, was that the plaintiffs had not established by a fair preponderance of evidence a violation of the Fair Labor Standards Act by the employer. Accordingly, he recommended that the complaint be dismissed. We have not deemed it essential to rewrite from the master’s report, which embraces seventy-four printed pages of the record, his discussion of the evidence in the case; but, from careful examination, we find that the master’s findings of fact were all supported by substantial evidence contained in the voluminous record and are not clearly erroneous.
  Notwithstanding the findings of the special master, which were adopted by the district court except as hereinafter specified, the court applied an arbitrary formula, set up in its labeled “Findings of Fact,” as follows:
  “2. The Court finds that some of the plaintiffs started work before the regular starting time at the beginning of the work day and at the resumption of work after the lunch periofl. Plaintiffs are not entitled to pay from the minute they punched the time clock; but in computing their hours of work there should be allowed 5 minutes for punching the clock plus an additional 2 minutes to go from the clock to' their place of employment, or a total of 7 minutes, before the beginning of work in the morning. There should be allowed a total of 5 minutes at the resumption of work after the lunch period.
  “3. In computing the hours of work of plaintiffs as employees of defendant Mt. Clemens Pottery Company there should be included in addition to the hours of work as computed by the company the following:
  “(a) In cases where an employee punched his time clock card more than 7 minutes before his regular starting time at the beginning of a shift, there shall be computed as part of his hours of work the number of minutes by which the punch-in time shown on his time card preceded 7 minutes before the regular starting time.
  “(b) In cases where an employee punched his time clock card more than 5 minutes before his regular starting time after his lunch period, there shall be computed as part of his hours of work the number of minutes by which the punch-in time shown on his time card preceded 5 minutes before the regular starting time.”
  The district court concluded as a matter of law that the “plaintiffs have established that work was done by some of them which the Company did not give them credit for, and the computation thereof, on the basis above stated, forms a basis for recovery of overtime pay.” Judgment was entered in favor of the employees on the basis of this formula; an equal amount was added thereto as liquidated damages; and the plaintiffs were allowed, as costs to be taxed against the appellant, $2,000 as fee compensation to their attorneys. The compensation of the special master was taxed to the appellant company.
  The judgment of the district court must be reversed. There was abundant substantial evidence to support the findings of the special master and it could not appropriately be said that such findings are clearly erroneous. Civil Procedure Rule 53 (e) (2), 28 U.S.C.A. following section 723c, distinctly provides that “in an action to be tried without a jury the court shall accept the master’s findings of fact unless clearly erroneous.”
  The district court is as much obliged to accept the findings of a master, unless clearly erroneous, as this court is to accept the findings of the district court unless clearly erroneous. See Santa Cruz Oil Corporation v. Allbright-Nell Co., 7 Cir., 115 F.2d 604, 607. Cf. Morris Plan Industrial Bank v. Henderson, 2 Cir., 131 F.2d 975, 976.
  Rule 53(e) (2), as well as Rule 52(a) which binds this court to accept the findings of the district judge unless clearly erroneous, is based on the same principle, long recognized in law, that the master or judge who personally observes the witnesses is in better position to pass upon conflicting testimony and the credibility of witnesses than is a tribunal which has neither seen nor heard the witnesses.
  Moreover, the arbitrary formula applied by the district judge, in lieu of acceptance of the master’s findings, produced a judgment based upon surmise and conjecture, which cannot be sustained. See Townsend v. New York Cent. R. Co., 7 Cir., 141 F.2d 483.
  The Fair Labor Standards Act is of course applicable to employees compensated on a piece rate basis. United States v. Rosenwasser, 323 U.S. 360, 65 S.Ct. 295. But the burden rested on each of the plaintiffs here to prove by a preponderance of the evidence that he did not receive the Wages that he was entitled to receive under the Fair Labor Standards Act, and to show by evidence, not resting upon conjecture, the extent of overtime worked. It does not suffice for the employee to base his right to recovery on a mere estimated average of overtime worked. To uphold a judgment based on such uncertain and conjectural evidence would be to rest it upon speculation. Jax Beer Co. v. Redfern, 5 Cir., 124 F.2d 172, 175. See also Tennessee Coal, Iron & R. Co. et al. v. Muscoda Local No. 123 et al., 5 Cir., 135 F.2d 320; Epps v. Weathers, D.C.Ga., 49 F.Supp. 2.
  In Tennessee Coal, Iron & R. Co. et al. v. Muscoda Local No. 123, et al., 321 U.S. 590, 593, 64 S.Ct. 698, 88 L.Ed. 949, the judgment of the Fifth Circuit Court of Appeals, in the same case cited supra, was affirmed, to the effect that iron ore miners were at work, within the meaning of the Fair Labor Standards Act, while engaged in underground travel which they were obliged to perform on the property of and under the direction of their employers as a necessary concomitant of their employment. It should be observed, however, that the Circuit Court of Appeals, whose judgment was affirmed, had also held that with respect to time spent by the employees in checking in and out and procuring and returning tools, lamps and carbide, no overtime was allowable. The Court of Appeals, in its opinion, said: “In addition to the practical difficulties incident to the computation of isolated moments so elusive in character, we think these pursuits should not be computed as work-time, since they fall within the category of duties incident to qualifying the employee to perform his work rather than within the scope of his actual employment.” 135 F.2d 320, 323, supra.
  It seemS appropriate to quote the language of Mr. Justice Jackson, writing the unanimous opinion of the Supreme Court in Skidmore v. Swift & Co., 323 U.S. 134, 65 S.Ct. 161, 163: “We have not attempted to, and we cannot, lay down a legal formula to resolve cases so varied in their facts as are the many situations in which employment involves waiting time. Whether in a concrete case such time falls within or without the Act is a question of fact to be resolved by appropriate findings of the trial court.”
  The crucial question of fact in the instant case had been resolved against the appellees, upon substantial evidence, by a special master to whom the district judge had referred the cause. The fact findings of the master were certainly not clearly erroneous. Wherefore, the district judge should have upheld the master’s findings and should have based his judgment thereon. This he failed to do; but, instead, supplied an arbitrary formula not derivable from substantial evidence of record.
  Accordingly, the judgment of the district court is reversed and the cause of action is ordered dismissed.