Without researching the matter (and thus preserving Internet Tradition), I'd say that it's because the input energy to a guitar is a single pluck whereas a violin is bowed giving a continuous energy transfer.
Pizzicato violins are not as loud a bowed.
music.stackexchange.com/users/23838/ttw
You are asking for loudness, not volume, correct?
Volume is refering to physical properties (i.e. the amplitude of the sound waves), whereas loudness is the perceived volume which can differ a lot from the actual SPL (sound pressure level), althoug the SPL is still a major factor.
The loudness is also dependent on frequencies and bandwidth of the audio signal.
One other factor, which can play a significant role, is your ears.
With age some form of hearing loss occurs.
Some people hear certain frequencies much louder than others.
I, for example did a hearing test and found out that I perceive a 2 kHz signal as loudest compared to other frequencies at the same SPL.
When I play my electric guitar without an amp, I clearly perceive the higher strings to be much louder than the lower strings.
But I have a calibrated decibel meter
and I have just run a test: it showed the same dbA value for the lowest and highest string (I know that dbA is different from db SPL but for the sake of this argument, the difference does not play a great role in this situation.)
This clearly proves that perceived loudness is highly subjective and it all happens in our brains.
music.stackexchange.com/users/68420/Matt
According to this post , higher-pitched sounds seem to the human ear to be louder than lower-pitched ones.
In general, a violin is going to be playing in a higher register than a guitar.
music.stackexchange.com/users/46541/John Doe
The idea, that the the size of an acoustic instrument is an indication of its loudness is somewhat astonishing.
It simply effects (based on trustworthy physical laws), that is maximum resonance frequency is in a different range.
So violas are typically likely less loud than violins.
As hinted in my comment, the material of the string can't be neglected either in respect to color of tone and volume, as the pure guitar-based comparison of nylon and steel strings shows.
music.stackexchange.com/users/2600/guidot
How loud an instrument sounds is not determined by its size.
It's determined by the amount of coupling between the string (or whatever is generating the tone) and the air around the instrument.
Compare an acoustic guitar with an electric guitar
: They are both of the same size, they both may use exactly the same strings (though they prefer different gauges).
But one is loud enough to sing along (the acoustic guitar)
while the other can hardly be heard unless you plug it into an amp.
The difference?
The electric guitar is basically a solid slap of wood that's purposefully way too heavy to vibrate significantly.
As such, the vibration energy stays in the strings for a longer time, giving the instrument a much longer sustained sound than the acoustic guitar does.
The acoustic guitar, by contrast, is built such that the thin planks of wood vibrate along with the strings, so that the vibrations can actually be turned into sound waves efficiently.
The acoustic guitar has a much, much higher coupling between the strings and the surrounding air than the electric guitar.
Of course, this coupling is a continuous scale.
You can find guitars that are louder (stronger coupling), and you can find violins that are quieter (weaker coupling) than other instruments of the same sort.
But the violin has seen very intensive use as an orchestra instrument where a certain amount of volume is a must.
And a strong coupling is not a problem for a violin because energy is constantly being supplied by the bow: There is no need to sustain a sound for a while.
The guitar, on the other hand, is a plucked instrument, and as such the amount of available energy is fixed.
The longer a note sounds, the quieter it gets.
And the stronger the coupling is, the quicker the note will fade away.
Which is not what most guitarists want: When they were able to reduce the coupling by relying on electric amplification instead, they almost immediately reduced the coupling to effectively zero in order to get a good, long sustain.
music.stackexchange.com/users/56638/cmaster - reinstate monica
If you want to reduce the amount of sound a violin makes then move the soundpost.
If you want to drastically reduce the amount of sound then remove it altogether (but be careful of the bridge falling down if you do that).
OK, not a serious suggestion to try on a good violin
but it makes the point that the quality and amount of sound a violin makes is determined by the way the instrument is "set up" and in particular the positioning of the soundpost.
According to Wikipedia : The position of the sound post inside a violin is critical, and moving it by very small amounts (as little as 0.5mm or 0.25mm, or less) can make a big difference in the sound quality and loudness of an instrument.
For non-violinists, the soundpost is a small wooden dowel which is placed (not glued) roughly under the bridge.
When the strings are tuned (i.e. tightened)
this applies pressure to the soundpost and it performs acoustic coupling with the back of the violin transferring additional sound energy.
A guitar doesn't have a soundpost and hence produces less sound.
music.stackexchange.com/users/58672/Brian Towers
Resonance.
Range and bow help too.
music.stackexchange.com/users/69763/Rodrigo B. Furman
The violin is comparatively louder than a guitar.  This is a surprising fact, given that:   the violin instrument is generally smaller than, say, a typical classical or folk guitar,  both use strings.    In other words, how can such a small instrument as a violin be so loud? Is the fact that the strings of a guitar are pinched compared to the bowed strings of a violin the main and only reason?
Why is a violin so loud compared to a guitar?
music.stackexchange.com
<guitar><violin><string-instruments>
music.stackexchange.com/questions/99132
music.stackexchange.com/users/69187/Michael Baudin
How loud an instrument sounds is not determined by its size. It's determined by the amount of coupling between the string (or whatever is generating the tone) and the air around the instrument. Loudness is the perceived volume which can differ a lot from the actual SPL (sound pressure level), although the SPL is still a major factor.    How loud an instrument sounds is not determined by its size. 
How loud an instrument sounds is not determined by its size. Some people hear certain frequencies much louder than others. Loudness is also dependent on frequencies and bandwidth of the audio signal. With age some form of hearing loss occurs, and your ears can also play a role in how loud you hear. The SPL (sound pressure level) is a major factor in the perceived volume of a sound. The loudness of an instrument is determined by the amount of coupling between the string (or whatever is generating the tone) and the air around it. Size doesn't determine the loudness but coupling between strings