How Much Weight Do You Actually Push Up During a Push-Up?
I'm sure many of you fitness gurus out there have asked yourself this question after doing a few hundred push-ups. Us non-fitness gurus have had the same aching question for quite a while too. "How much weight did I just lift?" you might ask yourself after a good round of push-ups. Was it 90% of my body weight? No, maybe it was 50%? Well, in this article I will calculate the percentage of your body weight that you would expect to "push up" during both regular and inclined push-ups.
Proper Push-Ups
Before I begin with the math, let's define what a push-up is. More specifically, let's discuss proper form and technique. First, get onto the ground. Elevate your body using your arms. Your back must be straight like a board. Don't let your gluteus maximus stick into the air or hang low. There should be a 90-degree angle between your arms and the floor. Your hands should be placed about one and a half times your shoulder width apart and pointed parallel to your body. Your body should be raised on the balls of your feet. Your feet should also be touching or no more than shoulder width apart. When you go downward, only bend your elbows. You can come back up once the elbows break the plane of your back.
Mathematical Assumptions
I will calculate the percentage of body weight resisted during a push-up for an average sized person (I used Leonardo Da Vinci's "Vitruvian Man" to properly scale the human structure because there was no other source of body measurements I could find). Since the resulting number will be a percentage, it will be correct for any person who has the same dimensions or ratio of dimensions as the average person calculated here. However, if you have abnormally short or long legs or arms compared to your height, the calculation will not necessarily be valid for you. For the purpose of the calculations, the center of gravity for a human is assumed to act through the hips.
The characteristics of an average 25-year-old American male are:
- Height: 70 inches (1.778 m)
- Palm to Shoulder length: 23 inches (0.5842 m)
- Shoulder to Hip Length: 24.75 inches (0.62865 m)
- Hip to Ankle Length: 31.5 inches (0.800 m)
For inclined push-ups, the following objects will be used for the calculations:
- Standard Chair Height: 18 inches (0.457 m)
- Standard Counter Top Height: 32 inches (0.813 m)
Method/Calculations
I will calculate the resultant forces in the hand (e.g. arms) of a human using the principles of engineering statics, Newton's Second Law of Motion, and the assumptions stated above.. The metric system will also be used to simplify the calculations.
Regular Push-Ups
Using trigonometry, the angle between the floor and the plane of the back is 24.1218 degrees. The horizontal distance from the foot to the hip is 0.7301 meters and to the hand is 1.304 meters.
The forces in the Horizontal Direction are zero. Fx = 0
The sum of the forces in the vertical direction are: FY = FHand + FFoot - W = 0
The sum of the moments about the foot is MFoot = (0.730m)×W - (1.304m)×FHand = 0
Because we have cleverly chosen where to place our moment equation, it is the only one we need to solve to determine the force in your hand.
1.304FHand = 0.730W
Therefore, FHand = 0.5598W
Inclined Push-Ups on a Chair
Here, an inclined push-up is performed on a standard chair with a seat 18 inches above the ground.
Using trigonometry and the Pythagorean theorem, the horizontal distance from the feet to the hands is 1.475 meters. The angle between the plane of the back and the floor is 39.24 degrees. The horizontal distance from the feet to the hip is 0.620 meters.
The net force in the horizontal direction is zero: FX = 0
The sum of the forces in the vertical direction are: FY = FHand + FFoot - W = 0
The sum of the moments about the foot is MFoot = (0.620m)×W - (1.475m)×FHand = 0
Rearranging the last equation, we can relate the force in the hand to the weight:
1.475FHand = 0.620W
FHand = 0.420W
Therefore, the upward force in the hands is 42% of your body weight.
Inclined Push-Ups on a Countertop
Here, an inclined pushup is performed on a standard countertop with the work surface 32 inches above the ground.
Using trigonometry and the Pythagorean theorem, the horizontal distance from the feet to the hands is 1.311 meters. The angle between the plane of the back and the floor is 53.96 degrees. The horizontal distance from the feet to the hip is 0.470 meters.
The net force in the horizontal direction is zero: FX = 0
The sum of the forces in the vertical direction are: FY = FHand + FFoot - W = 0
The sum of the moments about the foot is MFoot = (0.470m)×W - (1.311m)×FHand = 0
Rearranging the last equation, we can relate the force in the hand to the weight:
1.311FHand = 0.470W
FHand = 0.360W
Therefore, the upward force in the hands is 36% of your body weight.
Conclusion
Based on these calculations, we can say when you are doing a push-up, you are "lifting" about 56% of your body weight (the other 44% is held up by your feet). In other words, for an average 200-pound person, doing one pushup is similar to (but not exactly the same as) doing one repetition on a bench press with about 112 pounds of weight. Now you know about how much weight your body is pushing up during this awesome exercise.
Additionally, we can definitely say that inclined push-ups require significantly less force to perform than a regular push-up. For an inclined push-up on a standard 18-inch high chair, you will lift about 42% of your body weight. For an inclined push-up with your hands placed on a standard 32-inch high countertop, it is estimated that you will lift roughly 36% of your body weight.
Verification of Results
To verify this calculation I weighed myself on a scale in both the regular and inclined push-up positions as well as the standing position. I did my best to measure the forces in my arms in the above configurations using a standard bathroom scale. It was actually pretty hard to capture the measurements with the scale on the countertop because it kept trying to slide away from me, but I eventually got it (and a good abdominal workout too!). The table below summarizes my measurements and the calculations.
Weight (Standing)
| Weight (Push-Up)
| Measured Ratio
| Calculated Ratio
| |
|---|---|---|---|---|
(lbs)
| (lbs)
| (%)
| (%)
| |
Regular
| 211
| 125
| 59%
| 56%
|
Incline 18"
| 211
| 100
| 47%
| 42%
|
Incline 32"
| 211
| 80
| 38%
| 36%
|
Here is a Graph to help you visualize and compare the results of the calculations versus the measured values.
Based on the verification measurements, I would say that the results are a good representation of what you would expect to see in real life.
These calculations also agree with the currently published research on the matter which says that anywhere from 50 to 75% of your body weight is lifted during a standard push-up. Since everyone's body shape and weight distribution differs, the actual percentage of your weight that you lift during a push-up will vary.
Questions & Answers
Comments
Unfortunately there are some mistakes in the calculations. As mentioned below 1.475 is not correct. Also and more significantly, the angle of the arms is not accounted for. An incline push up with vertical arms is no easier than a regular push up. An incline push up with arms perpendicular to the body is easier. In the latter case, the maths is easier by just looking at the moments about the feet along the length of the body and resolving W to perpendicular to the body. Instinctively one full extension of vertical arms raise the CofG by the same amount regardless of incline, if the arms are perpendicular to the body, then a full extension of the arms raises the CofG by a lesser amount, which is why it's easier in this case.
What about a handstand pushup?
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How did you get the 1.475m to the hand? Shouldn't that be 1.22?
Also in the incline pushup, as the arms are not vertical, the Fhand should be resolved up the arm to get force experienced by the person.
I got 70%
Nice theories and whatever but the easiest way to measure this is to simply place your hands on a scale while doing a pushup. For me the result = 77% of my body weight.
Great article. I knew the angle made a difference, but did not understand the math. Thanks for your explanations.
Awesome Hub. Math usually puts me to sleep, but when it is applied to a subject I am interested in, it makes it makes a difference. Great job!
I must say, you made some assumptions that quite drastically change the value of the force on the hands. The arms on average are about 6% of your body weight, and while you aren't lifting your arms too terribly much, they shift the center of mass of the entire system which changes the force on the hands to be around 75% of your body weight at the top of the pushup.
In the incline pushup on countertop, what assumptions did you make on the body position? A person can do such a push up with different angles (between arms and the countertop)... that will change the calculation. Perhaps you can provide some input on the calculations?
Thanks a lot.
According to Marine Corps philosophy, you actually push up the earth. The Marine is in control and alters events around him. Oorah!
Excellent article. I've incorporated the plank also into my press-ups. Tough but good.
- AUTHOR
Jay - that's awesome! Keep up the good work.
I will admit to being terribly out of shape. But about 6 or 8 months ago, I started doing counter pushups while my coffee is brewing at work. I'm up to 50 two or three times a day, and recently started adding 15 windmills also. I'm 5'10 and about 255 or 260. I can say may arms are definitely solid now.
- AUTHOR
Frienderal - Agreed! Pushups are my favorite exercise that requires no equipment to complete.
An interesting hub! Push-ups are definitely the most convenient and cheapest way to get a good work-out to our core muscles! :)
- AUTHOR
MarkG - the weight of your head is implicitly included in the calulations already.
I agree with the overall method used for your calculations, however one important detail has been omitted.
Your calculations are perfect for a headless human.
When you do a pushup, you are also lifting your head and this needs to be factored into the calculation.
Wow now this is an interesting idea for a Hub. Extremely interesting answer to an age old question.
Honestly, I never thought about it. I learned something new. Hub is well documented and with good graphics. Thanks for the great hub!!
I like that you adjusted for the higher center of gravity of males. For women, these proportions will be slightly less.
Nice technical info there, good to know that. I always wondered what kind of weight I was pushing in a push up.
Thanks for sharing and great images too. Push ups are a great work out for your core and there are other tips for a flatter stomach here http://www.growtallerwithshinlengthening.com/flats...
i do 70 pushup in one serie
What an informative hub! Thanks for sharing, pal. Voted up :)
Very good article, I had never asked that question.
And much less know the answer.
Thank you.
Well done my friend; great message for millions of people. :)
@Ender: Your ass must have been really high in the air, seriously...
I don't know about all that. How do you explain the fact that I weigh about 185 pounds and did pushups with my hands resting on a scale and it read 135-140 pounds during the pushups? That's more like 75% of my body weight.
Im fairly unfit and decedid to change my habits. I can get through only one set and feel like dying in a good way. so ill do one set a day until i can get up 2 sets then do that every second day. Ive never sweated from any other cardio or weight session. even my eyes are sore ahahaha
Okay, after reading some of the comments, I think I'm going back to free weights... Less questions that way... LOL!
@Bob: Weighted vests are excellent additives to any body-weight exercise, as I have a couple different weighted vests myself that I use for dips, pull-ups, push-ups, etc.. Since they are attached to your upper body, it is not that hard to calculate the amount of weight to the existing percentage of body weight being applied during your routines. If you are really curious, just go buy a cheap set of free weights. Other than that, you will never know your true "max out" weight that you can lift; simple as that...
This is a great workout and much hdearr than anticipated, especially if you're over 210lbs! I adapted it in a couple of ways. Try plyometric lunges instead of walking lunges (x20) although these stress the performance of the wall squats quite dramatically. And after x3 through why not do a half-set instead of extra cardio?
hmmm... be interested to know about the body weight percentage of a decline pushup on a chair with a 25kg (55pound) backpack (im 70kg btw or 156 pounds)
- AUTHOR
Insane Mundane - haha it sure is! Not much trigonometry to remember.
The math is much easier for the vertical and/or handstand push-ups; ha!
- AUTHOR
Thanks Stan. I enjoy pushups and love working out in general too. Combine this with my natural curiosity and I just had to find out how much I was lifting. Thanks for reading.
Wow! You really thought outside-the-box on this one! I have done countless push-ups and the amount of weight I am lifting never crossed my mind; just knew it was a great exercise. This really got me thinking. Thank you!
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SidKemp - Thanks for reading. I often try to verify my calculations by an experiment of some kind. It helps add to the authenticity of the hub (and it's fun too!)
Thanks for taking the time to think this through and share your results. I particularly like that you tested the results with a bathroom scale - as I was reading, I was waiting for that. Voted up, useful, and interesting.
I do 100 inclined push-ups a day. It's a fantastic stress reliever and all over body workout. I had no idea I was lifting 36% - 42% of my body weight! Now I understand why I ache so much!! Ha!! Thanks for the great hub!!
I have always wondered but could never figure out how to count it out, my guess would have been 50%, but that would have been a number I pulled out of my hat. Great Visual aids.
Thanks! I've often wondered how much weight I was pressing when doing pushups but never took the time to do the research. Your hub and its comments consolidated my research efforts.
nice article nonetheless
A better way of find the actual force applied through the movement would be to start from an energy conservation standpoint. Take the initial energy of the system as the potential energy at the relative midpoint of the body. Then equate this value to the work done through the movement. The work is a function of r cross f , use a double integral for the varying theta and varying force. Solve and plot to get a varying force distribution with theta. If someone is bored and wants to MATLAB this go ahead. Alternatively you can solve for the limits of the force at the top and bottom of the movment.by assuming we take you're distrbution value of the hands at the top as a starting point we can solve for the force application on the bottom. But this method is more crude.
- AUTHOR
P - yes this is an analysis of a static system. Movement would cause a change in the magnitude of the forces. To solve that numerically would require a complex dynamic analysis. This is beyond the scope of this article.
You calculation essentially boils down to the ratio of l/h (hip to ankle distance over shoulder to ankel distance) to determine the percentage of the load that is applied on the hands. However this simpy shows the distribution of the weight from the hands and feet at the top holding position. If you take the results to its limits then you'll find it gives no actual indication of the amount of work applied by the hands ( even if we completely disregard the biomechanics of the pushup motion itself). For example if a person has relative long arms for his given height, this will increase his shoulder to ankle distance(the hypoteneus of the triangle) for a constant horizontal distance between the hands and feet on the ground. By your result the force distribution on the hands will be smaller since the l is kept constant while the h increases. This simply means that at a more elevated position a greater portion of the person's weight is supported at the feet( which makes perfect intuitive sense). Like wise for a person with shorter arms the hypotenues has to shrink for a constant hand to feet distance. the ratio of l/h is now larger since h*( in the denominator) is now smaller. Therefore this analysis merely shows a force distribution of a person's weight at the top of the pushup motion but can't really be credited to give any indication of the load or force application in the movement itself.
Bathroom scale
- AUTHOR
Gambit Joe - Sounds like a good idea. Perhaps I will calculate that in the future too.
What about push-ups on your knees? Any math wiz want to calculate?
Very fun hub. I generally do regular or decline where I put my feet on a chair or bench. I have asked this question before and it is nice to see someone answering it. Thanks.
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jravity1 - Thanks! This was a fun one to write.
Nicely done
Great article, I have recently perfected my push-up and really enjoy doing them.
I'm also interested in the decline push BW% ! Love the exercise math though thanks :)
Very informative @HubPages! Well documented and love the graphics. Super job!
Great article! Well done.
Looking back on previous comments it looks like my question was answered after all. However, the theoretical equation doesn't take in2 count a changing theta!! hmm this would also mean a changing force throughout the push up ae. As you get closer to the floor during th PU, theta gets smaller hence Fw on arms gets larger (well that's what it feels like..). For this reason, comparing the weight you push in a pushup should not be closely compared to other things that have a fixed weight like dun bells etc. Plz correct me if i'm wrong for i'm not certain if what I said is true.
DW team, I got it. Simple year 9 trig. All you need to do is reverse the diagram, making theta larger and hence the Fw on the hand becomes larger as well. Good effort guys nd gals!!
What about doing pu with your feet on something elevated?
- AUTHOR
Doing pushups with feet on a countertop should be harder than regular pushups because you "lifting" a larger percentage of your body weight. However, the higher your feet are the more your shoulder's play a role performing the exercise - this could make the exercise seem easier depending on how strong your shoulders are in comparison to your chest and triceps.
- AUTHOR
Kris - In that position the weight that you are pushing up increases. One day when I have more time I will update this article to include decline pushups. Thanks for reading.
I, asked that in a hurry. jajaja, well at work a friend did 15 regular push ups, he is about 150lbs, im 215lbs and did 35 push ups, inclined. My push ups , i had my feet up in the counter about 3 feet high. They said i did more because its way easy to do them the way i did. Is that True?
how about, if legs are up in counter and the hands on the floor??
do a push up on a beam scale
I must say the math is very impressive. Good job
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V-Dub - Yes It sounds like you probably did it right. Your body shape is probably very different from what I used in this analysis.
I actually used a weighing scale to measure the weight I exerted on the scale when I was in the up position and down position of a pushup and found out that I was using 75% of my body weight in the up position and around 80% in the down position! Not sure if this is accurate since it only measures the force exerted by my hands and not feet but maybe since the arms are the ones doing the movement maybe it's right
OMW, you finally just answered my question!!! I'm Chinese and I have abnormally long arms, and I have always wanted to know whether it would make a difference!!! TYSM!!!
hahaha...My may doing push-up is wrong.. Thanks for this
- AUTHOR
Most definitely elevating your feet makes the weight increase. Someday I will get around to updating this hub to include those kind of pushups too.
thejovial wrote:
"What happens when you elevate your feet? I know that my workouts get tougher. How does this apply in that case? Does the weight increase?"
My guess is that the answer to your question is yes. Let's look at the boundary condition, where you're upside down, and your feet are directly over your head. The feet are not holding up any of the body's weight, and all of it is supported by the palms of your hands. Assuming that you have excellent balance, these handstand push-ups are really tough!
However the fraction of your body weight that's supported by the hands would decrease as you lowered your feet, and transferred some of the weight 'downstairs'.
One non-obvious factor that may increase the difficulty of elevated-feet-push-ups is that the relatively strong pectoral muscles are used a bit less, and the relatively weak front deltoids (shoulder muscles) come into play.
Awesome post, I've always wondered about this too.
Great hub. I've always wondered this myself, since I often find myself on the road and switching to push-ups instead of bench presses to stay in shape. The number sounds about right intuitively in spite of differences in form, as well, since I'm doing about as many push-ups as I could do bench press reps at 50%-60% of my bodyweight.
I'd be curious to know how much weight gets added to the mix with decline push-ups, though.
What happens when you elevate your feet? I know that my workouts get tougher. How does this apply in that case? Does the weight increase?
Now I know why push ups are so hard!
- AUTHOR
Haha pizza sounds good. I weighed myself to see what the result would be and I got 58%. This is very close to Larry Field's estimate of 60%. More detailed information about this is in the article.
Interesting! I've always wondered
Well done, I've never seen anything on this before! You've almost inspired me to do a pushup. Well then again I could keep wasting time on hubpages. And my pizza looks good too.
- AUTHOR
Yeah, i've made a lot of assumptions for this calculation. Note that during the pushup motion, your weight distribution will change. The closer to horizontal your body is, the closer to 50% the estimate becomes. Of course, if you have abnormally long arms for your body, you may be lifting more than 56% of your weight.
In this example I assumed that all of your weight acts through your hips. Ideally, I would have calculated this using a series of distributed forces to represent a 'true' distribution of ones body weight. However, I could not locate any detailed information on a person's weight distribution.
And yes, a pushup is not exactly the same as a bench press. Depending on your technique and position, you could utilize different muscles during the exercise.
Thank you for that informative piece there, Cwanamaker.
I do pushups as often as possible and it is useful to know just how much of my body weight I am lifting while doing so. It is also a useful bit of info to impress my pushup doing buddies with!! :)
Take care. Rich :)
Interesting. Before reading your hub, my WAG (wild-assed guess) would have been 60% of body weight.
Here's the first fly in the ointment. The 56% figure is a good first approximation, assuming that the arms have negligible weight.
Your hands, which contain a small proportion of your total body weight, don't move at all during the PU. And the vertical component of your forearms' motion is almost negligible. And the center-of-mass of your upper arms is 'lifted' by approximately half of the elbow-shoulder distance. Therefore the 56% of body weight is an upper limit.
Second, the PU shown in the diagram is not really equivalent to a bench press. In the latter, your grip on the barbell guarantees that the relatively powerful pectoral muscles make a big part of the total effort.
On the other hand, PUs in which the hands are initially close to the torso (as shown in the diagram), recruit the front deltoids more, and place less emphasis on the pecs.
Anyway, voted up, and with some extra chutzpah points for pushing the envelope of your comfort zone.
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