I want to know what is the effective weight of doing push-ups. What would be the weight of the dumbbell/ barbell to do a bench press with the same resistance as a push-up. I understand this depends on the person's weight, maybe the answer can be an estimated percentage of the weight?
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I asked this question on physics.stackexchange.com for you: http://physics.stackexchange.com/questions/9129/what-is-the-force-on-the-arms-in-a-pushup . The answer is 50% of your body weight assuming equal distribution of mass vertically and weightless arms and head. It will be more than 50% when you factor in arm and head weight and your exact vertical mass distribution. If you're top heavy, you're pushing more weight. If you're bottom heavy, you're pushing less weight.
You can get a rough measurement by holding pushup position with your hands on a bathroom scale. I suggest doing this with your arms fully extended and locked to prevent yourself from actively pushing against the scale and skewing the reading.
For me, it ended up being about 75% of body weight.
Roughly 55-80% of bodyweight
Dick Moss has this overview on how much weight we are lifting in push-ups, "citing" an unnamed study:
He notes that the difference between the sexes is really just a function of body mass distribution between the upper and lower body:
Changes in resistance through the range of motion
It's also important, when trying this at home, to test both the top and the bottom of the push-up position, since the change in angle of course affects how much resistance is applied. Per Suprak, Dawes, and Stephenson 2011: