How to convert performance between machines or free weight exercises

Here’s the deal, you push a chest press, say 70kg, you reach fatigue at 8 reps. You change gym, different chest press, same weight:70 kg, FIVE reps to fatigue, What the hell???

Or…you’re in competition with a friend of yours (friendly competition is good, it provides motivation and results), he tells you his performance on his machine…how does that convert into a performance on your machine?

Well, yes, workout machines are very different from a brand to another, from a model to the newer model of the same brand. Worse, sometimes they don’t even show the unit (Kg or Lbs?), worse even more, the numbers sometimes mean neither Kg or Lbs, just numbering the iron plates.

If you use machines, as soon as you change gyms you’re in trouble when it comes to tracking performance. This affected me many times because I travel quite a lot and I’ve moved out almost every year over the past 12 years. I was tired of opening a new excel sheet for each gym with no continuity between the perfomances. I wanted to be able to graph my perfomance improvement regardless of the equipement brands and models that I used. Being a nerd, after trying a lot of methematical models, I finally translated this problem to a simple high-school level math set of equations with unknown conversion rates to find Solving that equation (automatic calculator available, link below) tells you how to convert your performance from the hotel’s gym in Thailand to my regular gym at home, or from my former place’s gym to the gyn at my new place…possibilities are endless!

The following presents a method to convert any performance to what it would be on a another machine or with free weights. The only hypothesis is that the exercises used in the conversion solicit the same muscle groups.


If used to convert a performance from a machine to free weights, this method provides a universal measure of performance.


In the following, mach1 and mach2 will be the names of the two different machines allowing to exercise the same muscle group in a very comparable manner.


  • Use the two-set method on a given machine (mach1) to assess your performance on it (say a chest press). Calculate the two coefficients (a_1 and b_1) that represent your performance on this machine. The details of how to use the two-set method to obtain these coefficients are presented on this page.
  • After some rest (~4/7 days), do the same on the other machine (mach2). You get two coeffients, a_2 and b_2.
  • Calculate the conversion rate from mach1 to mach2, therefore k_a= a_2/a_1, similarly k_b= b_2/b_1.


  • Everytime you want to convert your performance, you will need to go through the two-set method on the CURRENT machine you use (mach1). You therefore have a and b for mach1, not necessarily the same as those you had the day you established the conversion rates.


The equivalent performance on mach2 (the reference) is given by :


becomes by conversion:


Just fix either x2, meaning the number of reps (resp. y2, the weight) for mach2 and the equation yields you the corresponding weight (resp. number of reps). In other words, you have the equivalent performance :

By fixing reps (x_2) you get the equivalent weight:



By  fixing weight (y_2) you get the equivalent number of reps:

If you need some help to be able to convert your performance from one machine to another, from a machine to the free weights equivalent, or vice versa, and you didn’t quite understand what this post is talkng about, just drop a comment below, I’ll be hapy to help.

I am looking for publication help:

This article has been online since 2009, and I am a bit sad that no one in the fitness has come accross it and publicized it more. Changing gyms is disrupting performance tracking is just a problem that so many people face but still today I’ve never seen this method anywhere. Let me know if you want to publicize it. That would be the glazing on the cake for me after looking for a proper model for so long and managing to solve it with such a minimalistic formula! If you are an academic, there are some practical experiments I would like to do just to extra-confirm the practicality of this technique, and also to confirm that the conversion coefficients are universal, meaning that anyone can use the same conversion rates between say my Thailand gym and a universal bench press. Free weight equivalents can be used as a “universal” language of performance. I dream of the day that every apparel in gym would have the k_a and k_b conversion factors so that the user can convert the machine performance to a free weight equivalent (i.e. bench press), which can in turn be converted to other machines, for instance your prefered machines at home. AT any given point in time people can say “My bench press coefficients are (a) 1.2 and (b) 25” and that will sum up “I do 10 reps at 100kg, and 3 at 130 kgs”. Besides each coefficient has a meaning: the “a” is the slope, represents endurance, “b” is the y-axis value = the “0-RM”, meaning the power factor. It would be going a bit far, but I even think that the two-set method that gives the values of (a) and (b) can be a good field test for a novel non-invasive field assessment of muscle fiber composition (type I vs. type II muscle fibers).

I don’t want to sound rude but most people at the average gym poorly or don’t track their performance and they’re iron monkeys, they don’t read science beyond Men’s Health and will drink or swallow anything that has a catchy pitch or that is popular. These are facts. But I know there is a community of educated athletes to whom this will appeal like insulin to a dying diabetic, I just need some help to get it out there. Buzz me if you think you can help. I’ll be happy to collaborate on both magazines, blogs, and academic research papers. I have completed an  M.Eng in nanotechnology at the National University of Singapore, so I am very aware of the expectations of academic publications, and I already have in mind I the practical experiments would have to be conducted. I am just not affiliated anymore with any academic structure since graduation.

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