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I need some help with a formula for programming use!

It's strength training related, so lets say I squat $100kg$ for a max($100\%$)

And in one workout perform $80kg$ for a total of $20$ repetitions, thats $80\%$ relative to max.

And then I do $70kg$ for a total of $40$ repetitions, which is $70\%$ relative to max weight wise ofc.

So simply the average intensity (intensity being $\%$ relative to max) would be $80+70/2 = 75\%$.

But really I did the double amount of reps with $70\%$ so more work was done with a lighter weight and when you add the repetitions to the equation of average it changes, I happen to know that the average would then be $73,6\%$, I just dont know the formula.

I got some help with this yesterday with this formula $(20/(40+20) \times 80) + (40/(20+40) \times 70) = 73,3\%$ so while this is farely close, if I change the repetitions done with $80\%$ to only 1 repetition and plug that into the formula its returns like $35\%$ which ofc is wrong, it shouldnt be able to go lower than $70\%$ when that extra repetition was done at a heaver weight than $70\%$ if this makes sense?

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    The formula you wrote down looks right and will always give a number between 70 and 80. Are you sure you changed all the 20s in the formula to 1s? – 2017-01-13

1 Answers 1

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I'm not sure how you get 35%, but if you change to only 1 rep at 80% you need to change every 20 in the expression to a 1, so you get $\frac{1}{40+1}\times 80+\frac{40}{1+40}\times 70\approx 70.2$.

In general the formula is $\frac{(\text{reps at first weight})\times(\text{first weight})+(\text{reps at second weight})\times(\text{second weight})}{\text{total reps}}$.

This is called a "weighted mean" -- see the wikipedia article.