1RM Formulae and its Applications


Context


Earlier today I did a small workout using a hexagon bar (deadlift alternative). During it I managed to do 5 x 255 lb. I wondered as I got to my room what I could achieve as my ultimate rep. Bodybuilding.com put me at ~300 lb. (296 to be exact).

I then was perplexed that it offered no formulas anywhere on the page as to how it determined. I then set out to find them and found out that there is more than a couple.


Epley

{\displaystyle 1{\text{ RM}}=w\left(1+{\frac {r}{30}}\right),}

Brzycki

{\displaystyle 1{\text{ RM}}=w\cdot {\frac {36}{37-r}}={\frac {w}{{\frac {37}{36}}-{\frac {1}{36}}r}}\approx {\frac {w}{1.0278-0.0278r}}}

Formula 1 (Epley) and formula 2 (Brzycki) return identical results for 10 repetitions. However, for fewer than 10 reps, formula 1 returns a slightly higher estimated maximum.

These types of calculations may not always produce accurate results, but can be used as starting points. The weight can then be changed as needed to perform the number of reps called for by the training protocol.


McGlothin

{\displaystyle 1{\text{ RM}}={\frac {100w}{101.3-2.67123r}}}

Lombardi

{\displaystyle 1{\text{ RM}}=wr^{0.1}}

Mayhew et al.

{\displaystyle 1{\text{ RM}}={\frac {100w}{52.2+41.9e^{-0.055r}}}}

O'Conner et al.

{\displaystyle 1{\text{ RM}}=w\left(1+{\frac {r}{40}}\right)}

Wathan

{\displaystyle 1{\text{ RM}}={\frac {100w}{48.8+53.8e^{-0.075r}}}}

Reps at Specific Percents of 1RM


Bodybuilding.com uses this graph to decide reps at given percentages of an individuals max:


REPS% 1RM
1100
295
393
490
587
685
783
880
977
1075
1173
1270

Putting this through a regression algorithm I found that explonential and linear equations are the most accurate (99.71 -99.85% accuracy).


Various 1RM Estimations

Sources


Calculate Your One-Rep Max (1RM) by Bodybuilding.com

One-repetition maximum by Wikipedia

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