# One-repetition maximum

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One rep maximum (one repetition maximum or 1RM) in weight training is the maximum amount of weight one can lift in a single repetition for a given exercise. One repetition maximum can be used for determining an individual's maximum strength and is the method for determining the winner in events such as powerlifting and weightlifting competitions. One repetition maximum can also be used as an upper limit, in order to determine the desired "load" for an exercise (as a percentage of the 1RM).

## Calculating approximate 1RM

Various weight training protocols call for lifting some percentage of the lifter's 1RM. However, many consider the risk of injury when attempting a 1RM to be higher than when performing multiple rep sets. Therefore, there have been various proposals for ways to calculate an approximation of the 1RM.

There are two common formulas used to calculate the one rep maximum.[1][unreliable source?] If $r$ is the number of repetitions performed and $w$ is the amount of weight used (note that $w$ is a factor of each formula, so the unit of measurement doesn't matter), then

### Epley Formula

$1RM = w \left ( 1 + \frac{r}{30}\right )$

### Brzycki

This version of the one rep maximum calculation is often referred to as the Brzycki Formula after its creator, Matt Brzycki,[2] and can be written either in terms of integers or decimal approximation:

$1RM = w \cdot \frac {36}{ \left ( 37 - r \right ) } = \frac{w}{ \left [ \frac{37}{36} - \left ( \frac{1}{36} \cdot r \right ) \right ] } \approx \frac{w}{ \left [ 1.0278 - \left ( 0.0278 \cdot r \right ) \right ] }$

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. For example, if a person can lift 100 pounds on a given exercise for 10 reps, the estimated one rep max would be 133 pounds for both formulae. However, if the person were to complete only 6 reps, then formula 1 would estimate a one rep maximum of approximately 120 pounds, while formula 2 would return an estimate of approximately 116 pounds.

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.

Several more complex formulae have been proposed which use different coefficients for different rep numbers and sometimes even for different exercises.[3][unreliable source?] Using the same notation as above,

#### Lander

$1RM = \frac{100 \cdot w}{101.3 - 2.67123 \cdot r}$

#### Lombardi

$1RM = w \cdot r^{0.1}$

#### Mayhew et al.

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

#### O'Conner et al.

$1RM = w \cdot (1 + 0.025 \cdot r)$

#### Wathan

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

One rep maximum calculators are used to predict a one rep maximum lift. The degree of accuracy can vary largely depending on the weight training experience and muscular composition of the athlete. Also, most one rep maximum calculators are design for seasoned strength trainers, and those with little experience may find their actual one rep maximum is much lower because their nervous system cannot handle the stress of a high weight. This test should be performed with a spotter for reasons of safety.