One rep 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 rep 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 rep 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).
[edit] Calculating 1RM
Various weight training protocols call for lifting some percentage of 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.
For example, one common and simple formula is ((number of reps / 30) + 1) * weight used. So, if a person can lift 100 pounds on a given exercise for 10 reps, the estimated one rep max would be ((10 / 30) + 1) * 100 = 133.3 pounds. If this person were to follow a protocol calling for 80% of one rep max in this exercise, they would then choose a weight close to .8 * 133.3 = 106.6 pounds.
This kind of calculation may not always produce accurate results, but can be used as starting point. You can then increase or decrease the weight as needed to perform the number of reps that your training protocol calls for.
Several more complex formulas have been proposed which use different coefficients for different rep numbers and sometimes even for different exercises.