The Berger 1RM Formula

The Berger formula, introduced by Richard A. Berger in 1961, provides a method to estimate your one-rep max (1RM) using submaximal lifts, typically for 2-10 repetitions. This guide explores its history, mechanics, accuracy, and role in strength training.

Origin

Richard A. Berger was a researcher who published in 1961 on how to estimate maximal strength from submaximal lifts. In his study he used bench-press performance (up to 10 repetitions) to create a chart of percentages that related any lift of 1-10 reps to an estimated one-rep max. His goal was to improve the efficiency of strength testing in rehabilitation settings. Berger noted that although he collected data on the bench press, “the same proportional result should be obtained” in other lifts as well. His original paper appeared in the Journal of the Association for Physical and Mental Rehabilitation in 1961.

The Berger Formula

The Berger estimate is usually given as an exponential formula. In algebraic form it is:

1RM = w / (1.0261 × e^(-0.0262 × r))

where w is the weight lifted for r repetitions. In other words, you divide the submaximal weight by the factor 1.0261 × e^(-0.0262 × r) to get the predicted one-rep max.

Example Calculation:

As a quick example, suppose an athlete lifts 100 kg for 5 repetitions. Plugging into Berger’s formula gives:

1RM = 100 / (1.0261 × e^(-0.0262 × 5)) ≈ 111 kg.

Thus the estimated one-rep max is about 111 kg for this athlete’s bench press. This matches the percentages in Berger’s original chart.

Development and Variations

Original percentage table. Berger’s 1961 work was actually a lookup table of percentages (1RM = 100%, 2RM ≈97.4%, 3RM ≈94.9%, etc.) for converting 1-10 rep max values. Later authors adapted and published these percentages (for example Belanger et al. 1984 published an adapted version of Berger’s table).

Derived formula form. Years after Berger’s original paper, others fit a mathematical formula to his percentage table. The exponential equation above is one such “derived Berger formula” that closely reproduces his table values. Some published charts note that very slight differences can occur between the original table and this fitted equation.

Misattributed linear formula. Some modern websites and calculators mistakenly label a simpler linear model as the “Berger formula.” For instance, one fitness site gives Berger’s 1RM equation as 1RM = w + 0.033wr (i.e. w(1+0.033r)), which is actually just a form similar to the Adams and Epley formulas. This linear version does not appear in Berger’s 1961 paper and seems to stem from confusion with other formulas.

Accuracy and Use

Typical usage. Berger’s method is intended for submaximal lifts up to about 10 repetitions. Beyond 10 reps, its predictions become unreliable. In practice, a lifter would select a weight they could lift for a few reps (usually 3-10), perform as many clean reps as possible, and then apply Berger’s table or formula to estimate 1RM. For example, studies have used Berger’s chart for arm curl or bench-press tests, using the final reps and weight to look up the estimated 1RM. Although Berger collected bench-press data, his table has been applied with success to many exercises, assuming similar muscle fatigue patterns.

Accuracy. Like all rep-based formulas, Berger’s estimate is only approximate. In a 2001 validation study with healthy young adults, the estimated 1RM from Berger’s table correlated strongly (R² ≈ 0.93) with actual 1RM for bicep curls. In practice you can expect a few percent error in either direction. Berger’s method tends to be more accurate for moderate rep ranges (5-10 reps); at very low reps (near maximal) or very high reps (over 10) the estimate may be less precise. Note that individual differences (training level, muscle group, technique) also affect accuracy.

Berger’s Significance

Berger’s work was one of the early systematic approaches to estimating maximal strength without an all-out test. He explicitly framed his table as a way “to improve the efficiency” of determining muscle strength, a safer and quicker alternative to testing absolute max. In fact, submaximal tests like Berger’s became popular because, compared to a formal 1RM test, the submaximal estimation method is safer and quicker. His 1961 paper thus helped pave the way for later strength-testing methods and calculators. It appeared at a time when exercise physiology was formalizing weight-training routines; Berger’s table was an early tool for coaches and therapists to prescribe and track loads. While many new formulas have been developed since, Berger’s contribution remains a notable early attempt to quantify the link between reps and maximal strength using scientific data.

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