Key point: One Rep Max Formulas Compared works best as a model comparison. Research on repetition-to-failure prediction shows that equation accuracy depends on the movement, rep range and population, so no single generic equation should be treated as universally exact.
One Rep Max Formulas Compared: The 7 Equations
The seven equations below all use the same two inputs: the load lifted, written as w, and the repetitions completed, written as r. Their structures differ, which is the reason One Rep Max Formulas Compared can show a meaningful range even when your input set never changes.
These are prediction equations, not laws of physiology. A lifter with unusually strong repetition endurance may outperform one model, while another lifter with high peak strength and lower endurance may fall below it. Exercise selection also matters because a bench press, squat, deadlift, leg press and machine isolation movement do not necessarily share the same reps-to-percentage relationship.
Formula Reference
When the input is one completed rep, this calculator returns the entered weight as the observed one-rep result instead of extrapolating it through a multi-rep equation.
| Formula | Shape | What changes as reps rise | Practical use |
|---|---|---|---|
| Epley | Linear | Adds about 3.33% of the rep-set load per repetition in the equation. | Simple, transparent baseline and common programming estimate. |
| Brzycki | Rational | The denominator shrinks as reps rise, increasing the estimate nonlinearly. | Often useful for lower-rep sets and commonly compared with Epley. |
| Lander | Rational | Uses a similar denominator structure with different fitted coefficients. | Helpful as a second regression-style cross-check. |
| Lombardi | Power | Raises rep count to a small exponent, creating a smooth curved increase. | Useful for seeing how a power model differs from linear estimates. |
| Mayhew | Exponential | Uses an exponential decay term in the denominator. | A research-derived comparison that can sit higher than conservative estimates. |
| O'Connor | Linear | Adds 2.5% of the set load per repetition. | Simple and frequently more conservative than Epley at the same reps. |
| Wathen | Exponential | Uses a different exponential curve from Mayhew. | Useful as another curved estimate, especially when comparing clusters. |
One Rep Max Formulas Compared Example: 100 kg for 5 Reps
Suppose you bench press 100 kg for five good repetitions. Epley gives about 116.7 kg, Brzycki about 112.5 kg, Lander about 113.7 kg, Lombardi about 117.5 kg, Mayhew about 119.0 kg, O'Connor 112.5 kg and Wathen about 116.6 kg. The average is roughly 115.5 kg, with a range from about 112.5 to 119.0 kg.
One Rep Max Formulas Compared therefore gives a more useful message than a single-number calculator: the set supports an estimated maximum somewhere in a relatively narrow band. If the next training block uses percentages, you could select a conservative working maximum near the lower or middle part of that band rather than automatically programming from 119 kg.
Example programming choice: if the median estimate is around 116 kg, 80% is about 93 kg. In a gym with 2.5 kg loading increments, a practical target might be 92.5 kg rather than pretending that the estimate is precise to the nearest tenth.
Why One Rep Max Formulas Compared Diverges More at Higher Reps
As rep count increases, the formula must infer a farther-away endpoint. Ten or twelve repetitions reveal a mix of maximal strength, local muscular endurance, technique efficiency, pacing and tolerance of fatigue. Two lifters can perform the same 10RM yet have meaningfully different true one-rep maximums.
A 2006 study of multiple-repetition testing reported that five-repetition maximum data produced stronger 1RM predictions than 10RM or 20RM conditions for the tested chest press and leg press, and the authors advised against using more than 10 repetitions in their linear prediction approach. A large 2023 meta-regression also found substantial between-individual variation in the reps-to-%1RM relationship. Those findings support reading One Rep Max Formulas Compared as a range rather than a certainty.
Recent cross-validation work continues to show that prediction quality depends on the specific equation and exercise. A 2025 study cross-validating 18 published equations for bench press and leg extension recommended modified movement-specific equations under its own testing conditions and used sets of 4–10 repetitions to failure. That does not invalidate the classic formulas; it shows why context matters.
Which One Rep Max Formula Should You Use?
There is no universally best choice for every lift and lifter. For practical strength programming, consistency can be more valuable than formula shopping. If you have used Epley for six months, changing to Mayhew solely because it gives a larger number can create an artificial “gain” that came from the equation rather than your performance.
One Rep Max Formulas Compared works well when you use the cluster to choose a policy. You might track Epley as your main estimate, use Brzycki as a conservative cross-check, and watch the full seven-formula spread when the set is higher-rep. If the spread suddenly grows, that is a cue to inspect the input set rather than chase the most flattering output.
For simple tracking
Pick one formula, keep the movement standard constant, and compare the same estimate over time.
For cautious programming
Use the median or lower half of the formula cluster, especially after a high-rep or non-failure set.
For advanced autoregulation
Pair estimated 1RM with RPE, reps in reserve, bar speed or recent top-set performance.
One Rep Max Formulas Compared and the Best Rep Range
Lower-rep sets are generally closer to the outcome you are estimating. That does not mean everyone should test heavy triples, doubles or singles. Training age, exercise complexity, injury history, spotter access and technical confidence matter more than squeezing a little extra precision from a prediction model.
For healthy, experienced lifters who already perform low-rep strength work, sets in roughly the 3–8 rep region often provide a practical compromise between specificity and fatigue. For newer lifters, an RPE- or RIR-informed estimate may be more appropriate because technique can change quickly as loads approach maximum.
When One Rep Max Formulas Compared receives more than 10 reps, the calculator still computes the classic equations so you can see the divergence, but it displays a caution. The higher the rep count, the more strongly you should treat the result as a broad estimate rather than a target for an immediate maximal attempt.
Using One Rep Max Formulas Compared for Training Percentages
An estimated 1RM is most useful when it improves a training decision. This is where One Rep Max Formulas Compared becomes practical: once you have a reasonable working maximum, you can derive percentage-based loads, compare strength between blocks, or set a training max below estimated capability. The Lifting Percentage Calculator is the natural next step when you want percentages from a chosen max.
Do not confuse a percentage table with a guaranteed repetition count. The relationship between repetitions and percentage of 1RM varies substantially between individuals and exercises. The 2023 meta-regression on this topic found meaningful between-person variability, so 80% of 1RM should be treated as a load prescription, not a promise that every lifter can perform the same number of reps.
If your top set stopped before failure, use the RPE Based One Rep Max Calculator or the Reps in Reserve Calculator to capture effort. One Rep Max Formulas Compared assumes the repetition count is informative; stopping with several clean reps left can make a plain reps-to-failure equation understate your strength.
One Rep Max Formulas Compared: Limitations and Common Mistakes
Prediction equations are only as useful as the set used to feed them. A loose touch-and-go bench press should not be compared with a paused competition-style bench press as if the repetition standard were unchanged. The same applies to squat depth, deadlift straps, machine settings and range of motion.
- Choosing the highest estimate. A formula comparison is not an auction. The top result is not automatically the truest one.
- Using very high reps as if they were precise. Endurance contributes more as the rep count rises, so extrapolation can widen.
- Ignoring proximity to failure. Eight reps with four reps left is not the same input quality as an eight-rep maximum.
- Changing exercise technique. A new grip, range of motion, pause standard or equipment setup can change the meaning of the result.
- Testing maxes while fatigued. A direct 1RM and an estimated 1RM are both influenced by readiness, sleep, warm-up and recent training.
- Comparing formulas instead of progress. Use One Rep Max Formulas Compared to understand uncertainty, then track a consistent method.
- Programming from false precision. Round to loadable plates and leave room for day-to-day performance variation.
Direct one-repetition testing can be appropriate for trained lifters under suitable conditions, but it is not required to run a productive program. Current ACSM resistance-training guidance emphasizes matching load and volume to the goal rather than making maximal testing itself the goal. For general strength development, the program should remain adaptable to the individual.
Research Context for One Rep Max Formulas Compared
The classic equations were developed in different populations and eras, and later studies have repeatedly tested how well repetition performance predicts maximal strength. The value of One Rep Max Formulas Compared is that it exposes part of that uncertainty. The practical conclusion is not that estimation is useless; it is that prediction error should be expected and reported.
- Muscular endurance repetitions to predict bench press strength reported strong validity coefficients but also cautioned about prediction error, with Brzycki performing well in sets of 10 reps or fewer in that sample.
- Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry found stronger prediction from 5RM than 10RM or 20RM conditions in the tested chest press and leg press.
- Maximal Number of Repetitions at Percentages of the One Repetition Maximum synthesized 269 studies and highlighted substantial between-individual variability in the reps-to-%1RM relationship.
- Cross-validation of equations for estimating 1RM from repetitions to failure tested 18 equations and recommended movement-specific modified equations for its bench press and leg extension data.
- ACSM's 2026 resistance-training guideline update emphasizes goal-specific loading, individualization and consistency in resistance training.
One Rep Max Formulas Compared uses these sources as context, not as a claim that every classic formula has equal validation for every exercise. The calculator intentionally shows disagreement instead of hiding it behind one default number.