Epley · Brzycki · Lander · Lombardi · Mayhew
The Epley formula comes from Boyd Epley, longtime strength coach at the University of Nebraska and a founding figure of the National Strength and Conditioning Association (NSCA), who developed it in the 1980s to help his athletes gauge training loads without maxing out every session. Like several formulas from that era, it started life as a simple chart relating reps to percentage of max, which was later formalized into the equation now in common use.
The formula is 1RM = w × (1 + r/30), where w is the weight lifted and r is reps completed. It's linear, meaning each additional rep adds a constant fraction of the load rather than tapering.
Use it for sets in the roughly 2–10 rep range, where its linear assumption holds up reasonably well and it's one of the two most trusted formulas alongside Brzycki. Don't lean on it for high- rep sets (15+): because it never curves off, it keeps adding value per rep indefinitely and will meaningfully overestimate your true max compared to what you could actually lift once. It also shouldn't replace an actual max test before something like a competition — it's a training- planning tool, not a certification of your max.
Based on the Waikato Institute study (bench, squat, deadlift, n=9 trained lifters) and the Cyrino et al. comparison that included isolation work, here's how the Eply formula ranks by lift:
Matt Brzycki, a strength and conditioning coach, published this formula in 1993, deriving it by extrapolating from a graph plotting percentage of max load against reps to failure, based on earlier unpublished observations by Anderson and Haring. It's since become, alongside Epley, one of the two default formulas built into most gym calculators and apps.
The equation is 1RM = w × 36 / (37 − r). It's a bit more conservative than Epley at most rep ranges and mathematically curves rather than staying purely linear, though it still breaks down as reps get large.
It's best used in the same 2–10 rep window as Epley, and many coaches treat it as the slightly safer of the two since it tends to estimate a bit lower. The critical thing to avoid: never plug in 37 or more reps — the denominator (37 − r) hits zero and the formula produces a divide-by-zero error or a nonsensical negative number. Even well before r=37, accuracy has already fallen apart, so treat anything above 10–12 reps as unreliable territory regardless of what number it spits out.
Based on the Waikato Institute study (bench, squat, deadlift, n=9 trained lifters) and the Cyrino et al. comparison that included isolation work, here's how the Brzycki formula ranks by lift:
The Lander formula (sometimes attributed as O'Conner/Lander depending on the source) also dates to the mid-1980s, developed alongside Epley's work as part of that same generation of NSCA-affiliated regression-based prediction charts used to train athletes without repeated max testing. It's less commonly cited today than Epley or Brzycki but shows up in older strength-and-conditioning textbooks and research comparisons.
The formula is 1RM = (100 × w) / (101.3 − 2.67129 × r). Structurally it resembles Brzycki — a percentage-based denominator that shrinks as reps increase — but with different constants derived from its own regression dataset.
It's suited to the same low-to-moderate rep ranges as the other classic formulas, and is mostly useful today as a cross-check against Epley/Brzycki rather than a primary tool, since it's less validated in modern research. Avoid using it at high reps for the same structural reason as Brzycki: the denominator shrinks toward zero as r grows, so estimates become unstable and unreliable well before you'd expect.
Based on the Waikato Institute study (bench, squat, deadlift, n=9 trained lifters) and the Cyrino et al. comparison that included isolation work, here's how the Lander formula ranks by lift:
Lombardi's formula, published in 1989, took a different mathematical approach from the linear-regression charts of Epley and Lander. By his own account, it was built through curve fitting against training data with a fair amount of trial and error — adjusting the exponent until it matched observed lifting performance reasonably well.
The equation is 1RM = w × r^0.10, a power function rather than a linear or percentage-based one. This shape makes it grow more slowly as reps increase, which is mathematically the opposite tendency of Epley.
Because it's so simple, it's an easy mental-math option, but it's known to run a bit high compared to other formulas, especially as rep counts climb — despite growing "more slowly" in form, it still doesn't correct for high-rep inaccuracy the way exponential models do, and in practice tends toward overestimation. Don't use it as your sole formula for programming near- max attempts; treat it as one data point among several rather than the anchor.
Based on the Waikato Institute study (bench, squat, deadlift, n=9 trained lifters) and the Cyrino et al. comparison that included isolation work, here's how the Lombardi formula ranks by lift:
The Mayhew formula comes from a 1992 study by Mayhew, Ball, Arnold, and Bowen, built specifically from bench press research rather than a general strength-training chart. That bench-specific origin matters: unlike Epley, Brzycki, and Lander, it wasn't developed as an all- purpose gym tool but as a predictive equation validated against a particular lift and population.
The formula is 1RM = (100 × w) / (52.2 + 41.9 × e^(−0.055 × r)), an exponential model rather than linear or power-based. This shape lets it curve and flatten more naturally as reps increase, which is why it tends to hold up better than Epley or Brzycki once you get into the 10–20 rep range.
Use it when you're working with higher-rep sets or specifically estimating bench press max, where it was validated. Don't assume it transfers cleanly to lower-body lifts like squat or deadlift with the same accuracy it has for bench, since its coefficients were fit to bench press data specifically — for those lifts it's better used as a cross-check alongside Epley or Brzycki rather than the primary formula.
Based on the Waikato Institute study (bench, squat, deadlift, n=9 trained lifters) and the Cyrino et al. comparison that included isolation work, here's how the Mayhew formula ranks by lift: