One-Rep Max Formulas: What Epley and Brzycki Assume

DevOkk's One-Rep Max Calculator implements Epley and Brzycki from a submaximal set, caps reps at 12, and prints a percent table (95, 90, 85, 80, 75, 70) anchored to Epley. Default 100 kg × 5 reps → Epley 116.67 kg, Brzycki 112.50 kg. That spread is the point: you do not "have" a single true max from arithmetic alone.

This is strength planning, not medical advice. Not clearance for lifting after injury. Not a biomechanics audit of your squat depth. For protein ranges around training, see Protein grams per kg. For session energy, METs and calories burned. Hub: Fitness Calculators.

What a one-rep max is supposed to mean

A one-repetition maximum (1RM) is the heaviest load you can lift through a defined range of motion once with acceptable technique. Test protocols use warm-up singles, progressive jumps, long rests, and spotters. Competition powerlifting 1RMs include pause rules and judges.

A submax estimate asks: if you did weight w for r reps (r > 1), what might 1RM be? Statisticians fit curves to pooled data. The curves disagree because lifts, populations, and effort levels differ.

Online calculators never see:

• Bar speed and intent (grinding vs velocity)
• Range of motion ( quarter squat vs full )
• Rest before the set, sleep, caffeine
• Belt, wraps, shoes, monolift vs walkout

They see two numbers you typed.

Epley: the linear rep penalty

Epley (1985) is the common gym form:

1RM ≈ w × (1 + r/30)

Default w = 100 kg, r = 5:

1RM = 100 × (1 + 5/30) = 100 × 1.1667 = 116.67 kg

Interpretation baked into the formula: each rep adds 1/30 of the weight to the estimated max. It is simple, monotonic, and never singular for sane rep counts.

Epley tends to sit higher than Brzycki in the 3–10 rep range you actually use for estimates. DevOkk uses Epley as primary for the percent table because it is stable and widely printed on whiteboards - not because it won a universal accuracy contest.

Brzycki: the reciprocal curve

Brzycki:

1RM ≈ w × 36 / (37 − r)

Same default:

1RM = 100 × 36 / (37 − 5) = 3600 / 32 = 112.50 kg

4.17 kg lower than Epley at five reps - typical of the pair.

The denominator (37 − r) explodes as r → 37. At r = 36, you divide by 1 - nonsense territory. At r = 37, division by zero. That is why DevOkk enforces r ≤ 12. Even at 12 reps, muscular endurance and cardiovascular fatigue dominate; the curve is extrapolating far from maximal strength.

Brzycki often underestimates compared to Epley for moderate reps on bench and squat in some studies; for other lifts the gap shrinks. Treat the pair as bounds, not prophecy.

Other formulas you will hear about

Gym culture also cites Lombardi (w × r^0.1), Lander, Mayhew bench-specific, O'Conner, and Wathan. They were fit on different samples (college football, bench-only, etc.). Switching formulas until you like the higher 1RM is grade shopping.

DevOkk shows Epley + Brzycki so you see sensitivity without pretending one meta-analysis crowned a king. If your coach's spreadsheet uses Brzycki only, match the coach - consistency beats brand loyalty.

Submaximal sets: what "5 reps" must mean

Estimates assume the set was hard:

• RPE 9–10 or 0–2 reps in reserve for strength-focused lifters
• Not a warm-up set of five easy reps at 60%
• Not five reps stopped because form broke on rep 3

A 100 kg × 5 at RPE 6 might truly be a 120+ kg max. Typing it into Epley still prints 116.67 because the formula cannot hear your breathing.

Rep speed matters. Velocity-based training uses different math entirely. Submax formulas were not built for tempo 4-0-4 hypertrophy sets with 90 s rest.

The rep cap at 12

DevOkk rejects r > 12 with an explicit error. Reasons:

1. Brzycki stability - denominator still large at 12 (25), but beyond that the model was never meant for high reps.
2. Physiology - a set of 15+ at moderate load is endurance, not a window into maximal force production.
3. Error growth - published RMSE for any formula widens as reps increase.

If your best set is 100 kg × 15, the honest move is test a heavier triple or single with safety, not extrapolate from 15.

Not for beginners with bad form

Beginners gain strength from neuromuscular learning faster than formulas predict. A month of technique work can add kilos without a true max test.

More importantly: maximal loads magnify form faults. A beginner estimating 1RM from a bouncy bench or a high squat may plan 90% loads that injure when attempted.

Use the calculator when:

• You have stable technique on the lift
• The set was near maximal within rep range
• You want programming anchors (5×5, 3×3, backoff sets)

Avoid when:

• You are week one in the gym
• Pain, not fatigue, stopped the set
• The lift was on a machine you cannot replicate free-weight

None of that is a moral judgment. It is signal quality.

Programming with %1RM

After Epley 1RM 116.67 kg, DevOkk prints:

%1RM	Load (kg)
95%	110.83
90%	105.00
85%	99.17
80%	93.33
75%	87.50
70%	81.67

Classic templates map to these rows:

• Strength: 5×5 @ ~80% (93.33 kg in the default story)
• Power: 3×3 @ ~85–90%
• Hypertrophy: 3×8–12 @ ~65–75% (below the printed table - calculate or extend)

Percent programs assume you update the anchor when the set that produced the estimate improves. If 100×5 becomes 100×6 at the same RPE, re-run the calculator. Stale 1RMs produce stale "90%."

Daily undulating periodization mixes percents within a week. The table is a reference, not a calendar.

Units: kg vs lb

Toggle kg or lb on the page. The formulas are unit-agnostic if weight and output share units. 220 lb × 5 is not the default 100 kg × 5 - do not mix unit stories when comparing to this article's numbers.

Percent loads scale linearly; rounding to 2.5 lb or 1.25 kg plates matters on the platform.

What formulas ignore

Exercise selection: deadlift 1RM ≠ squat 1RM. One calculator page does not know which lift you typed.

Equipment: Smith machine, trap bar, and axle bar change true max vs straight bar.

Eccentric loading, bands/chains, partial ROM - all off-model.

Fatigue across the session: the estimate set should be fresh, not after five prior exercises.

Age and sex: regressions pooled mixed cohorts; they do not auto-adjust for masters lifters or adolescents. Youth max testing has policy guidance from sports medicine groups - not covered here.

Tie-in: nutrition estimates are also not prescriptions

Heavy training increases protein needs versus sedentary life, but grams from Protein Calculator are ranges from weight and activity, not a blood test and not renal clearance. Macro Calculator splits energy if you already have a calorie target from Calorie Calculator / BMR vs TDEE. None of it replaces a dietitian.

BMI screens weight vs height, not strength: Why BMI is not a diagnosis.

Safety culture the page cannot enforce

DevOkk will not:

• Provide a spotter
• Stop you from attempting a true max alone
• Judge depth on video
• Clear you post-injury

If shoulder pain appears at 80% of an estimated max, the estimate is irrelevant. Stop and get evaluated.

Worked comparison at different reps

Same 100 kg weight, Epley vs Brzycki:

Reps	Epley (kg)	Brzycki (kg)
1	103.33	100.00
3	110.00	106.45
5	116.67	112.50
8	126.67	120.00
10	133.33	125.81
12	140.00	131.03

Gap widens with reps - another reason the cap exists.

At 1 rep, Epley gives 103.33 from 100 kg - implying a single at 100 was not maximal. Many coaches treat r = 1 as "just use the weight." DevOkk allows r = 1; interpret carefully.

Privacy

Weight and reps run in the browser. localStorage may hold drafts 30 days on device. No account. Not uploaded to compute the formulas.

Honest workflow

1. Perform a controlled set (e.g., 5 reps, 1–2 RIR) with safe technique.
2. Enter load and reps on One-Rep Max Calculator.
3. Read both Epley and Brzycki; note the spread.
4. Program using Epley percents if you want to match DevOkk's table - or pick Brzycki if your coach does.
5. Re-estimate when the anchor set improves; do not hero a true max to feed the form.

The barbell still wins on meet day. The calculator wins on Tuesday when you need 93 kg for "80%" without loading 116 on your spine.