How it works

An estimated 1RM that knows how hard you pushed

Standard one-rep-max formulas assume every set went to failure at a normal speed. Iron Diary corrects for effort and tempo first, so the same weight × reps reads as strong as it really was.

The formula

A plain formula like Epley turns weight × reps straight into a 1RM. Iron Diary normalizes the set first — to what it would have been at failure (RPE 10) and at a normal tempo (1010) — then applies Epley:

1. Effort → reps to failure
   rrpe = reps + (10 − RPE)

2. Tempo → weighted slowness, in seconds beyond 1010
   S = 1.0 · max(0, eccentric − 1)
     + 1.5 · bottom pause
     + 2.0 · max(0, concentric − 1)
     + 0.5 · top pause

3. Slowness → extra reps (saturating)
   bonus = 0.51 · (1 − e−S / 2)

4. Reps at RPE 10 and tempo 1010
   requiv = rrpe · (1 + bonus)

5. Epley
   e1RM = weight · (1 + requiv / 30)

Tempo is the standard four digits — [eccentric][bottom pause][concentric][top pause] in seconds, with X for an explosive concentric. So 31X0 is a 3-second lower, a 1-second pause at the bottom, an explosive press, and no pause at the top.

The constants

Effort: reps you had left

Every rep-max formula is really a reps-to-failure curve. Feed it a set you stopped short of failure and it under-reads you. On the resistance-training RPE scale, reps in reserve = 10 − RPE, so a set of 225 × 5 at RPE 8 had two reps left: it was a 7-rep-max effort at 225. Iron Diary adds those reps back before estimating.

A plain formula scores all three as 263 lb.

Tempo: how you moved the weight

A slow negative, a dead-stop pause, or a deliberately slow lift all cut the load and reps you can manage, so a tempo set understates your normal-tempo strength. How much depends on the phase:

• Concentric (2.0) — the phase where you fail. Slowing the lift itself is the most rep-costly thing you can do.
• Bottom pause (1.5) — a stop in the stretched position kills the rebound and forces you to restart from the worst leverage.
• Eccentric (1.0) — the anchor, and the one phase with a direct 1RM measurement (Wilk et al., 2020). A slow negative pre-fatigues you and removes the bounce.
• Top pause (0.5) — usually near lockout, where you can rest; the cheapest.

The effect levels off. Doubling how slow a set is doesn’t double the effect — you’re already fatigue-limited — so the tempo bonus follows a saturating curve capped at +51% reps rather than a straight line. Wilk’s data shows the same plateau: going from an 8-second to a 10-second eccentric barely moved the 1RM.

Effort first, then tempo. The reps you had in reserve are tempo-adjusted too, because your full capacity at that load and tempo — reps done plus reps left — is what maps to normal-tempo reps.

Worked examples

Each row shows both steps: add the reps in reserve (@ RPE 10), then the tempo reps (@ RPE 10 and 1010), then Epley.

Research basis

The structure comes from published work. The exact size of the tempo effect for everyday training is calibrated from experience — see the note below the list.

• Epley formula — Epley, B. (1985). Poundage Chart. Boyd Epley Workout, Lincoln, NE.
• RPE → reps in reserve — Zourdos, M. C., et al. (2016). Novel resistance training–specific rating of perceived exertion scale measuring repetitions in reserve. J Strength Cond Res, 30(1), 267–275.
• Tempo → 1RM — Wilk, M., et al. (2020). The effects of movement tempo on the one-repetition maximum bench press results. Journal of Human Kinetics. 1RM fell about 5.8% at a 5-second eccentric, 11.4% at 8 s, and 12.4% at 10 s versus ~2 s — the eccentric anchor, and the evidence the effect plateaus.
• Tempo → max reps — LaChance, P. F., & Hortobagyi, T. (1994). Influence of cadence on muscular performance during push-up and pull-up exercise. J Strength Cond Res, 8(2), 76–79.
• Concentric speed → reps — Sakamoto, A., & Sinclair, P. J. (2006). Effect of movement velocity on the relationship between training load and the number of repetitions of bench press. J Strength Cond Res, 20(3), 523–527.
• Reps ↔ %1RM — Nuzzo, J. L., et al. (2024). Maximal number of repetitions at percentages of the one repetition maximum. Sports Medicine.

Limitations

• RPE is the exercise’s target, not measured per set. Iron Diary records target RPE per exercise, and it applies to every working set that day. If you routinely over- or under-shoot your target, estimates skew with you. No RPE logged means RPE 10 — no inflation.
• Phase weights beyond the eccentric are reasoned, not individually measured.
• The tempo research is bench-press-specific; one tempo model is applied to every exercise as a first approximation.
• Bounced reps (a 0 eccentric) aren’t penalized, so they’re slightly over-credited.
• Epley loses accuracy at very high reps — true of any rep-max formula.

Warm-up sets are left out, and the chart plots one point per workout: the best estimate across that session’s working sets.