What is a One‑Rep Max (1RM) and how do these formulas work?

Your one‑rep max (often written as 1RM) is the maximum weight you can lift for one repetition with proper form. It’s the number people use to compare strength (“My bench is 225”), but it’s also a very practical programming tool. Many training plans prescribe intensity as a percentage of your 1RM: for example, “5 sets of 5 at 75%” or “3 singles at 90%.”

The challenge is that a true 1RM test can be fatiguing, time‑consuming, and sometimes risky—especially if you’re not used to heavy singles, you don’t have a spotter, or your technique changes under maximal effort. That’s why lifters often use submaximal sets (like 185 × 5) and apply a formula to estimate what a single might be. These formulas all share the same idea: as reps increase, the weight you can lift decreases. If we model that relationship, we can reverse it: given weight and reps, estimate the max.

• Weight lifted: the load on the bar (or the dumbbell, machine, etc.).
• Reps completed: how many clean reps you performed at that weight.
• Formula choice: different researchers and coaches fit the rep‑to‑max curve differently.

Different formulas behave differently as reps rise. Some are very similar from 2–6 reps and diverge more at 10–12+. For most people, the best approach is not to argue about which one is “the” correct formula, but to use a formula consistently and refine with real‑world feedback. That’s why this calculator includes an Average option that blends several popular models. It tends to behave conservatively at higher reps while staying realistic for typical strength sets.

• Epley: 1RM = W × (1 + R/30). Very common, simple, and works well for moderate reps.
• Brzycki: 1RM = W × 36 / (37 − R). Often slightly more conservative above ~8 reps.
• Lombardi: 1RM = W × R^0.10. Uses a power relationship; can be higher for some rep ranges.
• Mayhew: 1RM = 100W / (52.2 + 41.9 e^(−0.055R)). A curve‑fit model used in some testing contexts.
• O’Conner: 1RM = W × (1 + R/40). Similar to Epley but slightly less aggressive per rep.
• Wathan: 1RM = 100W / (48.8 + 53.8 e^(−0.075R)). Another curve‑fit model that often sits mid‑range.

Even if you know your true 1RM, many systems (especially strength‑focused ones) use a Training Max, commonly 90% of 1RM, to reduce fatigue and keep bar speed crisp. Think of TM as a “confidence max”: it’s heavy enough to anchor percentages but light enough that you can hit prescribed sets on your average day. This calculator lets you pick 85–95% (or 100% if you want the raw estimate).

Worked examples (with practical interpretation)

Here are a few common scenarios so you can sanity‑check your result and decide how to use it in training. (Numbers are rounded to the nearest 0.5 unit.)

Suppose you benched 185 lb for 5 reps. Using Epley:
1RM = 185 × (1 + 5/30) = 185 × 1.1667 ≈ 216 lb. Brzycki gives a similar answer. If you choose Average, you’ll typically land in the same ballpark. A practical Training Max at 90% would be about 194 lb.

Ten reps adds more fatigue, so formulas diverge more. Epley: 1RM = 100 × (1 + 10/30) = 133.3 kg. Brzycki: 100 × 36 / 27 ≈ 133.3 kg (same here). Others may be slightly higher or lower. This is why, if your set was a true grind, 10‑rep estimates can still be useful—but treat them as “directional,” not absolute truth.

Low reps tend to be more stable. Epley: 315 × (1 + 3/30) = 346.5 lb. A 90% TM would be about 312 lb, which conveniently matches your working set weight—this is a common pattern when you’re lifting in a sensible, sustainable intensity zone.

• 50–60%: warmups, technique practice, easy volume, recovery days.
• 65–75%: hypertrophy‑style sets (6–12 reps) for many lifters.
• 80–85%: strength building (3–6 reps), heavier practice, lower volume.
• 90–95%: heavy singles/doubles, peaking work, “test prep” intensity.

Step‑by‑step: what this calculator is doing behind the scenes

This tool takes your inputs and computes one or more estimated 1RMs. If you pick a specific formula, it shows that formula’s estimate. If you pick Average, it calculates each formula, drops anything that looks mathematically invalid for your rep range, and then averages the remaining values. That approach reduces “formula whiplash” and usually produces a sensible number across a wider variety of lifters.

• Reps must be ≥ 1. If you did 1 rep, your 1RM is the weight you entered.
• Best range is 2–10 reps. Above that, the estimate becomes more sensitive to endurance.
• Negative or zero weight is rejected (because physics).

The calculator rounds to the nearest 0.5 unit. That’s a practical compromise: it fits both plates and common gym increments, while still feeling “precise enough” for planning.

If you’re actually going to attempt a new max, yes—especially for bench press. This calculator is designed to help you estimate and program so you can progress safely. Use it to choose reasonable jumps and to avoid the classic trap of “feeling strong today” and adding too much too fast.

Frequently Asked Questions

• Which 1RM formula is best?

  For most people, there isn’t one perfect formula. If your reps are between 2–6, most formulas cluster closely. If your reps are 8–12, results spread out more. That’s why the Average option is a solid default: it smooths out extremes and keeps your plan realistic.

• Can I use this for dumbbells or machines?

  Yes, as a rough estimate. But machines have different resistance curves and dumbbells can be limited by stability. Treat your estimate as exercise‑specific—your dumbbell press 1RM estimate won’t map perfectly to barbell bench, for example.

• My estimate feels low or high—what happened?

  Two common reasons: (1) the set wasn’t near failure (you had many reps in reserve), which makes the estimate look low, or (2) the set was very high‑rep and limited by conditioning rather than strength, which can distort the curve. Try another set in the 3–8 rep range or use a heavier day to calibrate.

• Should I train at 100% of 1RM?

  Usually no. Most programs use 85–95% occasionally and spend much more time below that. Heavy singles are a tool, not the whole toolbox. A Training Max (like 90%) helps you progress without burning out.

• What’s the difference between 1RM and Training Max?

  1RM is your best possible single on a great day. Training Max is a slightly reduced “programming anchor” that helps you hit your planned sets more reliably across normal days. Many lifters get stronger faster using a TM, because they can recover and accumulate quality volume.

• Is the calculator accurate for 12–15 reps?

  It can be directionally helpful, but it’s less reliable. Endurance, pacing, and mental tolerance matter more as reps climb. If you care about accuracy, do a lower‑rep set or a single‑rep test with proper warmups and safety.