# One-Rep Max Calculator

> Estimates the one-repetition maximum from a weight lifted for 2–12 repetitions using the Epley, Brzycki and Lombardi equations, reports their average, and lists training loads at 95 % to 70 % of that 1RM.

- Calculator id: `one-rep-max` · Category: Sports & Fitness (`fitness`) · Tool name: `estimate_one_rep_max`
- Canonical page: https://tttkmbb.com/fitness/one-rep-max · This document: https://tttkmbb.com/fitness/one-rep-max.md · JSON definition: https://tttkmbb.com/fitness/one-rep-max.json

## Purpose

Estimates the one-repetition maximum from a weight lifted for 2–12 repetitions using the Epley, Brzycki and Lombardi equations, reports their average, and lists training loads at 95 % to 70 % of that 1RM.

**Use when:** You want to estimate maximal strength or program training percentages without attempting a true single-rep maximum.

**Do not use when:** The set was more than 12 repetitions (prediction error grows quickly) or was not taken close to failure; use a heavier, lower-rep set instead.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `weight_lifted` | number | kg or lb | required | Load lifted for the set, in any unit; outputs use the same unit. (> 0, max 2000) |
| `reps` | integer | reps | required | Repetitions completed with that load, ideally to (near) failure. (min 2, max 12) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `one_rep_max` | number |  | Mean of the Epley, Brzycki and Lombardi estimates, in the unit of weight_lifted. |
| `epley` | number |  | 1RM = w × (1 + reps / 30). |
| `brzycki` | number |  | 1RM = w × 36 / (37 − reps). |
| `lombardi` | number |  | 1RM = w × reps^0.10. |
| `percentages` | list |  | Load at 95, 90, 85, 80, 75 and 70 % of the averaged 1RM. |

## Formula

`Epley: 1RM = w × (1 + reps/30); Brzycki: 1RM = w × 36 / (37 − reps); Lombardi: 1RM = w × reps^0.10; one_rep_max = (Epley + Brzycki + Lombardi) / 3; load_p = one_rep_max × p / 100`

The equations agree within about 2 % for 2–6 reps and Epley and Brzycki coincide at 10 reps; beyond that Brzycki rises fastest and Lombardi stays lowest, so estimates diverge. Percentages use the averaged estimate.

## Data Sources

- Reynolds JM, Gordon TJ, Robergs RA (2006) Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry, J Strength Cond Res 20:584-592 — https://pubmed.ncbi.nlm.nih.gov/16937972/ (peer_reviewed, retrieved 2026-09-23)
- Wikipedia – One-repetition maximum (formula collection with original citations: Epley 1985, Brzycki 1993, Lombardi 1989) — https://en.wikipedia.org/wiki/One-repetition_maximum (reference, retrieved 2026-09-23)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/one-rep-max?weight_lifted=…&reps=…`
- `POST https://tttkmbb.com/api/v1/calculate/one-rep-max` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/one-rep-max · OpenAPI operationId `estimate_one_rep_max` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "one-rep-max", "inputs": {…}}`

## Example

- 100 kg × 5 reps: inputs `{"weight_lifted":100,"reps":5}` → `{"epley":116.7,"brzycki":112.5,"lombardi":117.5,"one_rep_max":115.5,"percentages":[{"percent":95,"load":109.8},{"percent":90,"load":104},{"percent":85,"load":98.2},{"percent":80,"load":92.4},{"percent":75,"load":86.7},{"percent":70,"load":80.9}]}`
- 60 kg × 10 reps: inputs `{"weight_lifted":60,"reps":10}` → `{"epley":80,"brzycki":80,"lombardi":75.5,"one_rep_max":78.5}`

```
GET https://tttkmbb.com/api/v1/calculate/one-rep-max?weight_lifted=100&reps=5
```

## Limitations

The set was more than 12 repetitions (prediction error grows quickly) or was not taken close to failure; use a heavier, lower-rep set instead. The equations agree within about 2 % for 2–6 reps and Epley and Brzycki coincide at 10 reps; beyond that Brzycki rises fastest and Lombardi stays lowest, so estimates diverge. Percentages use the averaged estimate. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Which formula is best?**

For 2–6 reps they agree closely; Brzycki is widely used in the USA for bench press, Epley for squat and deadlift. Averaging reduces the influence of any one equation's bias.

**Can I use pounds?**

Yes. The equations are unit-free: enter pounds and every output is in pounds.

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