# One-Rep-Max & Plate Loader

> 1RM from any set (7 formulas + average), % and RPE tables, and which plates to load. Estimates your one-repetition maximum from the weight and reps of a set to failure (or with an RPE) with the Epley, Brzycki, Lander, Lombardi, Mayhew, O'Conner and Wathan equations and their average, prints a percentage table and an RPE table, and tells you which plates to put on each side of a kg or lb bar using only the plates you actually have.

Part of usefulweb.site (https://usefulweb.site/). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://onerepmaxcalculator.usefulweb.site/ (interactive tool at https://onerepmaxcalculator.usefulweb.site/tool)
- JSON API: POST https://onerepmaxcalculator.usefulweb.site/api/v1/calculate with a JSON object of inputs (schema: https://onerepmaxcalculator.usefulweb.site/api/v1/tool)
- OpenAPI: https://onerepmaxcalculator.usefulweb.site/openapi.json
- MCP (Streamable HTTP): https://onerepmaxcalculator.usefulweb.site/mcp - tool `one_rep_max_calculator`

## Inputs
- weight (number, required): Weight lifted
- reps (integer, required): Repetitions - Reps completed in the set. Estimates are most reliable up to about 10 reps.
- unit (select): Unit
- rpe (number): RPE of the set - Optional (6–10). 10 = to failure; 8 = two more reps were possible. Reps in reserve are added before estimating.
- targetWeight (number): Weight to load - Optional total bar weight for the plate loader.
- targetPercent (number): Or: percentage of 1RM to load - Used when no weight to load is given; default 100% of the average estimate.
- barWeight (number): Bar weight - Default 20 kg or 45 lb.
- collarWeight (number): Collars (both together)
- plates (table): Plates available - Plate weight and how many you have in total (both sides). Empty = a standard set (kg: 25–1.25, lb: 45–2.5).

## Method
- Seven published equations estimate the 1RM from the weight w and repetitions r to failure, as tabulated by LeSuer et al. (1997): Epley w(1 + 0.0333r); Brzycki 100w/(102.78 − 2.78r); Lander 100w/(101.3 − 2.67123r); Lombardi w·r^0.10; Mayhew 100w/(52.2 + 41.9e^(−0.055r)); O'Conner w(1 + 0.025r); Wathan 100w/(48.8 + 53.8e^(−0.075r)). The average of all seven is the headline estimate.
- With 1 rep (and no RPE) the 1RM is the weight lifted.
- RPE: reps in reserve = 10 − RPE are added to the reps (e.g. 5 reps at RPE 8 count as 7 reps to failure). The RPE table uses the same idea with the Epley relation %1RM = 1 ÷ (1 + 0.0333 × (reps + 10 − RPE)); it is derived, not a copy of a published RPE chart.
- Percentage table: weight = % × average 1RM; the approximate reps at each percentage invert the Epley equation: reps = (1/% − 1) ÷ 0.0333.
- Plate loader: per side = (target − bar − collars) ÷ 2. Plates are taken heaviest first (greedy) from the pairs you have; if that misses but an exact combination exists (possible with unusual plate sets), an exact subset-sum search finds the combination with the fewest plates. If the weight cannot be loaded exactly, the nearest loadable weights below and above are shown.