# Horsepower, Torque and RPM Calculator

> Solves the rotational power relation for whichever of power, torque or rotational speed is missing (HP = torque_lb_ft × rpm / 5252; kW = torque_nm × rpm / 9549) and reports the results in hp, PS, kW, lb·ft and N·m.

- Calculator id: `horsepower-torque-rpm` · Category: Engineering & Automotive (`engineering`) · Tool name: `solve_horsepower_torque_rpm`
- Canonical page: https://tttkmbb.com/engineering/horsepower-torque-rpm · This document: https://tttkmbb.com/engineering/horsepower-torque-rpm.md · JSON definition: https://tttkmbb.com/engineering/horsepower-torque-rpm.json

## Purpose

Solves the rotational power relation for whichever of power, torque or rotational speed is missing (HP = torque_lb_ft × rpm / 5252; kW = torque_nm × rpm / 9549) and reports the results in hp, PS, kW, lb·ft and N·m.

**Use when:** You know two of engine/motor power, torque and rpm (from a dyno sheet or a datasheet) and need the third, or want to convert a torque-at-rpm figure to horsepower.

**Do not use when:** You only need a unit conversion of power (use power) or torque (use torque) without rpm, or you need road speed from rpm (use gear-ratio-speed).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `power_hp` | number | hp | optional | Mechanical horsepower (1 hp = 745.7 W). Give power as power_hp or power_kw, not both. (> 0) |
| `power_kw` | number | kW | optional | Power in kilowatts. Give power as power_hp or power_kw, not both. (> 0) |
| `torque_lb_ft` | number | lb·ft | optional | Torque in pound-feet (1 lb·ft = 1.3558 N·m). Give torque as torque_lb_ft or torque_nm, not both. (> 0) |
| `torque_nm` | number | N·m | optional | Torque in newton-metres. Give torque as torque_lb_ft or torque_nm, not both. (> 0) |
| `rpm` | number | rpm | optional | Revolutions per minute at which the torque or power applies. Omit to solve for it. (> 0, max 1000000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `solved_for` | string |  | power, torque or rpm. |
| `power_hp` | number | hp | Mechanical horsepower. |
| `power_ps` | number | PS | Metric horsepower (1 PS = 735.5 W). |
| `power_kw` | number | kW | Power in kilowatts. |
| `torque_lb_ft` | number | lb·ft | Torque in pound-feet. |
| `torque_nm` | number | N·m | Torque in newton-metres. |
| `rpm` | number | rpm | Revolutions per minute. |
| `angular_speed_rad_s` | number | rad/s | ω = 2π × rpm / 60. |

## Formula

`P_W = torque_nm × rpm × 2π / 60; power_hp = torque_lb_ft × rpm / 5252.113; power_kw = torque_nm × rpm / 9549.297; torque = P / ω; rpm = P × 60 / (2π × torque)`

Uses the exact constants 33,000 ft·lbf/min per hp (so 5252.113 = 33,000 / 2π) and 1 hp = 745.69987 W; the familiar rounded 5252 gives results within 0.003 %. Torque and power curves cross at 5252 rpm when plotted in lb·ft and hp.

## Data Sources

- Wikipedia – Horsepower – relationship with torque — https://en.wikipedia.org/wiki/Horsepower#Relationship_with_torque (reference, retrieved 2026-09-24)
- NIST Special Publication 811 – Guide for the Use of the SI, Appendix B (conversion factors) — https://www.nist.gov/pml/special-publication-811 (standard, retrieved 2026-09-24)

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/horsepower-torque-rpm?`
- `POST https://tttkmbb.com/api/v1/calculate/horsepower-torque-rpm` 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/horsepower-torque-rpm · OpenAPI operationId `solve_horsepower_torque_rpm` 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": "horsepower-torque-rpm", "inputs": {…}}`

## Example

- 300 lb·ft at 5252 rpm: inputs `{"torque_lb_ft":300,"rpm":5252}` → `{"solved_for":"power","power_hp":300,"power_kw":223.705,"torque_nm":406.75,"angular_speed_rad_s":549.9853}`
- Torque of 100 kW at 3000 rpm: inputs `{"power_kw":100,"rpm":3000}` → `{"solved_for":"torque","torque_nm":318.31,"torque_lb_ft":234.77,"power_hp":134.1,"power_ps":135.96}`

```
GET https://tttkmbb.com/api/v1/calculate/horsepower-torque-rpm?torque_lb_ft=300&rpm=5252
```

## Limitations

You only need a unit conversion of power (use power) or torque (use torque) without rpm, or you need road speed from rpm (use gear-ratio-speed). Uses the exact constants 33,000 ft·lbf/min per hp (so 5252.113 = 33,000 / 2π) and 1 hp = 745.69987 W; the familiar rounded 5252 gives results within 0.003 %. Torque and power curves cross at 5252 rpm when plotted in lb·ft and hp. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why do horsepower and torque curves cross at 5252 rpm?**

Because hp = lb·ft × rpm / 5252: at exactly 5252 rpm the two numbers are equal. In metric units (kW and N·m) the crossing is at 9549 rpm.

**Which horsepower is this?**

Mechanical (imperial) horsepower, 745.7 W. Metric PS (735.5 W) is also reported; electrical (746 W) and boiler horsepower are different units.

## Related

- [Torque Converter](https://tttkmbb.com/conversion/torque.md) — Convert torque between N·m, lb·ft and kgf·m.
- [Power Converter](https://tttkmbb.com/conversion/power.md) — Convert power between W, kW, hp and PS.
- [Gear Ratio and Speed Calculator](https://tttkmbb.com/engineering/gear-ratio-speed.md) — Road speed at a given engine rpm.