# Work & Power Calculator

> Computes the mechanical work done by a constant force over a displacement, allowing for the angle between force and motion, and the average power when the duration is supplied.

- Calculator id: `work-power` · Category: Physics (`physics`) · Tool name: `calculate_work_and_power`
- Canonical page: https://tttkmbb.com/physics/work-power · This document: https://tttkmbb.com/physics/work-power.md · JSON definition: https://tttkmbb.com/physics/work-power.json

## Purpose

Computes the mechanical work done by a constant force over a displacement, allowing for the angle between force and motion, and the average power when the duration is supplied.

**Use when:** You know a constant force, the distance it acts over (optionally the angle and the time taken) and need the work in joules or the average power in watts, kilowatts or horsepower.

**Do not use when:** The force varies with position (for springs use hookes-law), you need electrical power from volts and amps (use electric-power), or you need energy of motion (use kinetic-energy).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `force_n` | number | N | required | Magnitude of the constant force in newtons (weight = mass × 9.80665). (min 0) |
| `distance_m` | number | m | required | Displacement of the point of application in metres. (min 0) |
| `angle_degrees` | number | ° | optional, default 0 | 0° when the force acts along the motion; 90° gives zero work; more than 90° gives negative work (e.g. friction). (min 0, max 180) |
| `time_s` | number | s | optional | Optional duration over which the work is done; enables the power outputs. (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `work_j` | number | J | W = F × d × cos θ. |
| `work_kj` | number | kJ | Work in kilojoules. |
| `work_kwh` | number | kWh | Work in kilowatt-hours. |
| `power_w` | number | W | P = W / t (only when time_s is given). |
| `power_kw` | number | kW | Power in kilowatts (only when time_s is given). |
| `power_hp` | number | hp | Power in mechanical horsepower, 1 hp = 745.69987 W (only when time_s is given). |

## Formula

`work_j = force_n × distance_m × cos(angle_degrees); power_w = work_j / time_s; power_hp = power_w / 745.69987`

## Data Sources

- Wikipedia – Work (physics) — https://en.wikipedia.org/wiki/Work_(physics) (reference, retrieved 2026-09-23)
- Wikipedia – Power (physics) — https://en.wikipedia.org/wiki/Power_(physics) (reference, retrieved 2026-09-23)
- 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 2026-09-23)

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/work-power?force_n=…&distance_m=…`
- `POST https://tttkmbb.com/api/v1/calculate/work-power` 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/work-power · OpenAPI operationId `calculate_work_and_power` 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": "work-power", "inputs": {…}}`

## Example

- 50 N over 10 m in 4 s: inputs `{"force_n":50,"distance_m":10,"time_s":4}` → `{"work_j":500,"work_kj":0.5,"power_w":125,"power_kw":0.125,"power_hp":0.1676}`
- 100 N at 60° over 20 m: inputs `{"force_n":100,"distance_m":20,"angle_degrees":60}` → `{"work_j":1000,"work_kj":1}`

```
GET https://tttkmbb.com/api/v1/calculate/work-power?force_n=50&distance_m=10&time_s=4
```

## Limitations

The force varies with position (for springs use hookes-law), you need electrical power from volts and amps (use electric-power), or you need energy of motion (use kinetic-energy). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why is the work zero at 90°?**

Only the force component along the displacement does work; a force perpendicular to the motion (like the normal force on a sliding block) transfers no energy.

**Which horsepower is used?**

Mechanical (imperial) horsepower, 745.69987 W. Metric horsepower (PS) is 735.49875 W, about 1.4 % smaller.

## Related

- [Kinetic Energy Calculator](https://tttkmbb.com/physics/kinetic-energy.md) — Net work equals the change in kinetic energy.
- [Electric Power Calculator](https://tttkmbb.com/physics/electric-power.md) — Electrical power from voltage and current.
- [Force Calculator](https://tttkmbb.com/physics/newtons-second-law.md) — Get the force from mass and acceleration.