# Force Calculator

> Computes net force from mass and acceleration with Newton's second law, reported in newtons, kilonewtons and pounds-force, together with the object's weight under standard gravity.

- Calculator id: `newtons-second-law` · Category: Physics (`physics`) · Tool name: `calculate_force`
- Canonical page: https://tttkmbb.com/physics/newtons-second-law · This document: https://tttkmbb.com/physics/newtons-second-law.md · JSON definition: https://tttkmbb.com/physics/newtons-second-law.json

## Purpose

Computes net force from mass and acceleration with Newton's second law, reported in newtons, kilonewtons and pounds-force, together with the object's weight under standard gravity.

**Use when:** You know a mass and its acceleration (or deceleration) and need the net force, or you need an object's weight in newtons or pounds-force from its mass.

**Do not use when:** You need the gravitational pull between two bodies (use gravitational-force), a spring force (use hookes-law) or the force in circular motion (use centripetal-force).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `mass_kg` | number | kg | required | Mass of the object in kilograms. (> 0) |
| `acceleration_m_s2` | number | m/s² | required | Acceleration of the mass; negative for deceleration. Use 9.80665 for the force needed to hold the object against gravity. |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `force_n` | number | N | Net force F = m·a. |
| `force_kn` | number | kN | Force in kilonewtons. |
| `force_lbf` | number | lbf | Force in pounds-force (1 lbf = 4.4482216152605 N). |
| `weight_n` | number | N | Weight of the mass under standard gravity: m × 9.80665. |
| `weight_lbf` | number | lbf | Weight in pounds-force. |

## Formula

`force_n = mass_kg × acceleration_m_s2; weight_n = mass_kg × 9.80665; force_lbf = force_n / 4.4482216152605; force_kn = force_n / 1000`

## Data Sources

- HyperPhysics – Newton's laws — http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html (reference, retrieved 2026-09-23)
- NIST CODATA – standard acceleration of gravity g_n = 9.80665 m/s² — https://physics.nist.gov/cgi-bin/cuu/Value?gn (standard, 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/newtons-second-law?mass_kg=…&acceleration_m_s2=…`
- `POST https://tttkmbb.com/api/v1/calculate/newtons-second-law` 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/newtons-second-law · OpenAPI operationId `calculate_force` 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": "newtons-second-law", "inputs": {…}}`

## Example

- 1200 kg car accelerating at 3 m/s²: inputs `{"mass_kg":1200,"acceleration_m_s2":3}` → `{"force_n":3600,"force_kn":3.6,"force_lbf":809.3122,"weight_n":11767.98}`
- 0.145 kg baseball at 2000 m/s²: inputs `{"mass_kg":0.145,"acceleration_m_s2":2000}` → `{"force_n":290,"weight_n":1.422}`

```
GET https://tttkmbb.com/api/v1/calculate/newtons-second-law?mass_kg=1200&acceleration_m_s2=3
```

## Limitations

You need the gravitational pull between two bodies (use gravitational-force), a spring force (use hookes-law) or the force in circular motion (use centripetal-force). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**What is the difference between mass and weight?**

Mass (kg) is the amount of matter; weight is the gravitational force on it, W = m·g, measured in newtons. A 1 kg mass weighs 9.80665 N on Earth and about 1.62 N on the Moon.

**Is the force the net force?**

Yes. F = m·a gives the resultant of all forces; individual forces such as friction or thrust must be combined with vector addition to obtain a.

## Related

- [Acceleration Calculator](https://tttkmbb.com/physics/acceleration.md) — Get acceleration from velocities and time first.
- [Gravitational Force Calculator](https://tttkmbb.com/physics/gravitational-force.md) — Force between two masses by Newton's law of gravitation.
- [Pressure Calculator](https://tttkmbb.com/physics/pressure-force-area.md) — Divide a force by area to get pressure.