# Acceleration Calculator

> Computes average acceleration from initial velocity, final velocity and elapsed time, plus the velocity change, the distance covered assuming constant acceleration, and the acceleration expressed in g.

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

## Purpose

Computes average acceleration from initial velocity, final velocity and elapsed time, plus the velocity change, the distance covered assuming constant acceleration, and the acceleration expressed in g.

**Use when:** You have start and end velocities over a known time interval and need the acceleration or deceleration, or the distance covered while changing speed uniformly (0–100 km/h times, braking).

**Do not use when:** You know the net force and mass instead of velocities (use force), the motion is vertical under gravity alone (use free-fall), or you only need speed from distance and time (use speed-distance-time).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `initial_velocity_m_s` | number | m/s | optional, default 0 | Velocity at the start of the interval; 0 when starting from rest (km/h ÷ 3.6). |
| `final_velocity_m_s` | number | m/s | required | Velocity at the end of the interval; use 0 for coming to a stop. |
| `time_s` | number | s | required | Duration of the velocity change in seconds. (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `acceleration_m_s2` | number | m/s² | Average acceleration; negative values mean deceleration. |
| `acceleration_g` | number | g | Acceleration as a multiple of standard gravity (÷ 9.80665). |
| `velocity_change_m_s` | number | m/s | final_velocity − initial_velocity. |
| `distance_m` | number | m | Displacement during the interval for constant acceleration: (u + v) / 2 × t. |

## Formula

`a = (final_velocity_m_s − initial_velocity_m_s) / time_s; acceleration_g = a / 9.80665; distance_m = (initial_velocity_m_s + final_velocity_m_s) / 2 × time_s`

Assumes constant acceleration over the interval; for varying acceleration the result is the average acceleration and the distance is approximate.

## Data Sources

- HyperPhysics – Motion equations for constant acceleration — http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html (reference, retrieved 2026-09-23)
- Wikipedia – Acceleration — https://en.wikipedia.org/wiki/Acceleration (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)

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/acceleration?final_velocity_m_s=…&time_s=…`
- `POST https://tttkmbb.com/api/v1/calculate/acceleration` 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/acceleration · OpenAPI operationId `calculate_acceleration` 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": "acceleration", "inputs": {…}}`

## Example

- 0 to 100 km/h (27.78 m/s) in 8 s: inputs `{"initial_velocity_m_s":0,"final_velocity_m_s":27.78,"time_s":8}` → `{"acceleration_m_s2":3.4725,"acceleration_g":0.3541,"velocity_change_m_s":27.78,"distance_m":111.12}`
- Braking from 30 m/s to rest in 5 s: inputs `{"initial_velocity_m_s":30,"final_velocity_m_s":0,"time_s":5}` → `{"acceleration_m_s2":-6,"acceleration_g":-0.6118,"distance_m":75}`

```
GET https://tttkmbb.com/api/v1/calculate/acceleration?initial_velocity_m_s=0&final_velocity_m_s=27.78&time_s=8
```

## Limitations

You know the net force and mass instead of velocities (use force), the motion is vertical under gravity alone (use free-fall), or you only need speed from distance and time (use speed-distance-time). Assumes constant acceleration over the interval; for varying acceleration the result is the average acceleration and the distance is approximate. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why is my acceleration negative?**

The final velocity is lower than the initial one, i.e. the object is slowing down (deceleration). The magnitude is the same as for speeding up.

**How do I convert km/h to m/s?**

Divide by 3.6: 100 km/h = 27.78 m/s. Mph × 0.44704 gives m/s.

## Related

- [Force Calculator](https://tttkmbb.com/physics/newtons-second-law.md) — Multiply by mass to get the net force (F = m·a).
- [Speed, Distance & Time Calculator](https://tttkmbb.com/physics/speed-distance-time.md) — Uniform motion without acceleration.
- [Free Fall Calculator](https://tttkmbb.com/physics/free-fall.md) — Acceleration due to gravity alone.