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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.

When to use

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).

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.

Inputs

Parameter	Type	Unit	Required	Description
`initial_velocity_m_s`	number	m/s	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	yes	Velocity at the end of the interval; use 0 for coming to a stop.
`time_s`	number	s	yes	Duration of the velocity change in seconds. Range: > 0

Outputs

Output	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.

Example

0 to 100 km/h (27.78 m/s) in 8 s: {"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: {"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

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/acceleration (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/acceleration · Markdown: https://tttkmbb.com/physics/acceleration.md · JSON definition: https://tttkmbb.com/physics/acceleration.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="acceleration"
OpenAPI operationId: calculate_acceleration
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

HyperPhysics – Motion equations for constant acceleration (reference)
Wikipedia – Acceleration (reference)
NIST CODATA – standard acceleration of gravity g_n = 9.80665 m/s² (standard)

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 calculators

Force Calculator — Multiply by mass to get the net force (F = m·a).
Speed, Distance & Time Calculator — Uniform motion without acceleration.
Free Fall Calculator — Acceleration due to gravity alone.