Acceleration Calculator
Acceleration is how quickly velocity changes over time. Enter your starting velocity, final velocity, and elapsed time, and this calculator returns the average acceleration in metres per second squared (m/s²), the equivalent g-force, and the raw change in velocity. It is the everyday way to answer questions like “how hard did that car brake?” or “what acceleration does a 0-to-100 km/h sprint really mean?” using the kinematic relation a = (v − u) / t.
How the calculation works
-
1
Enter the two velocities
Initial velocity (u) and final velocity (v), both in m/s. They can be equal, or v can be smaller than u for deceleration.
-
2
Enter the elapsed time
The time (t) in seconds over which the velocity changed. It must be greater than zero for a defined acceleration.
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3
Read the results
You get acceleration in m/s², the same figure expressed in g (1 g = 9.80665 m/s²), and the change in velocity v − u.
The formula
Average acceleration is the change in velocity divided by the time taken:
a = (v − u) / t
Where:
- a = acceleration (m/s²)
- v = final velocity (m/s)
- u = initial velocity (m/s)
- t = elapsed time (s)
A negative result means deceleration (slowing down): the object’s velocity decreased over the interval. To express the answer as a multiple of standard gravity, divide by g = 9.80665 m/s².
Worked example
A car goes from rest to 100 km/h in 5 seconds. First convert: 100 km/h = 100 ÷ 3.6 = 27.78 m/s. With u = 0:
a = (27.78 − 0) / 5 = 5.56 m/s²
g-force = 5.56 ÷ 9.80665 ≈ 0.57 g
So the occupants feel a little over half their body weight pushing them back into the seat.
Reference values
| Scenario | Approx. acceleration | In g |
|---|---|---|
| Comfortable car start | 2 m/s² | 0.20 g |
| Sports car 0–100 km/h in 4 s | ~6.9 m/s² | 0.71 g |
| Hard emergency braking | 8 m/s² | 0.82 g |
| Free fall (gravity) | 9.81 m/s² | 1.00 g |
| Roller-coaster peak | ~40 m/s² | ~4 g |
| Fighter-pilot sustained turn | ~88 m/s² | ~9 g |
Common pitfalls
- Mixing units. The formula expects velocities in m/s and time in seconds. Convert km/h to m/s by dividing by 3.6, and mph to m/s by multiplying by 0.44704 first.
- Average vs instantaneous. This gives the average acceleration over the interval. Real acceleration may vary moment to moment; only the start and end velocities matter here.
- Sign matters. If the final velocity is below the initial velocity, acceleration is negative (deceleration). That is physically correct, not an error.
- Zero time. Acceleration over zero seconds is undefined; the calculator returns 0 rather than dividing by zero.
Frequently Asked Questions
The SI unit is metres per second squared (m/s²), meaning the velocity changes by that many metres per second every second. This tool also shows the value as a multiple of g, where 1 g = 9.80665 m/s².
Divide a km/h value by 3.6 to get m/s (100 km/h = 27.78 m/s). Multiply an mph value by 0.44704 to get m/s (60 mph = 26.82 m/s). Enter the converted m/s figures into the velocity fields.
It means the object is slowing down (decelerating) over the interval: the final velocity is lower than the initial velocity. The minus sign simply shows the direction of the velocity change; it is not an error.
No. The calculation runs in your browser and the numbers are not stored or sent anywhere for processing. Nothing you type is uploaded, saved, or shared.
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