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Acceleration measures how quickly velocity changes — speeding up, slowing down, or changing direction. Over a period of time it's simply the change in velocity divided by the time it took: a = (v_final − v_initial) ÷ t.
Pick what you're solving for, enter the values you know, and the result comes back in m/s², m/s or seconds.
Acceleration Calculator: step-by-step worked example
- Solve for
- Acceleration (from velocities & time)
- Initial velocity (m/s)
- 0
- Final velocity (m/s)
- 27.78
- Time (s)
- 8.5
- 1
Change in velocity
Δv = v final − v initial
27.78 − 0 = 27.78 m/s
- 2
Average acceleration
a = Δv ÷ t
27.78 ÷ 8.5 = 3.2682 m/s²
- 3
In g-force
a ÷ 9.80665
3.2682 ÷ 9.80665 = 0.3333 g
- Velocity:0 m/s → 27.78 m/s
Good to know: 0–100 km/h (27.78 m/s) in 8.5 s is ≈ 3.27 m/s², about 0.33 g. Divide km/h by 3.6 to get m/s (or multiply mph by 0.447).
Acceleration Calculator — how it works
The average-acceleration relation
| Solve for | Formula |
|---|---|
| Acceleration a | (v_final − v_initial) ÷ time |
| Final velocity v_f | v_initial + acceleration × time |
| Time t | (v_final − v_initial) ÷ acceleration |
Velocities are in metres per second and time in seconds, so acceleration comes out in m/s².
Negative acceleration is deceleration
If the final velocity is lower than the initial, the acceleration is negative — the object is slowing down. A car braking from 30 m/s to 0 in 6 seconds has an acceleration of −5 m/s². The minus sign just means the change opposes the motion.
The initial velocity matters
Many problems start from rest, so v_initial = 0 and the formula simplifies to a = v_final ÷ t. But if the object was already moving, you must subtract the starting velocity — leaving it out is the most common mistake. The calculator defaults the initial velocity to 0, so set it if the object wasn't at rest.
Where it helps
0–100 km/h times, braking distances, projectile setups, and physics homework. This gives *average* acceleration over the interval; instantaneous acceleration at a single moment needs calculus. For the force behind that acceleration, use a force calculator.
Worked example
A car goes from rest (0 m/s) to 100 km/h in 5 seconds. First convert: 100 km/h = 27.8 m/s. Then a = (27.8 − 0) ÷ 5 = 5.56 m/s². If instead it accelerated at 5.56 m/s² for 5 seconds starting at 10 m/s, the final velocity would be v_f = 10 + 5.56 × 5 = 37.8 m/s.
Frequently asked questions
How do I calculate acceleration?+
Subtract the initial velocity from the final velocity and divide by the time: a = (v_final − v_initial) ÷ t. From 0 to 20 m/s in 4 s is 5 m/s².
What are the units of acceleration?+
Metres per second squared (m/s²), meaning the velocity changes by that many metres per second every second. Use m/s for velocities and seconds for time.
What is negative acceleration?+
A negative value means the object is slowing down (decelerating): the final velocity is lower than the initial. Braking from 30 to 0 m/s in 6 s is −5 m/s².
Do I need the initial velocity?+
Yes, unless the object starts from rest. If it was already moving you must subtract that starting velocity; the tool defaults it to 0 for objects starting from rest.
Is this average or instantaneous acceleration?+
It is the average acceleration over the time interval. Instantaneous acceleration — the value at one exact moment — requires the derivative of velocity and isn’t computed here.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
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