Acceleration calculator
Acceleration from a change in velocity over time, or final velocity from acceleration.
Fill in the fields and the result will appear here automatically.
Find average acceleration from a change in velocity, or final velocity under constant acceleration along one line. Velocities are signed components on the same chosen axis. Two different results are shown: signed displacement and non-negative distance travelled. After a reversal they differ, so returning to the starting point does not imply that no motion occurred.
How it works
Formula and logic
a = (v − v₀)/t. For constant a, v = v₀ + at and Δx = (v₀ + v)t/2. Distance is L = ∫|v₀ + aτ|dτ. Without reversal, L = |Δx|; when the endpoint velocities have opposite signs, L = t(v₀² + v²)/(2(|v₀| + |v|)). This includes the stop and reversal inside the interval.
Example
From 0 to 27.8 m/s in 8.4 s: a = 3.3095… → 3.31 m/s² and both distance and displacement are 116.76 m. From +10 to −10 m/s in 4 s: a = −5 m/s², displacement is 0 m, but distance is 20 m.
Fields and units
- What to find — list option
- Initial velocity — m/s
- Final velocity — m/s
- Acceleration — m/s²
- Time — s
How to use
- — Choose acceleration or final velocity and enter a positive time interval in seconds.
- — Use velocities in m/s on one fixed axis; divide km/h by 3.6 before entering them.
- — When finding final velocity, enter signed acceleration and keep the axis direction unchanged.
- — Use the distance and displacement results only if acceleration stays constant throughout the interval.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: motion with constant acceleration
- Limitation
- One-dimensional constant-acceleration model; endpoint velocities give average acceleration but do not determine the actual distance for arbitrary acceleration.
FAQ
Can acceleration be negative?
Yes. Its sign indicates an axis direction. If v < 0 and a < 0, speed increases; slowing down requires velocity and acceleration to point in opposite directions.
How do I convert km/h to m/s?
Divide by 3.6: 100 km/h = 27.777… m/s. The example uses the rounded 27.8 m/s, so it is not an exact calculation to 100 km/h.
Why are displacement and distance different after a reversal?
Signed displacement allows oppositely directed segments to cancel. Distance adds their lengths: for +10 to −10 m/s in 4 s, the two segments are 10 m each.
Does this work if acceleration is not constant?
(v − v₀)/t still gives average acceleration, but the final-velocity, distance and displacement model assumes velocity changes linearly. Arbitrary motion cannot be reconstructed from endpoint velocities alone.
What do I enter for a start from rest, and is drag included?
Enter 0 for initial velocity. Forces, air resistance and velocity-dependent acceleration are not modelled; provide measured endpoint velocities or an assumed constant acceleration.