Acceleration Calculator
A car that goes from 0 to 100 km/h in 8.5 seconds is the example. Enter your own speeds and time in the acceleration calculator; the answer comes back in m/s², ft/s² and multiples of g.
Acceleration a
- Acceleration a From v = u + at: a = (v − u) / t = (27.7778 − 0) / 8.5 = 3.268 m/s².
- 3.268 m/s²
- Displacement s From s = ½(u + v)t: s = ½ × (0 + 27.7778) × 8.5 = 118.1 m.
- 118.1 m
- Knowns used (SI) Everything is converted to meters, seconds and meters per second before the equations run, so mixed units cannot leak into the arithmetic.
- u = 0 m/s, v = 27.78 m/s, t = 8.5 s
- Average velocity ½(u + v). Under constant acceleration, and only then, the average velocity is the mean of the start and end velocities, which is why s = ½(u + v)t works.
- 50 km/h (13.89 m/s)
- Acceleration in g Divided by standard gravity, 9.80665 m/s². A useful sense check: a hard road-car launch is a fraction of 1 g, and free fall is exactly 1 g.
- 0.3332 g
- Displacement in other units
- 118.1 m 0.1181 km 387.3 ft 0.07336 mi
| Equation | Leaves out | Left side | Right side | Used here |
|---|---|---|---|---|
| v = u + at | s | 27.78 | 27.78 | yes |
| s = ut + ½at² | v | 118.1 | 118.1 | |
| v² = u² + 2as | t | 771.6 | 771.6 | |
| s = ½(u + v)t | a | 118.1 | 118.1 | yes |
| s = vt − ½at² | u | 118.1 | 118.1 |
- The a and s boxes are ignored: those are the two being solved for.
- These equations assume the acceleration is constant for the whole interval. If it changes (a car shifting gear, anything with real air resistance), split the motion into pieces that are each roughly constant.
- Results are shown to four significant figures. Round the answer to the precision of your least precise measurement.
How the Kinematics Calculator works
The acceleration formula is a = (v − u) / t: the change in velocity divided by the time it took. Its unit is meters per second per second, m/s², because it is a velocity (m/s) changing every second.
Worked example, the one above: 0 to 100 km/h in 8.5 s. First convert the speed, because the time is in seconds: 100 km/h is 100 / 3.6 = 27.78 m/s. Then a = (27.78 − 0) / 8.5 = 3.268 m/s². Divided by standard gravity that is 0.333 g, a third of the acceleration of free fall. The car covers s = ½(u + v)t = ½ × 27.78 × 8.5 = 118.1 m doing it.
Unit conversion is where this formula usually goes wrong. Plugging 100 straight in as the velocity with 8.5 s gives 11.8, which looks plausible and is wrong by a factor of 3.6. The calculator converts every input to SI first and shows the knowns it used, so the mismatch is visible.
Deceleration is negative acceleration. A car braking from 27.78 m/s to rest in 3 s has a = (0 − 27.78) / 3 = −9.26 m/s². The minus sign says the acceleration points against the motion. "Deceleration of 9.26 m/s²" and "acceleration of −9.26 m/s²" mean the same thing; do not use both a minus sign and the word deceleration, or the sign flips twice.
Acceleration in g is a ratio to standard gravity, 9.80665 m/s². It is how pilots, drivers and ride designers talk, because the body feels it as a fraction or multiple of its own weight. A third of a g pressed back into the seat is a brisk road car; one g is free fall.
If you do not have the time, the other two routes are a = (v² − u²) / 2s, from speeds and distance, and a = 2(s − ut) / t², from distance and time. Pick the matching pairing in the solve-for box.
This is average acceleration over the interval. A real car accelerates hardest in first gear and less as it goes faster, so its peak acceleration is higher than this figure and its acceleration near the end is lower. The SUVAT equations treat it as constant, which gives the right final speed and time but not necessarily the right distance for a motion that was not actually constant.
Kinematics Calculator FAQ
What is the formula for acceleration?
a = (v − u) / t: final velocity minus initial velocity, divided by time. From 0 to 27.78 m/s (100 km/h) in 8.5 s that is 3.268 m/s². Without time, use a = (v² − u²) / 2s.
How do I convert acceleration to g?
Divide by standard gravity, 9.80665 m/s². 3.268 m/s² is 0.333 g. In feet, 1 g is 32.174 ft/s², so divide an ft/s² figure by that instead.
Is deceleration negative acceleration?
Yes. Deceleration means the acceleration points against the direction of motion, which with motion taken as positive makes a negative. Braking from 27.78 m/s to rest in 3 s is a = −9.26 m/s², or a deceleration of 9.26 m/s².