Acceleration Calculator
Acceleration is how quickly velocity changes. This calculator works it out from a change in speed over time, or from the force applied to a mass.
Formula
a = (v − u) ÷ t
- u = starting velocity, v = final velocity, t = time
- Distance covered: s = ut + ½at²
0 to 27.8 m/s (100 km/h) in 6 s: 27.8 ÷ 6 = 4.63 m/s²
The Formula
a = (v − u) ÷ t
Where u is the starting velocity, v the final velocity and t the time taken.
A car going from rest to 27 m/s (about 60 mph) in 9 seconds accelerates at 27 ÷ 9 = 3 m/s².
The unit reads as "metres per second, per second": every second, the speed changes by that many metres per second.
Acceleration Includes Slowing and Turning
In physics, acceleration is any change in velocity, which has direction as well as magnitude. That means three things count:
- Speeding up — positive acceleration
- Slowing down — negative acceleration, or deceleration
- Changing direction at constant speed — still acceleration
A car going round a roundabout at a steady 20 mph is accelerating continuously, which is exactly why you feel pushed sideways.
g and Free Fall
Objects in free fall near Earth accelerate at about 9.81 m/s², regardless of mass. A feather falls more slowly than a hammer only because of air resistance — in a vacuum they land together, as demonstrated on the Moon during Apollo 15.
Accelerations are often quoted in multiples of g: a road car pulls around 1 g under hard braking, while fighter pilots can experience 9 g.
Quick Reference
| 0–100 km/h | Acceleration | In g | Distance covered |
|---|---|---|---|
| 3 s | 9.26 m/s² | 0.94 g | 41.7 m |
| 6 s | 4.63 m/s² | 0.47 g | 83.3 m |
| 9 s | 3.09 m/s² | 0.31 g | 125.0 m |
| 12 s | 2.31 m/s² | 0.24 g | 166.7 m |
Frequently Asked Questions
- How do I calculate acceleration?
- Subtract the initial velocity from the final velocity and divide by the time taken. Reaching 27 m/s from rest in 9 seconds is 3 m/s².
- Is slowing down acceleration?
- Yes, negative acceleration. Any change in velocity counts, including deceleration and changes of direction at constant speed.
- What is 1 g?
- 9.81 m/s², the acceleration of free fall at Earth's surface. It is used as a convenient unit for comparing other accelerations.
- Do heavy objects fall faster?
- No. In the absence of air resistance all objects accelerate at the same rate regardless of mass, which is why a hammer and feather land together in a vacuum.