Acceleration Calculator
Acceleration from velocity change and time, with force check.
What it does
Acceleration rates velocity change: a car gaining 27.78 m/s across 8 seconds averages 3.47 m/s2, and the same magnitude with flipped sign describes braking back to rest. Time sits underneath everything, so halving the time doubles the rate.
The tool above takes start and end speeds with time and mass in metric or imperial. It returns acceleration, speed change, and the force check. The default 0 to 27.78 m/s in 8 s at 1500 kg gives 3.47 m/s2 with 5,209 N.
Forms match OpenStax with HyperPhysics beside them: average acceleration is delta v over delta t in m/s2, and force is mass times acceleration. Worked checks agree, from the subway train at plus 0.42 m/s2 to braking at minus 1.04 m/s2.
Sign is direction, not failure. Positive follows the chosen forward while negative opposes it, and g units divide by 9.80665 to grade rides against gravity: the default pulls about 0.354 g.
How to use
- Pick metric or imperial speeds.
- Type start and end speeds in matching units.
- Type the elapsed seconds.
- Type mass for the force check.
- Read acceleration first, force beside it.
- Read sign as direction along the road.
Formula
- u, v
- Start and end speeds in matching units.
- t
- Elapsed time in seconds, above 0.
- F
- Net force in newtons for mass m.
Imperial speeds convert first (mph x 0.44704) with mass through 0.45359237, then run identical SI math. Constant rate assumed; varying thrust needs integration.
Worked example
Example: 0 to 27.78 m/s in 8 s
Metric defaults: u 0, v 27.78 m/s, t 8 s, m 1500 kg.
- Change: 27.78 minus 0 = 27.78 m/s (100 km/h).
- Rate: 27.78 / 8 = 3.47 m/s2.
- g: 3.47 / 9.80665 = 0.354 g.
- Force: 1500 x 3.47 = 5,209 N.
- Imperial check: 0 to 62.14 mph gives the same 3.47.
- Tool shows 3.47 m/s2, 27.78 m/s, 5,209 N.
Reference table
| Change and time | Acceleration | Note |
|---|---|---|
| 0 to 27.78 m/s, 8 s | 3.47 m/s2 | Default car case |
| 0 to 8.333 m/s, 20 s | 0.42 m/s2 | Subway train |
| 8.333 to 0 m/s, 8 s | -1.04 m/s2 | Braking |
| 0 to 30 m/s, 7 s | 4.29 m/s2 | Cheetah sprint |
| 0 to 60 mph, 8 s | 3.35 m/s2 | About 11 ft/s2 |
Limits
- Average rate; varying thrust differs.
- Straight line; curves add centripetal terms.
- Air drag and grade excluded.
- Mass constant; rockets lighten.
Common mistakes
- Dividing speed by time without subtracting start.
- Mixing mph with seconds unconverted.
- Reading negative as error instead of direction.
- Forgetting mass in force checks.
- Using km/h directly as m/s.
Try it yourself
Quick checks. Answers sit tucked under each question.
0 to 8.333 m/s in 20 s?
0.42 m/s2.
8.333 to 0 m/s in 8 s?
-1.04 m/s2, braking direction.
0 to 30 m/s in 7 s?
4.29 m/s2.
Questions
What is the default acceleration?
3.47 m/s2 with 5,209 N at 1500 kg.
Negative acceleration?
Slowing along the chosen forward; magnitude still bites.
g force here?
3.47 / 9.80665 is 0.354 g.
60 mph in 8 s?
3.35 m/s2, about 11 ft/s2.
Imperial match?
Yes: 0 to 62.14 mph mirrors 27.78 m/s exactly.
Force page versus this?
Force multiplies a known rate; this derives the rate from speeds.