Acceleration measures how quickly an object’s velocity changes. This free calculator solves the constant-acceleration kinematics relationship for any one unknown — acceleration, initial velocity, final velocity, or elapsed time — making it handy for physics homework, engineering estimates, and motion problems. Pick what you want to find, enter the known values in SI units, and the answer appears instantly.
How it works
The core equation is average acceleration:
a = (v_f − v_i) ÷ t
where v_i is the initial velocity, v_f is the final velocity, and t is the time taken. The tool rearranges this single relationship to solve for whichever quantity you leave unknown:
- Acceleration: a = (v_f − v_i) ÷ t
- Final velocity: v_f = v_i + a·t
- Initial velocity: v_i = v_f − a·t
- Time: t = (v_f − v_i) ÷ a
With velocity in metres per second (m/s) and time in seconds (s), acceleration comes out in metres per second squared (m/s²). A negative result means deceleration — the object is slowing down.
Three worked examples
Example 1 — solve for acceleration: A car speeds up from rest to 20 m/s over 10 seconds.
a = (20 − 0) ÷ 10 = 2 m/s² — the car gains 2 m/s of speed each second.
Example 2 — solve for final velocity: A bicycle starts at 3 m/s and accelerates at 1.5 m/s² for 8 seconds.
v_f = 3 + (1.5 × 8) = 3 + 12 = 15 m/s
Example 3 — solve for time (deceleration): A train moving at 30 m/s brakes at −1.5 m/s² (i.e. decelerates). How long to stop?
t = (0 − 30) ÷ (−1.5) = 20 seconds
Unit conversions before you start
This calculator works cleanest in SI units, but many real-world problems give speed in km/h or mph. Convert first:
| Given speed | In m/s |
|---|---|
| 60 km/h | 16.67 m/s |
| 100 km/h | 27.78 m/s |
| 30 mph | 13.41 m/s |
| 60 mph | 26.82 m/s |
To convert km/h → m/s: divide by 3.6. To convert mph → m/s: multiply by 0.44704.
Average versus instantaneous acceleration
This tool computes average acceleration — the total change in velocity divided by the total elapsed time. It assumes acceleration is constant throughout. Real-world scenarios often have varying acceleration (a car engine, for instance, produces different force at different speeds), and this simple formula captures only the net change. Instantaneous acceleration at a moment in time requires knowing the velocity function and differentiating it, which is beyond the scope of this calculator. For most homework and engineering estimation problems, average acceleration is what is needed.
| Quantity | Symbol | SI Unit |
|---|---|---|
| Initial velocity | v_i | m/s |
| Final velocity | v_f | m/s |
| Time | t | s |
| Acceleration | a | m/s² |
All calculations run locally in your browser — nothing is uploaded.