Acceleration Calculator
Calculate acceleration from initial velocity, final velocity and time. Get an instant result in m/s² with the change in velocity, g-force and the formula shown.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the formula & steps
How the Acceleration Calculator Works
This calculator finds the average acceleration of an object from how its velocity changes over time. Enter the initial velocity (vᵢ), the final velocity (v_f) in metres per second, and the time (t) in seconds. It instantly returns the acceleration in m/s², along with the change in velocity and the equivalent in g-force.
Acceleration describes how quickly an object speeds up or slows down. The larger the change in velocity in a given time, the larger the acceleration.
The Formula
Average acceleration is defined as the change in velocity divided by the change in time:
a = (v_f − vᵢ) ÷ t
Where:
- a = average acceleration (m/s²)
- v_f = final velocity (m/s)
- vᵢ = initial velocity (m/s)
- t = elapsed time (s)
The quantity v_f − vᵢ is the change in velocity, often written Δv (“delta-v”). A positive result means the object is speeding up; a negative result means it is slowing down.
Worked Example
A car accelerates from rest to a highway speed of 27 m/s (about 60 mph) in 6 seconds:
- Change in velocity: Δv = 27 − 0 = 27 m/s
- Acceleration: a = 27 ÷ 6 = 4.5 m/s²
- In g-units: 4.5 ÷ 9.80665 ≈ 0.46 g
So the car gains 4.5 m/s of speed every second.
Common Acceleration Values
Comparing your result to everyday examples helps build intuition for what a number in m/s² actually feels like.
| Situation | Approximate acceleration |
|---|---|
| Free fall near Earth’s surface | 9.81 m/s² (1 g) |
| Sports car 0–100 km/h in 4 s | ≈ 6.9 m/s² |
| Commuter train pulling away | ≈ 1.0–1.3 m/s² |
| Passenger jet at takeoff | ≈ 1.5–2.5 m/s² |
| Hard emergency braking in a car | ≈ −8 m/s² |
Tips for Accurate Results
- Keep units consistent. Velocities must both be in m/s and time in seconds. If you have km/h, divide by 3.6 to convert to m/s first.
- Mind the sign. Define one direction as positive. If the object reverses or slows, the acceleration will come out negative — that is expected.
- Use average depth of the interval. This formula gives the average acceleration over the whole interval, which equals the instantaneous value only when acceleration is constant.
Frequently asked questions
What is the formula for acceleration?+
Average acceleration is the change in velocity divided by the time taken: a = (v_f − v_i) ÷ t. Here v_f is the final velocity, v_i is the initial velocity, and t is the elapsed time. The result is in metres per second squared (m/s²).
How do you calculate acceleration from velocity and time?+
Subtract the initial velocity from the final velocity to get the change in velocity, then divide by the time. For example, going from 0 to 27 m/s in 6 s gives a = (27 − 0) ÷ 6 = 4.5 m/s².
Can acceleration be negative?+
Yes. If the final velocity is less than the initial velocity, the change in velocity is negative, so acceleration is negative. Negative acceleration means the object is slowing down (decelerating) in the direction of motion.
What are the units of acceleration?+
Acceleration is measured in metres per second squared (m/s²) in SI units. This means the velocity changes by that many metres per second every second. Other units include feet per second squared (ft/s²) and g (1 g ≈ 9.80665 m/s²).
What is the difference between average and instantaneous acceleration?+
Average acceleration uses the total change in velocity over a finite time interval, which is what this calculator finds. Instantaneous acceleration is the acceleration at a single moment, found by taking the limit as the time interval approaches zero (the derivative of velocity).