Acceleration calculator with working

The top line is often written as $a = \dfrac{\Delta v}{t}$, where $\Delta v$ ("delta v") means the change in velocity.

• Speeding up: a car goes from rest to 20 m/s in 8 s. $a = (20 - 0) \div 8 = 2.5$ m/s².
• Slowing down: a cyclist slows from 25 m/s to 5 m/s in 4 s. $a = (5 - 25) \div 4 = -5$ m/s², a deceleration of 5 m/s².
• Finding time: a ball speeds up from 10 m/s to 30 m/s at 4 m/s². $t = (30 - 10) \div 4 = 5$ s.

Check each answer makes sense: a family car accelerating at 2.5 m/s² is realistic; 250 m/s² would mean a unit went wrong.

Acceleration is measured in metres per second squared (m/s²): how many metres per second the velocity changes each second. If speeds are given in km/h, divide by 3.6 to get m/s before using the equation; the calculator does this and shows the step. Times in minutes need converting to seconds (multiply by 60).

On a velocity-time graph, the gradient (slope) is the acceleration: rise ÷ run, which is change in velocity ÷ time. A straight sloping line means constant acceleration, a horizontal line means constant velocity (zero acceleration), and a line sloping down means deceleration. The area under the line is the distance travelled. Our SUVAT calculator finds distance too when acceleration is constant.

• Writing $u - v$ instead of $v - u$: always final minus initial, so slowing down gives a negative answer.
• Forgetting that "starts from rest" means $u = 0$.
• Mixing km/h with seconds.
• Confusing acceleration with speed: a car at a steady 30 m/s has zero acceleration.

For practice with answers, try our acceleration questions, then link acceleration to force with the F = ma calculator.

• Write the equation first, then substitute: the equation line often earns its own mark.
• Underline the words that give values in disguise: "from rest" ($u = 0$), "comes to a stop" ($v = 0$), "steady speed" ($a = 0$).
• Give a deceleration as a positive number only if the question asks for the "deceleration"; if it asks for the acceleration, keep the minus sign.
• Check the size: everyday accelerations are a few m/s², and objects falling freely accelerate at about 9.8 m/s².