Acceleration calculator

An acceleration calculator finds how quickly velocity changes. Acceleration = change in velocity ÷ time, a = (v − u)/t, measured in metres per second squared (m/s²). The calculator below is our SUVAT solver: type any three of displacement s, initial velocity u, final velocity v, acceleration a and time t, and it finds the acceleration and the last value, and says which equation it used.

It starts on a car doing 8 m/s that accelerates at 2 m/s² for 5 s. To find an acceleration, clear the a box and fill in three of the others. The full SUVAT calculator adds unit choices, graphs and practice.

How to use the acceleration calculator

1. Type the three values you know in the s, u, v, a and t boxes, leaving the acceleration box empty.
2. Use metres, seconds and metres per second. In the full calculator you can pick km/h, mph and other units instead.
3. Read the acceleration, and the other value the calculator works out.
4. Check which equation it used. It always picks the one that leaves out the value you did not need.

A negative answer means the object is slowing down: a deceleration. The full calculator draws the velocity-time graph, gives both answers when an object passes a point twice, and sets practice questions on cars, falling objects and trains.

The acceleration formula

This gives the average acceleration over the time. If the acceleration is constant, as in most school problems, the average and the actual acceleration are the same. When you know the distance instead of the time, use v² = u² + 2as, rearranged:

Our acceleration formula guide covers every form in depth, and the SUVAT equations guide covers all five equations of motion.

Worked examples you can check in the calculator

Example 1: from velocity and time

A car speeds up from rest to 27 m/s in 9 s. What is its acceleration?

Type u = 0, v = 27 and t = 9. The calculator gives a = 3 m/s² and also the distance, s = 121.5 m.

Here x is time in seconds and y is velocity in m/s. Acceleration is the gradient (slope) of this line: it rises 27 m/s in 9 s, which is 3 m/s². Reading the gradient off a velocity-time graph is a common question:

Example 2: braking, with no time given

A cyclist doing 25 m/s brakes steadily and stops in 62.5 m. Find the acceleration.

Negative means slowing down here, so the cyclist decelerates at 5 m/s². Type u = 25, v = 0 and s = 62.5: the calculator gives a = −5 and the stopping time, 5 s.

Example 3: from distance and time

A train moving at 4 m/s speeds up steadily and covers 60 m in 6 s. Using s = ut + ½at²:

Type u = 4, s = 60 and t = 6. The calculator gives a = 2 m/s² and a final velocity of 16 m/s.

Example 4: a car's 0 to 100 km/h time

A car does 0 to 100 km/h in 8.0 s. First convert: 100 ÷ 3.6 = 27.8 m/s. Then a = 27.8 ÷ 8.0 = 3.47 m/s². In the full calculator you can type 100 km/h directly and it converts for you.

Other ways to find acceleration

For example, a 1,200 kg car pushed by a net force of 3,000 N accelerates at 3,000 ÷ 1,200 = 2.5 m/s². The standard acceleration due to gravity is 9.80665 m/s², usually rounded to 9.81 or 9.8. The Force Calculator handles F = ma, and the Circular Motion Calculator handles centripetal acceleration.

Common mistakes

• Subtracting the wrong way. It is final minus initial, v − u. Slowing down gives a negative answer, not a positive one.
• Mixing units. Convert km/h to m/s by dividing by 3.6 before using the formulas.
• Getting the units wrong. Acceleration is in m/s², metres per second per second, not m/s.
• Using SUVAT when the acceleration changes. The equations only hold for constant acceleration. Otherwise, use the gradient of a velocity-time graph at a point.
• Forgetting "from rest". It means u = 0, one of your three values.

Practise motion in a short timed paper

Acceleration comes up in High School Physics and AP Physics 1 practice, and in GCSE Physics Higher in the UK. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. The Laws of Motion course starts with velocity-time graphs.

Read next

Physics · MechanicsAcceleration formula: a = Δv/t with worked examplesThe acceleration formula a = (v − u)/t, units, deceleration, acceleration from force or distance, centripetal and angular acceleration, with examples.