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Acceleration Calculator

Work out acceleration from a change in speed, from force and mass, or from distance travelled, and solve any of those formulas for the missing value.

Level: Grades 9–10

Printable worksheet

Acceleration Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Formula
Solve for

Result

Acceleration

2.5 m/s²

Acceleration is 2.5 m/s².

In feet per second squared
8.2021 ft/s²
In standard gravity
0.2549 g

See the step-by-step solution ↓

Step-by-step solution

  1. Find how much the speed changed, then divide by the time it took. That gives the gain each second: a = (v − u) ÷ t

    30−108=2.5 m/s²

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how quickly something speeds up or slows down. That's its acceleration: how fast its velocity (speed in a given direction) changes. Say an object goes from 10 m/s to 30 m/s in 8 seconds. It gains 2.5 m/s every second, so its acceleration is 2.5 m/s² (meters per second, every second). Slowing down is acceleration too. It just has the opposite sign to the velocity.

There are three everyday ways to work out acceleration, and this calculator handles all of them. You can use the change in velocity over a time. You can use the net force on a known mass (Newton's second law). Or you can use the change in velocity over a distance. Each formula can be turned around too. So you can also find the time to reach a speed, the force needed, the mass being pushed, or the distance needed to stop.

Where it's used

Why this math matters outside the classroom:

  • Car performance. A car that goes from 0 to 27 m/s in 9 seconds has an average acceleration of 27 ÷ 9 = 3 m/s².
  • Braking distance. Driving instructors show that a car at 20 m/s braking at 5 m/s² needs 20² ÷ (2 × 5) = 40 m to stop.
  • Rocket launches. Engineers divide a rocket's net force by its mass, so 30,000 N on a 2,000 kg craft gives 15 m/s² of acceleration.
  • Ramp experiments. Students time a cart rolling down a ramp from rest to 1.2 m/s in 2 seconds and find an acceleration of 0.6 m/s².

Grade level and standards: Grades 9–10; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Pick the formula that matches what you know: velocity change and time, force and mass, or velocity change and distance.
  2. Choose which value to solve for. The inputs you need appear automatically.
  3. Enter each value with its unit. Use negative numbers for velocities, forces or accelerations that point the other way.
  4. Choose the unit for the answer, and read the working underneath.

What the inputs mean

Initial velocity (u)
The velocity at the start (u). Use 0 for something starting from rest.
Final velocity (v)
The velocity at the end (v).
Net force (F)
The net force: what's left after you subtract friction, drag and other forces pushing the other way.
Distance travelled (s)
How far the object moves while its velocity changes from u to v, measured along its direction of travel. Physicists call this the displacement.
Acceleration (a)
Negative means slowing down when the velocity is positive.

Formula and method

a = (v − u) ÷ t
a = F ÷ m
v² = u² + 2 × a × s  →  a = (v² − u²) ÷ (2 × s)

a is acceleration, u is the starting velocity, v is the final velocity and t is the time. F is the net force, m is the mass and s is the distance.

The first formula is the definition of average acceleration. The second is Newton's second law, F = m × a, rearranged. The third links speeds and distance without needing the time. It comes from combining two other motion formulas, v = u + at and s = ut + ½at².

All three assume the acceleration stays the same the whole time. The calculator converts inputs to metric (SI) units: m/s, s, N, kg and m. It solves the formula you chose, then converts the answer. When the distance formula gives a squared velocity, the calculator reports the positive square root.

Worked example

A car brakes evenly from 30 m/s to a stop with an acceleration of −5 m/s². How far does it travel while braking?

  1. Choose the distance formula and solve for distance.
  2. s = (v² − u²) ÷ (2a) = (0² − 30²) ÷ (2 × (−5)).
  3. s = −900 ÷ −10 = 90 m.

Result: The car needs 90 m to stop (about 295.28 ft). With the default velocity-change inputs, going from 10 m/s to 30 m/s in 8 s is an acceleration of 2.5 m/s², or about 0.2549 g.

Understanding the result

The sign tells you the direction. If velocity is positive and the acceleration is negative, the object is slowing down. A result in g compares the acceleration with standard gravity: 1 g is 9.80665 m/s².

For a sense of scale, a typical family car pulling away briskly manages around 2 to 4 m/s². Hard braking on dry pavement slows a car at roughly 7 to 9 m/s².

Assumptions and limitations

  • Acceleration stays the same the whole time (or you want the average acceleration).
  • Motion is along a single straight line, with one direction counted as positive.
  • The force in a = F ÷ m is the net force, and the mass doesn't change.
  • Real acceleration usually varies, so the result is an average or an ideal case.
  • The distance formula can't tell whether the object turned around partway. It reports the positive square root for a velocity.
  • Rocket-like problems where the mass changes, and speeds near the speed of light, need different equations.

Frequently asked questions

What does negative acceleration mean?

It means the acceleration points in the negative direction. If the object is moving in the positive direction, it's slowing down. If it's already moving in the negative direction, it's speeding up that way.

How do I find a 0 to 60 mph acceleration?

Use the velocity-change formula with u = 0, v = 60 mph and the time in seconds. A 6-second run gives 26.8224 m/s ÷ 6 = 4.4704 m/s², about 0.46 g.

Why does the distance formula sometimes give an error?

If u² + 2as is negative, the object would stop before it covered the distance you entered. So no final velocity exists. Check the signs: an object that's slowing down needs a negative acceleration when its velocity is positive.

How is this different from the force calculator?

The force calculator focuses on F = m × a alone. This one also covers acceleration from velocity and time, and from velocity and distance. That's what most motion problems give you.

How this calculator is checked

Method: Definition of average acceleration, Newton's second law (F = ma) and the constant-acceleration relation v² = u² + 2as. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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