Acceleration Calculator

1. Enter any three of acceleration, initial velocity, final velocity and time.
2. Leave the one you want to find blank.
3. Read the result.
4. See which value was solved for and the formula used.

Here is what each result means:

Acceleration is the rate at which velocity changes. If an object speeds up, slows down or turns, it is accelerating. On this page it means average acceleration under a constant rate: the change in velocity divided by the time taken. Speeding from rest to 20 meters per second in 4 seconds is an acceleration of 5 meters per second squared.

A positive acceleration means the object is speeding up in the direction of motion, while a negative value, often called deceleration, means it is slowing down. Because acceleration measures a change in velocity, it has a direction just like velocity does. In SI units it is measured in meters per second squared, which reads as the number of meters per second added to the speed each second.

Acceleration is the link between force and motion. Newton's second law says the acceleration of an object equals the force on it divided by its mass, so knowing the acceleration lets you work back to the force involved. That is why acceleration sits at the heart of mechanics and appears in almost every motion problem you will meet.

It rearranges one kinematic relation to solve for whichever value you leave blank.

1. For acceleration, divide the change in velocity by the time.
2. For final velocity, add the change to the initial velocity.
3. For initial velocity, subtract the change from the final velocity.
4. For time, divide the change in velocity by the acceleration.

Acceleration connects to force and motion; see the force calculator and velocity calculator.

A car speeds up from 0 to 20 meters per second in 4 seconds.

Calculation: a = (20 - 0) / 4 = 5 meters per second squared. To find the final velocity after 6 seconds at 3 meters per second squared from a start of 5, add: 5 plus 3 times 6 is 23 meters per second.

One relation, rearranged for whatever you need to find.

All four come from the single definition a equals the change in velocity over time, so any three of the values give the fourth. This is one of the standard equations of motion for constant acceleration, and it holds whenever the rate of change of velocity stays steady across the interval.

The two are easy to confuse, but they describe different things.

An object can have a high velocity and zero acceleration if it moves at a steady pace, or zero velocity and large acceleration at the instant it starts to move. The two are independent, which is why a car at the top of its speed can be accelerating hard one moment and coasting the next.

The Change in Velocity

A larger change in velocity over the same time means a bigger acceleration, in direct proportion.

The Time

Spreading the same change over more time lowers the acceleration. A gentle stop takes longer than a sudden one.

The Direction

Slowing down gives a negative acceleration, or deceleration, opposite to the motion.

Physics Homework

Solve for acceleration, a velocity or time in a constant-acceleration problem.

Vehicles

Work out how hard a car brakes or how quickly it reaches a target speed.

Sports and Engineering

Find the rate a sprinter or machine changes speed over a measured interval.

1. Swapping Initial and Final

The change is final minus initial velocity. Reversing them flips the sign.

2. Forgetting the Sign

Slowing down gives a negative acceleration. Keep the sign to show direction.

3. Mixing Units

Use meters per second for velocity and seconds for time, or convert first.

4. Zero Time

Solving for acceleration cannot divide by a time of zero.

5. Assuming It Is Not Constant

This formula assumes a steady rate of change over the interval.

The relation is exact; only the displayed decimals are rounded.

Acceleration is the rate at which velocity changes. It equals the change in velocity divided by the time. Speeding from 0 to 20 meters per second in 4 seconds is 5 meters per second squared.

Subtract the initial velocity from the final velocity, then divide by the time. Going from 0 to 20 meters per second in 4 seconds gives 20 divided by 4, which is 5 meters per second squared.

Add the acceleration times the time to the initial velocity. Leave the final velocity blank and enter the other three, and the calculator solves for it.

Deceleration is acceleration that slows an object down. It shows up as a negative acceleration, pointing opposite to the direction of motion.

The SI unit is meters per second squared, written m/s squared. It means the number of meters per second added to the velocity every second.

Yes. The formula assumes a steady rate of change over the interval. For acceleration that varies, you would need the average over the interval or calculus.

Yes. A negative acceleration means the object is slowing down or speeding up in the opposite direction. Keep the sign to show which way the velocity is changing.

By Newton's second law, the acceleration equals the net force divided by the mass. A larger force or a smaller mass gives a bigger acceleration.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Acceleration (Wikipedia).
• Equations of motion (Wikipedia).
• Acceleration explained (Maths Is Fun).