Acceleration Calculator

What the acceleration calculator does

Acceleration ties together four quantities: a starting speed, a final speed, the time between them, and the acceleration itself. Know any three and the fourth is fixed. This calculator finds whichever one you are missing.

So you can find the acceleration from a change in speed over a time, or work backwards to the time it would take, or to the speed you would start or end at. Below is what acceleration actually measures, the single equation behind all four answers, and a worked example.

How to use it

1. Choose what to find. Acceleration, final speed, initial speed, or the time needed.
2. Enter the other three. Speeds come with a unit selector, and acceleration can even be entered or read in g, multiples of Earth's gravity.
3. Enter the duration in hours, minutes, and seconds, however your figure is given.
4. Press Calculate for the answer, shown in every unit at once, or Reset to clear it.

What acceleration really is

Acceleration is how quickly velocity changes. Not how fast you are going, but how fast your speed is changing. Step on the accelerator and your velocity climbs each second, and the rate of that climb is the acceleration. Because it is a change in velocity over a time, its unit is a speed divided by a time, metres per second per second, which we write as metres per second squared.

Two things follow that surprise people. Acceleration can be negative, which just means the velocity is dropping, what we usually call braking or deceleration. And because velocity includes direction, you can be accelerating even at a steady speed, simply by turning, since changing direction changes velocity. This calculator deals with the straight-line case, where acceleration speeds you up or slows you down along a line.

The equation it solves

All four answers come from one equation, the first of the equations of motion for constant acceleration. With u for the initial speed, v for the final speed, a for acceleration, and t for time, it reads:

v = u + a t

In words, the final speed is the starting speed plus whatever the acceleration adds over the time. Rearranging that one relationship gives the other three the calculator can find:

• Acceleration: a = (v − u) ÷ t
• Time: t = (v − u) ÷ a
• Initial speed: u = v − a t

The one condition is that the acceleration is steady over the time in question. For a changing acceleration this gives the average, which is still the right tool for most problems.

Units, g, and precision

The SI unit of acceleration is the metre per second squared, and the calculator works in it internally before converting to whatever you choose. Speeds can be entered in metres per second, kilometres per hour, miles per hour, feet per second, knots, and more. Acceleration has its own list, including g, where 1 g is the acceleration of Earth's gravity, the defined value of 9.80665 m/s². Expressing an acceleration in g is how a car's launch or a pilot's turn is often described, as so many times the familiar pull of gravity.

The answer is shown in every unit of its kind at once, each rounded to a sensible number of places, with more decimals kept for small values so they do not collapse to zero. The arithmetic itself carries full precision, so the rounding is only in what you read, not in what is computed.

A worked example

A sports car reaches 100 km/h from a standstill in 2.5 seconds. What is its acceleration?

First put the speed in SI units: 100 km/h is 27.78 m/s. The car starts from rest, so u is 0. Then a = (27.78 − 0) ÷ 2.5 = 11.11 m/s². In the more relatable unit of gravity, that is about 1.13 g, so the launch presses you back into the seat with a little more than your own body weight.

Questions people ask

What is the acceleration formula?

For constant acceleration, a = (v − u) ÷ t, where u is the initial speed, v is the final speed, and t is the time. It is the equation v = u + at rearranged.

Is deceleration just negative acceleration?

Yes. Slowing down is acceleration with the opposite sign to the motion. The calculator returns a negative value when the final speed is lower than the initial one.

What does acceleration in g mean?

It expresses acceleration as a multiple of Earth's gravity, where 1 g is 9.80665 m/s². An acceleration of 2 g is twice that, the kind of pull you feel pressed into a seat on a hard launch.

Can something accelerate when its speed is zero?

Yes, for an instant. A ball thrown straight up is momentarily still at the top of its arc, yet gravity is accelerating it the whole time, which is why it does not stay up there.

References

A quick note on where the physics comes from. Acceleration as the rate of change of velocity, and the constant-acceleration equation v = u + at, are standard kinematics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The value of standard gravity, 9.80665 m/s², used by the g unit, and the SI units throughout, follow the US National Institute of Standards and Technology.

1. OpenStax, University Physics Volume 1, Section 3.3, Average and Instantaneous Acceleration. https://openstax.org/books/university-physics-volume-1/pages/3-3-average-and-instantaneous-acceleration
2. HyperPhysics, Georgia State University, Description of Motion. http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811