What is the formula for acceleration?

The everyday formula is a = (v − u) ÷ t, where u is the initial velocity, v is the final velocity, and t is the time. When you know the force and mass instead, use Newton's second law, a = F ÷ m. From a distance covered, rearrange s = ut + ½at² to a = 2(s − ut) ÷ t².

What is the unit of acceleration?

The SI unit is metres per second squared (m/s²) — a change in velocity (m/s) for every second (s). In US units you may see feet per second squared (ft/s²), and accelerations are often quoted in g, multiples of Earth's gravity (1 g = 9.81 m/s²).

What is negative acceleration (deceleration)?

Negative acceleration means the object is slowing down in its direction of motion — commonly called deceleration. It happens when the final velocity is less than the initial velocity, making (v − u) negative. A car braking from 30 m/s to 0 in 6 s has an acceleration of −5 m/s².

What's the difference between velocity and acceleration?

Velocity is how fast something moves and in which direction (m/s). Acceleration is how quickly that velocity changes over time (m/s²). An object can move very fast at constant velocity with zero acceleration — only a change in speed or direction is acceleration.

How do you find acceleration from force and mass?

Use Newton's second law: a = F ÷ m. Divide the net force in newtons by the mass in kilograms. A 1500 N net force on a 1200 kg car gives 1500 ÷ 1200 = 1.25 m/s². 'Net' matters — subtract friction and drag from the driving force first.

What acceleration is a 0–60 mph time?

Convert 60 mph to 26.82 m/s, then divide by the 0–60 time. A car that hits 60 mph in 4 seconds averages 26.82 ÷ 4 ≈ 6.7 m/s², or about 0.68 g. A 2-second hypercar averages roughly 13.4 m/s² (about 1.4 g) — more than free fall.

g-force expresses an acceleration as a multiple of standard gravity, 9.81 m/s². At 1 g you feel your normal weight; at 2 g you feel twice as heavy. Dividing any acceleration by 9.81 converts it to g. Fighter pilots black out near 5 g without a g-suit.

Physics

Acceleration Calculator

Find acceleration three ways — from a change in velocity, from force and mass, or from a distance covered. See every step, the result in g-force, and where it lands among real-world examples.

Velocity & time

a = (v − u) ÷ t

The change in velocity over the time it took.

Initial velocity (u)

m/s

Final velocity (v)

m/s

Time (t)

Acceleration

5.4

Speeding up — positive acceleration

ft/s²

17.717

0.551

km/h/s

19.44

g = standard gravity, 9.80665 m/s². A result above 1 g means the push exceeds free fall.

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The basics

What is acceleration?

Acceleration is how quickly velocity changes. Speed up, slow down, or turn a corner and you are accelerating. It is a vector — it has both a size and a direction — and in SI units it is measured in metres per second squared. There are two ways to think about it, and they agree.

a = (v − u) ÷ t

The kinematic view

The change in velocity per unit time. Take the final velocity v, subtract the initial velocity u, and divide by the time t. This is the everyday definition.

(27 − 0) ÷ 5 = 5.4 m/s²

F = m · a

The dynamic view

Newton's second law: a net force F on a mass m produces acceleration. Rearranged to a = F ÷ m, it tells you the same number from a force instead of a clock.

1500 N ÷ 1200 kg = 1.25 m/s²

Method

How to calculate acceleration by hand

For the standard case — a change in velocity over a known time — it is three steps.

1
Find the change in velocity
Subtract the initial velocity u from the final velocity v. Keep the sign: a drop in speed gives a negative number.
Δv = v − u = 27 − 0 = 27 m/s
2
Divide by the time taken
Divide that change by the elapsed time t in seconds. The result is the average acceleration over that interval.
a = 27 ÷ 5 = 5.4 m/s²
3
Read the sign and the units
A positive result means speeding up, negative means slowing down. The unit is m/s². Divide by 9.81 to express it in g if you want the felt force.
5.4 m/s² ÷ 9.81 ≈ 0.55 g

Worked examples

The same answer, three ways in

Whichever quantities you are handed — velocities, a force, or a distance — the working follows the same shape. Switch tabs to see each route.

Given A car goes from rest to 27 m/s in 5 s. u = 0, v = 27, t = 5

a = (v − u) ÷ t

a = (27 − 0) ÷ 5

a = 27 ÷ 5

a = 5.4 m/s²

Quick chart

What acceleration is a 0–60 time?

Car launches are quoted as a 0–60 mph time. Convert it to an average acceleration — pick a time, and compare it against familiar cars.

0–60 mph in

Average acceleration

6.706 m/s²

In g-force

0.684 g

Tesla Model S Plaid

0–60 in 2s

13.41

m/s² · 1.37 g

Bugatti Chiron

0–60 in 2.4s

11.18

m/s² · 1.14 g

Porsche 911 Turbo S

0–60 in 2.6s

10.32

m/s² · 1.05 g

Typical sports car

0–60 in 4s

6.71

m/s² · 0.68 g

Hot hatch

0–60 in 6.5s

4.13

m/s² · 0.42 g

Family sedan

0–60 in 8s

3.35

m/s² · 0.34 g

City car

0–60 in 12s

2.24

m/s² · 0.23 g

60 mph is 26.82 m/s. These are average accelerations — real launches peak higher off the line, then taper.

Reference

A sense of scale

Acceleration spans an enormous range. Here is where common things sit, in m/s² and in g, so a calculated number has something to lean against.

Situation	m/s²	≈ g-force
Commuter train pulling away	1	0.1 g
Family car, gentle	2	0.2 g
Free fall (gravity, g)	9.81	1 g
Sports car launch	11	1.12 g
Hard braking (car)	−10	−1.02 g
Space Shuttle at liftoff	29	2.96 g
Fighter-jet pilot blackout (~5 g)	49	5 g
Bullet in a rifle barrel	500000	50985.81 g

Where it shows up

Why acceleration matters

The same quantity governs a braking distance, a rocket's climb, and the pull you feel in a lift.

F = m · a

Vehicles & safety

Braking distance and crash forces both come from acceleration. Stopping a heavy car quickly demands a large negative acceleration — and a large force.

a = (v − u) ÷ t

Rockets & flight

Launch profiles are accelerations against time. Crews train for several g; structures are built to survive the peak.

g = 9.81 m/s²

Everyday gravity

A dropped object accelerates at g. Lifts, lift-offs, and theme-park rides are all measured against that one familiar number.

Worth knowing

Rules and edge cases

A handful of facts that keep acceleration problems honest.

a < 0

Deceleration is just negative

Slowing down is not a different quantity — it is acceleration with the opposite sign to the motion. Keep the signs consistent and the formula handles it.

a ≠ 0 at v = 0

Zero speed can still accelerate

At the top of a throw an object is momentarily still, yet gravity is still pulling — its acceleration is unchanged even as its velocity passes through zero.

constant a

Average vs instantaneous

This calculator finds the average over an interval. If the acceleration is steady, the average equals the value at every instant; if it varies, it is the overall figure.

a = v² ÷ r

Turning is accelerating too

Velocity is a direction as well as a speed, so rounding a bend at constant speed is still acceleration — pointed toward the centre of the turn.

net F only

Use the net force

In a = F ÷ m, F is the net force. Subtract friction and drag from the driving force first, or the acceleration comes out too high.

check the units

Mind the units

The formula gives m/s² only when velocity is in m/s and time in seconds. Convert km/h or mph first, or the answer is meaningless.

Related equations

The kinematic family

Acceleration sits inside the four equations of motion for constant acceleration. Each one lets you find a missing quantity without computing acceleration directly first.

v = u + at

Final velocity

Get the velocity after a time once you know the starting velocity and the acceleration.

s = ut + ½at²

Displacement from time

How far an object travels in a time under constant acceleration — the route this calculator reverses in its distance mode.

v² = u² + 2as

Velocity from distance

Links the velocities to the distance covered, with no time involved — handy for braking distances.

s = ½(u + v)t

Displacement from average

Distance as the average velocity times time — useful when you have both velocities but not the acceleration.

FAQ

Common questions

Acceleration is the change in velocity divided by the time taken: a = (v − u) ÷ t. Subtract the initial velocity from the final velocity, then divide by the elapsed time. Going from 0 to 27 m/s in 5 s gives (27 − 0) ÷ 5 = 5.4 m/s².

Keep going

Related calculators

Guide

How to calculate acceleration

Keep reading

Velocity & time