About the Acceleration Calculator
Acceleration is how quickly velocity changes. A car that goes from standstill to 100 km/h in eight seconds accelerates harder than one that takes twelve; a car braking to a stop decelerates. Acceleration is measured in metres per second squared (m/s²) — metres per second of speed gained every second — and often compared with g, the acceleration of an object falling freely near the Earth's surface.
This acceleration calculator finds acceleration three ways: from a change in speed over a time, from a change in speed over a distance, or from a force and a mass using Newton's second law. Speeds can be in m/s, km/h, mph, ft/s or knots. It gives the answer in m/s², g, ft/s², and km/h or mph gained per second, along with the distance covered or the time taken.
How to Use the Acceleration Calculator
Choose From speed and time, From speed and distance or From force and mass.
For speed and time, enter the initial and final speed, choose the speed unit, and enter the time in seconds.
For speed and distance, enter both speeds and the distance.
For force and mass, enter the net force and the mass.
The Formulas
from speed and time: a = (v − u) ÷ t
from speed and distance: a = (v² − u²) ÷ 2s
from force and mass: a = F ÷ m
u = initial speed, v = final speed, t = time, s = distance
1 g = 9.80665 m/s²Step-by-Step Examples
0 to 100 km/h in 8 seconds.
v = 100 km/h ÷ 3.6 = 27.778 m/s
a = (27.778 − 0) ÷ 8 = 3.4722 m/s² (0.3541 g)
distance = average speed × time = 13.889 × 8 = 111.1 m0 to 60 mph in 6 seconds.
v = 60 × 0.44704 = 26.822 m/s
a = 26.822 ÷ 6 = 4.4704 m/s² (0.4559 g)0 to 30 m/s over 100 metres.
a = (30² − 0²) ÷ (2 × 100) = 4.5 m/s²
time = 2s ÷ (u + v) = 200 ÷ 30 = 6.667 sBraking from 100 km/h to rest in 4 seconds: a = (0 − 27.778) ÷ 4 = −6.9444 m/s², a deceleration of about 0.7081 g.
Acceleration Is a Vector
Acceleration has a direction as well as a size. Speeding up in the direction of travel is a positive acceleration; slowing down is a negative acceleration, usually called deceleration. Changing direction is an acceleration too, even at constant speed: a car going round a bend at a steady 50 km/h is accelerating towards the centre of the curve, which is why passengers feel pushed sideways. This calculator deals with straight-line motion, where the sign of the answer tells you whether the object is speeding up or slowing down.
Typical Accelerations
family car, 0–100 km/h in 10 s about 2.8 m/s² (0.28 g)
sports car, 0–100 km/h in 4 s about 6.9 m/s² (0.71 g)
hard braking on a dry road about 8 m/s² (0.8 g)
free fall near the Earth 9.81 m/s² (1 g)
roller coaster peak up to about 4–5 g
fighter pilot in a tight turn up to about 9 gWhat g-Force Feels Like
At 1 g you feel your normal weight. In a lift that accelerates upwards you feel heavier, and in one that accelerates downwards you feel lighter, because the floor pushes on you with more or less force than usual. Racing drivers experience several g in corners and under braking; trained pilots in special suits tolerate about nine g for short periods. Sustained high g drains blood from the brain, which is why sustained accelerations above a few g can cause people to black out.
Average and Instantaneous Acceleration
The formulas in this calculator give the average acceleration over the interval. Real acceleration often varies: a car accelerates hardest in first gear and more gently as it speeds up, because air resistance grows and engine power is limited. The distance and time figures shown assume the acceleration is constant, which is a good approximation over short intervals and the standard assumption in physics problems using the SUVAT equations.
Acceleration and Braking Distance
Deceleration decides how far a vehicle travels before it stops. Rearranging v² = u² + 2as gives the braking distance: s = u² ÷ 2a. A car at 100 km/h, 27.8 m/s, braking at a steady 7 m/s² needs about 55 metres to stop once the brakes are on. Because the distance depends on the square of the speed, doubling the speed quadruples the braking distance. Wet or icy roads reduce the deceleration the tyres can achieve, so the distance grows further. Add the distance travelled during the driver's reaction time — often a second or more — and the full stopping distance is considerably longer. That is why speed limits near schools are low, and why keeping a safe gap to the vehicle ahead matters so much more at motorway speeds.
Acceleration in Sport and Nature
Sprinters produce their greatest acceleration in the first few strides out of the blocks, often around 5 to 10 m/s², then gradually less as they approach top speed. A cheetah can reach about 100 km/h in roughly three seconds, averaging close to 1 g. Fleas and click beetles jump with accelerations of dozens of g for tiny fractions of a second. Measuring acceleration helps coaches judge the power an athlete produces, since by Newton's second law the force behind the acceleration is the athlete's mass multiplied by it.
Understanding Your Result
The headline is the acceleration in m/s².
The in g line compares it with the acceleration of free fall.
The other units line gives ft/s² and the km/h and mph gained each second.
The detail line gives the speed change and the distance or time involved.
When Should You Use This Calculator?
Use it for physics homework on motion and Newton's laws.
Use it to compare the performance of cars, bikes or athletes.
Use it to estimate braking distances and stopping forces.
Common Mistakes
Mixing units. Convert km/h to m/s by dividing by 3.6; the calculator does it for you.
Forgetting the starting speed. Acceleration uses the change in speed.
Treating deceleration as positive. Slowing down gives a negative acceleration.
Assuming acceleration is constant. Real vehicles accelerate unevenly.