Acceleration Calculator

About the acceleration calculator

Acceleration describes how quickly a speed changes. A car that goes from rest to 100 km/h in eight seconds, a sprinter leaving the blocks and a ball dropped from a window are all accelerating, and the quantity that links them is the change in speed divided by the time it took.

This calculator solves the constant-acceleration relationship for whichever quantity you are missing. Pick Acceleration, Initial Speed, Final Speed or Time, and only the fields you need are shown.

• Speeds can be entered in miles per hour, kilometres per hour, miles or kilometres per second, metres per second, yards or feet per second, or knots. Choosing a unit for the initial speed sets the same unit for the final speed, which you can still change afterwards.
• The duration is the sum of the hours, minutes and seconds boxes. An empty box counts as zero.
• Acceleration can be entered in any of seven units, from m/s² to miles/h².

Standard gravity and the g unit

Large accelerations are often quoted in multiples of g, the acceleration of an object in free fall near the Earth's surface. By convention one g is exactly 9.80665 m/s², a value fixed by the General Conference on Weights and Measures in 1901. The calculator shows every acceleration result in g as well, so you can see at a glance that, say, 2.7 m/s² is a gentle 0.28 g.

Acceleration formula

For constant acceleration, the change in speed equals the acceleration multiplied by the elapsed time. With u as the initial speed, v as the final speed, a as the acceleration and t as the time:

a = (v − u) ÷ t

A positive result means the object is speeding up, a negative result means it is slowing down. Rearranging the same relation gives the other three modes of the calculator.

u = v − a × t

v = u + a × t

t = (v − u) ÷ a

All of these assume that the acceleration stays constant for the whole interval. If it varies, the answer is an average over that interval.

Calculation examples

Acceleration from a launch. A car goes from 0 to 60 mph in 3.2 seconds. Since 60 mph is 26.8224 m/s, a = 26.8224 ÷ 3.2 = 8.382 m/s², or 0.8547 g. In the calculator's miles/h² unit the same figure is 67,500, because 60 mph ÷ (3.2 ÷ 3,600 h) = 67,500 miles per hour squared.

Braking. A vehicle slows from 30 m/s to 10 m/s over 5 seconds: a = (10 − 30) ÷ 5 = −4 m/s², which is −0.4079 g. The minus sign marks the slowdown.

Final speed. A cyclist starts a descent at 5 m/s and accelerates at 2 m/s² for 12 seconds. v = 5 + 2 × 12 = 29 m/s, about 64.9 mph.

Initial speed. A train is moving at 60 mph (26.8224 m/s) after accelerating at 2 m/s² for 5 seconds, so it started at 26.8224 − 2 × 5 = 16.8224 m/s.

Time. How long does a vehicle accelerating at 3 m/s² take to go from rest to 100 km/h? 100 km/h is 27.78 m/s, so t = 27.78 ÷ 3 ≈ 9.26 seconds.

How units and results work

Inside the calculator everything is converted to metres and seconds, then reported back in a convenient form.

• Acceleration: the first line is given in the acceleration unit that matches the initial-speed unit you chose (km/h² for km/h, ft/s² for knots, and so on). Unless you worked in m/s, a second line gives m/s², and the last line gives g.
• Initial and final speed: the answer is returned in m/s.
• Time: the answer is returned in seconds.
• The calculator asks you to correct the inputs when a divisor is zero: a duration of zero when solving for acceleration, an acceleration of zero when solving for time, or an acceleration or duration of zero when solving for a speed.

The speed fields do not accept negative numbers. To describe a slowdown, enter a final speed that is lower than the initial speed, or use a negative acceleration when solving for speed or time.

Common mistakes

• Mixing units, for instance entering the speed in km/h but the time in minutes and reading the answer as m/s². Select the units shown in the form and check the label of each result.
• Treating g-force and acceleration as the same thing. A g-force is a ratio to 9.80665 m/s², not a unit of acceleration by itself.
• Assuming constant acceleration when it is not constant. A real car delivers less acceleration at higher speed, so the number you get is an average.
• Typing the duration into the wrong box, such as seconds into the minutes box, which changes the answer by a factor of 60.

To relate acceleration to distance or force, see the speed calculator, the average speed calculator and the impact force calculator. For converting between speed units on their own, use the speed converter.