Acceleration Converter
Convert acceleration between m/s², ft/s², in/s², standard gravity (g), gals, km/h per second and mph per second.
Updated Formula covered by automated tests
Acceleration is the rate at which speed changes, and it is reported in surprisingly varied ways. Physics and engineering use meters per second squared, US aerospace and ballistics texts use feet per second squared, car reviewers think in "0 to 100 km/h" or "0 to 60 mph" times, accelerometers and ride designers talk in g, and geophysicists measuring tiny gravity differences work in gals and milligals. This converter turns a value in any of those units into all the others.
Typical uses include turning a car’s sprint time into g, reading the output of a phone or data-logger accelerometer, checking an earthquake’s peak ground acceleration against a building code given in another unit, or converting a braking figure from a test report. Negative values are allowed, so deceleration converts with its sign intact.
The formula
- a
- Acceleration, in meters per second squared
- Δv
- Change in velocity, for example from 0 to 100 km/h
- Δt
- Time over which the change happens, in seconds
- g₀
- Standard gravity, a fixed reference value rather than the gravity at any particular place
- Gal
- The gal, named after Galileo, the CGS unit used in gravimetry and seismology
Acceleration is velocity per unit time, so its units are a speed unit divided by a time unit. Some, like km/(h·s) and mph/s, keep the everyday speed unit and say how much it rises each second; a car gaining 10 mph every second has an acceleration of 10 mph/s, or 4.47 m/s². Converting them to SI simply means converting the speed part: 1 km/h is 1/3.6 m/s and 1 mph is exactly 0.44704 m/s.
The g unit is defined by convention. In 1901 the General Conference on Weights and Measures fixed standard gravity at exactly 9.80665 m/s², close to sea-level gravity at about 45° latitude. Actual free-fall acceleration ranges from about 9.78 m/s² at the equator to about 9.83 m/s² at the poles and falls slightly with altitude, so "1 g" on an accelerometer is a reference unit rather than the local gravity you stand in.
Worked example
Chen’s new hatchback is advertised at 0 to 100 km/h in 6.5 seconds. Chen wants to know the average acceleration in m/s², in g, and in ft/s² for a US forum.
- 1 Average rate of speed gain: 100 km/h ÷ 6.5 s = 15.385 km/(h·s).
- 2 Convert to SI: 15.385 ÷ 3.6 = 4.2735 m/s².
- 3 Express in g: 4.2735 ÷ 9.80665 = 0.4358 g.
- 4 Express in feet: 4.2735 ÷ 0.3048 = 14.02 ft/s².
Result: The car averages about 4.27 m/s², or 0.44 g, over the sprint. The peak is higher than this average because acceleration falls off as speed builds.
Before you rely on the result
- Sprint and braking times give only the average acceleration over the run; peak values can be considerably higher.
- Converting to g uses standard gravity. If you need the ratio to the actual gravity at a specific site, divide by the local value instead, which can differ by up to about half a percent.
Frequently asked questions
How do I turn a 0 to 60 mph time into g?
Divide 60 mph by the time to get mph per second, multiply by 0.44704 to get m/s², then divide by 9.80665. A 5.0 second run is 12 mph/s, which is 5.364 m/s² or 0.547 g on average.
Why does my phone’s accelerometer read about 9.8 m/s² while lying still?
An accelerometer senses the support force that stops it falling, so at rest it reports roughly 1 g pointing up. Apps often subtract gravity to show only the motion part, labeled "linear acceleration".
What is a milligal used for?
One milligal is 10⁻⁵ m/s², about one millionth of Earth’s gravity. Gravimeters used in geology, oil and mineral prospecting, and geodesy measure differences in gravity at this scale to map rock density below the surface.
Is deceleration measured in the same units?
Yes. Deceleration is acceleration opposite to the direction of motion, so it uses the same units with a negative sign or the word "braking". A car stopping from 100 km/h in 3.5 s averages about −7.94 m/s², or −0.81 g.