Hong Life CalculatorsUnderstanding the acceleration converter — concept and principle
Acceleration is the rate at which velocity changes, and it is reported in very different units depending on the field: engineers and physicists use metres per second squared (m/s²), pilots, drivers and ride designers talk about g-forces, seismologists and geodesists use the gal, and older US engineering documents use feet per second squared. This converter moves between these units so you can compare a car's launch, a roller coaster's loop or an earthquake's ground motion on the same scale.
How it is calculated
The value is converted to m/s² first and then to the target unit: result = value × (from-unit in m/s²) ÷ (to-unit in m/s²).
- 1 g (standard gravity) = 9.80665 m/s² exactly
- 1 Gal = 1 cm/s² = 0.01 m/s²
- 1 ft/s² = 0.3048 m/s² exactly
The principle
Acceleration has the dimension length ÷ time², so converting it only requires the length factor: the time unit (second) is the same in all these units. One foot is defined as exactly 0.3048 m, so 1 ft/s² is exactly 0.3048 m/s². Standard gravity, g₀, is a conventional value adopted by the General Conference on Weights and Measures in 1901 for defining weights; it is not the gravity at any particular place. Actual free-fall acceleration on Earth ranges from about 9.78 m/s² at the equator to about 9.83 m/s² at the poles. The gal, named after Galileo Galilei, is a CGS unit kept alive in gravimetry and earthquake engineering because local gravity differences are conveniently expressed in milligals.
Worked example
- Input: 1 g, target m/s².
- Convert to m/s²: 1 × 9.80665 = 9.80665 m/s².
- The same value in other units: 9.80665 ÷ 0.01 = 980.665 Gal and 9.80665 ÷ 0.3048 = 32.17404856 ft/s².
How to read the result
A value in g tells you how strong an acceleration feels compared with gravity. A car going from 0 to 100 km/h in 3 seconds averages about 9.26 m/s², or roughly 0.94 g. Passenger aircraft and ordinary driving involve fractions of a g, while trained fighter pilots in anti-g suits can briefly tolerate around 9 g. Peak ground acceleration in earthquakes is often given as a fraction of g or in gal.
Common mistakes
- Treating g as the unit of mass "gram"; in this context g is standard gravity.
- Using 9.8 or 9.81 and then calling the result exact; only 9.80665 is the defined value.
- Forgetting that the gal is centimetres, not metres, per second squared.
- Confusing acceleration (m/s²) with speed (m/s).
Frequently asked questions
How many m/s² is 1 g?
Exactly 9.80665 m/s², by international definition.
How many gal is 1 g?
980.665 Gal, because 1 Gal is 1 cm/s².
Why does a g-force feel like weight?
Your body resists changes in motion; the seat must push on you with a force equal to mass × acceleration, which you feel like extra or reduced weight.
Sources: BIPM, The International System of Units (SI Brochure), 9th edition · NIST Special Publication 811 (2008), Guide for the Use of the International System of Units, Appendix B