How to use
- Type the acceleration value in the Value box. Decimals are fine; use a full stop, not a comma.
- Pick the unit your number is currently in from the From list: m/s², g or ft/s².
- Pick the unit you want in the To list.
- Press Convert. The answer appears in the output panel with up to 10 significant digits.
- Round the answer yourself to the precision your source data actually has — a sensor quoting 2 decimals does not become more precise after conversion.
- To go back the other way, swap the From and To selections and convert again.
Formula / how it works
Every conversion goes through metres per second squared, the SI unit. The tool multiplies your value by the factor for the From unit to get m/s², then divides by the factor for the To unit.
result = value × factor(from) ÷ factor(to)
The three factors are fixed by definition, not measured:
- 1 m/s² = 1 (the base)
- 1 g (standard gravity, gₙ) = 9.80665 m/s² exactly — adopted by the 3rd General Conference on Weights and Measures (CGPM) in 1901 and still the value used in ISO 80000-3
- 1 ft/s² = 0.3048 m/s² exactly, because the international foot has been defined as 0.3048 m since 1959
So 1 g in ft/s² is 9.80665 ÷ 0.3048 = 32.174048… ft/s², which is the "32.2 ft/s²" figure printed in many US textbooks.
Standard gravity is not local gravity. Real gravitational acceleration varies with latitude and altitude: roughly 9.780 m/s² at the equator and 9.832 m/s² at the poles. When an aircraft manual or a ride-safety sheet quotes "g", it means multiples of the fixed 9.80665 m/s² reference, which is exactly what this converter uses. If you need the gravity at a particular place — for precise weighing or geophysics — you need a local gravity model, not a unit converter.
g as a load factor. In aviation and motorsport, "g" is often the load factor: the ratio of the lift or seat force to the occupant's weight. A level 60° banked turn produces 1 ÷ cos(60°) = 2 g. Converting 2 g gives 19.6133 m/s² of total acceleration felt by the pilot, which is the vector sum of gravity and the centripetal component, not the centripetal part alone. Keep that distinction in mind when you compare a g reading from a phone accelerometer with a value you computed from speed and radius.
Typical magnitudes worth knowing when you sanity-check a result: a family car braking hard reaches about 0.8–1.0 g (8–10 m/s²); a passenger jet on take-off roll about 0.3 g; a launch-style roller coaster 1.5–2 g longitudinally; fighter pilots in G-suits sustain around 9 g; crash pulses in a 50 km/h barrier test briefly exceed 30 g. If your converted number is wildly outside these ranges, check whether the source was in ft/s² and you selected m/s² by mistake.
Precision. The converter keeps 10 significant digits (JavaScript toPrecision(10)), so tiny trailing digits are floating-point residue rather than real precision. Values are not range-checked: negative numbers (deceleration) convert the same way and keep their sign.
Worked examples
Standard gravity in SI units
Inputs: 1, From g, To m/s²
Enter 1, choose g as the From unit and m/s² as the To unit, then press Convert. The tool multiplies 1 by 9.80665 and divides by 1.
Result: 9.80665
This is the defined value of gₙ, so the answer is exact.
Reading a US test report in g
Inputs: 100, From ft/s², To g
A vintage brake-test sheet lists a peak of 100 ft/s². 100 × 0.3048 = 30.48 m/s², then 30.48 ÷ 9.80665 gives the value in g.
Result: 3.108095017
About 3.1 g — far above what tyres can produce on a road, which suggests the figure is an impact pulse rather than braking.
A 3.5 g aerobatic pull in ft/s²
Inputs: 3.5, From g, To ft/s²
Enter 3.5 with g → ft/s². The tool computes 3.5 × 9.80665 = 34.323275 m/s² and divides by 0.3048.
Result: 112.6091699
Round to 112.6 ft/s² — the input only had two significant figures.
Use cases
- Turning a smartphone accelerometer log (often in m/s²) into g so it can be compared with a ride or vehicle specification.
- Converting legacy aerospace or ballistics tables written in ft/s² into SI for a physics assignment.
- Checking a quoted "0–100 km/h in 3 s" claim: 27.8 m/s ÷ 3 s ≈ 9.26 m/s², which converts to roughly 0.94 g.
- Expressing drop-test or packaging shock limits (usually quoted in g) in m/s² for an engineering calculation.
- Teaching the difference between standard gravity and local gravitational acceleration.
Tips & limitations
- If a source just says "32.2", it is almost certainly ft/s² and means 1 g.
- A minus sign means deceleration; the converter keeps it.
- Do not convert g-forces measured as load factor straight into velocity change — you also need the duration of the pulse.
- Keep the same number of significant figures as your measured input.
- For gravity at a specific location, use a geodetic gravity model; 9.80665 is only the conventional reference.
FAQ
Why does the tool use 9.80665 instead of 9.81?
9.80665 m/s² is the exact conventional value of standard gravity set by the CGPM. 9.81 is a rounded classroom value; using it would put a 0.03% error into every conversion.
Is 1 g the same everywhere on Earth?
No. Actual gravitational acceleration ranges from about 9.780 m/s² at the equator to 9.832 m/s² at the poles. The unit "g" is fixed at 9.80665 m/s² precisely so readings can be compared regardless of location.
How many ft/s² is 1 g?
Exactly 9.80665 ÷ 0.3048 = 32.1740486 ft/s² to nine significant figures. The converter shows it if you enter 1 with g → ft/s².
Can I convert km/h per second or mph per second here?
Not directly; the tool covers m/s², g and ft/s². Divide km/h/s by 3.6 to get m/s², or multiply mph/s by 0.44704, then convert from m/s².
What does a phone accelerometer reading of 9.8 at rest mean?
The sensor reports proper acceleration, so lying still on a table it reads about +9.8 m/s² upward, which converts to 1 g. In free fall it would read close to zero.
Why are there so many digits in the answer?
The tool prints up to 10 significant digits so you can choose your own rounding. Report only as many digits as your original measurement justifies.
Results are calculated from the values you enter. Double-check measurements and allow a margin before buying materials or making decisions.