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Acceleration converter

Convert g-force to m/s², m/s² to g, ft/s² and gal (cm/s²), using standard gravity g₀ = 9.80665 m/s² exactly.

Updated Checked against 4 worked examples

A number in the “from” unit, or with its own unit
Try
Converted value
m/s²
Converted value: 9.80665 m/s²
Shown to 12 significant figures, half-up
Conversion
1 g = 9.80665 m/s²
Conversion factor
9.80665
Exactness
Exact

1 g is exactly 9.80665 m/s².

The same amount counted in each unit

g1 gm/s²9.80665 m/s²
1 g in every acceleration unit (4 rows)
UnitValueDefinition
metre per second squared (m/s²)9.80665Base unit
standard gravity (g)11 g = 9.80665 m/s², exact
foot per second squared (ft/s²)32.174051 ft/s² = 0.3048 m/s², exact
gal (galileo)980.6651 Gal = 0.01 m/s², exact
How it's calculated S
  1. Convert standard gravity to metre per second squared

    1 g×9.80665 m/s2g=9.80665 m/s21\ \text{g} \times 9.80665\ \tfrac{\text{m/s$^{2}$}}{\text{g}} = 9.80665\ \text{m/s$^{2}$}

    1 g = 9.80665 m/s², exact. Both units are defined exactly and the converted value is a terminating decimal, so every digit shown in it is exact.

About the acceleration converter

Acceleration is change of speed per unit time, and each unit here is a fixed number of metres per second squared. The g of g-force is standard gravity, g₀ = 9.80665 m/s², fixed by the 3rd CGPM in 1901; a foot per second squared is 0.3048 m/s², and a gal (galileo) is 1 cm/s².

The default converts 1 g to 9.80665 m/s². Vehicle performance is the everyday use: a car that reaches 100 km/h from rest in 3 seconds averages 9.26 m/s², or 0.94 g.

Standard gravity is a conventional value. Real free-fall acceleration runs from about 9.78 m/s² at the equator to 9.83 m/s² at the poles, and geophysicists measure its local variations in milligals.

Worked examples

1 g in m/s²

Value
1 g
From
standard gravity (g)
To
metre per second squared (m/s²)
Converted value
9.80665 m/s²

Checked against: Standard gravity g₀ = 9.80665 m/s² exactly (CGPM 1901)

1 g in ft/s²

Value
1 g
From
standard gravity (g)
To
foot per second squared (ft/s²)
Converted value
32.1740485564 ft/s²

Checked against: 9.80665 / 0.3048 = 196133/6096 (Python 3.8 fractions from the legal definitions)

1 gal in m/s²

Value
1 Gal
From
gal (galileo)
To
metre per second squared (m/s²)
Converted value
0.01 m/s²

Checked against: 1 Gal = 1 cm/s² (NIST SP 811 App. B)

9.80665 m/s² is exactly 1 g

Value
9.80665 m/s²
From
metre per second squared (m/s²)
To
standard gravity (g)
Converted value
1 g
Exactness
Exact

Checked against: Definition of g₀

Questions

What is 1 g in m/s²?

Exactly 9.80665 m/s², the standard acceleration of gravity adopted by the 3rd General Conference on Weights and Measures in 1901. It equals 32.174 ft/s². Local gravity differs slightly; 9.80665 is the convention used for g-force and for units such as the kilogram-force.

How do I work out g-force from a 0–60 or 0–100 time?

Divide the speed gained by the time, then divide by 9.80665. 0–60 mph (26.8224 m/s) in 3 s averages 8.94 m/s², or 0.91 g; 0–100 km/h (27.78 m/s) in 3 s averages 9.26 m/s², or 0.94 g. The peak acceleration during the run is higher than this average.

What is a gal (Gal) in acceleration?

One centimetre per second squared, 0.01 m/s², named after Galileo. Earth's surface gravity is about 980 Gal, so gravity surveys work in milligals, where 1 mGal is about one millionth of g. The symbol is Gal, and the unit has nothing to do with the gallon.

How do I convert ft/s² to m/s²?

Multiply by 0.3048, the exact number of metres in a foot. 32.174 ft/s² is 9.80665 m/s² (1 g), and 10 ft/s² is 3.048 m/s². To go from m/s² to ft/s², divide by 0.3048, which is the same as multiplying by 3.28084.

Is gravity 9.81 m/s² everywhere?

No. Free-fall acceleration is about 9.780 m/s² at the equator and 9.832 m/s² at the poles, because the Earth spins and bulges at the equator, and it falls slightly with altitude. 9.81 is 9.80665 rounded, the conventional value between those extremes that g-force is measured against.

How accurate is the acceleration converter?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 4 worked examples whose answers come from independent sources; for example, “1 g in m/s²” is checked against Standard gravity g₀ = 9.80665 m/s² exactly (CGPM 1901).

Where does the method come from?

NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors; NIST Handbook 44, Appendix C — General tables of units of measurement.

About this calculator

xto=xfrom×ffromftof=one unit expressed in m/s2\begin{gathered} x_{\text{to}} = x_{\text{from}} \times \dfrac{f_{\text{from}}}{f_{\text{to}}} \\ f = \text{one unit expressed in } \text{m/s$^{2}$} \end{gathered}

Sources

  1. NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors
  2. NIST Handbook 44, Appendix C — General tables of units of measurement

Checked against references

4 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.

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