Acceleration Converter — m/s², g-force, ft/s² and Gal

The acceleration converter above takes a rate of change of velocity in any common unit and expresses it in every other unit at once. Acceleration is one of the few quantities where engineers, physicists, automotive testers, geophysicists and aerospace teams all use different units for the same thing, and where the conversion factor between two of them is often a defined constant rather than a rounded measurement. Getting that distinction right is the difference between a correct answer and one that quietly drifts by a fraction of a percent.

Arb Digital builds and maintains this converter as part of a free reference library used by students, technical writers and engineering teams. Every factor here traces back to the SI definitions published by the BIPM and the conversion tables in NIST Special Publication 811, and nothing that is defined exactly has been rounded.

What This Acceleration Converter Does

Acceleration is the rate at which velocity changes, so its dimensions are always length divided by time squared. That single fact governs every unit on this page. Metres per second squared is the SI coherent unit, formed directly from the metre and the second with no numerical factor attached. Everything else is either a decimal multiple of that unit, a unit built from a different length standard, or a unit built from a mixed pair of time bases such as kilometres per hour per second.

The converter accepts a value in any supported unit and returns the equivalent in your chosen target unit in the headline result. Below it, four supporting panels always show the same acceleration expressed in metres per second squared, in multiples of standard gravity, in feet per second squared, and in Gal, the centimetre-gram-second unit still used across gravimetry and seismology. Those four cover the overwhelming majority of contexts in which an acceleration figure is quoted, so you can read across from a spec sheet in one convention to a calculation in another without a second conversion step.

How to Use It

1. Type the value. Enter the acceleration you have. Decimals and scientific values are both fine, and negative numbers work if you are describing deceleration along a chosen axis.
2. Choose the unit you are converting from. The list is grouped from the SI unit outward through metric multiples, imperial units, gravitational units and the geophysical Gal family.
3. Choose the unit you want. The headline figure updates immediately, together with the full conversion sentence beneath it showing the factor that was applied.
4. Read the four supporting panels. They give you the same acceleration in the four most commonly quoted units at once, which is usually faster than running four separate conversions.
5. Use Swap to reverse direction when you want to check the inverse conversion, which is the quickest way to confirm you have not inverted a factor by mistake.

The Formula and How It Is Calculated

Every unit on this page is stored as a single multiplier that converts it to metres per second squared. Conversion is therefore a two-step operation with no accumulated rounding: the input value is multiplied by the source unit factor to reach the SI base, then divided by the target unit factor. In symbols, result = value × factor(from) ÷ factor(to).

Three of those factors are exact by definition rather than by measurement. The international foot has been exactly 0.3048 metres since the 1959 agreement, so one foot per second squared is exactly 0.3048 m/s². The international mile follows from that at exactly 1609.344 metres, which makes one mile per hour per second exactly 0.44704 m/s². And standard gravity, the symbol g_n, was fixed by the third General Conference on Weights and Measures at exactly 9.80665 m/s². The BIPM SI Brochure and NIST Special Publication 811 both carry these values, and this converter uses them at full precision rather than the truncated 9.81 or 0.305 that appear in many textbooks.

Why Standard Gravity Is Not the Same as Local Gravity

This is the single most common misreading of an acceleration figure. Standard gravity is a conventional constant adopted so that weight, pressure and force units could be defined unambiguously. It is not a claim about the gravitational field at any particular place. Real free-fall acceleration at the Earth's surface ranges from roughly 9.764 m/s² on high equatorial ground to about 9.834 m/s² near the poles, a spread of around 0.7%, driven by the planet's oblate shape, its rotation, altitude and local rock density.

The practical consequence is that converting a mass to a weight force with the standard value is exactly right for legal and specification purposes and slightly wrong for precision metrology. A load cell calibrated in one city and installed in another can read differently by a few parts per thousand purely because of the gravity change, which is why calibration certificates for high-accuracy scales record the local gravity value. If you are working with force rather than acceleration, our force converter handles the newton, kilogram-force and pound-force side of that relationship.

Gal, Milligal and the Geophysics Convention

Geophysicists almost never write acceleration in metres per second squared. The working unit is the Gal, named for Galileo and equal to one centimetre per second squared, which puts the Earth's field at roughly 980,000 Gal. Because gravity surveys are looking for anomalies far smaller than that, the practical unit is the milligal, one thousandth of a Gal or 10⁻⁵ m/s², and high-resolution work goes down to the microgal.

The scale is worth internalising. A buried void, a salt dome or an ore body might shift the local field by a few tenths of a milligal. That is a change of a few parts in ten million of the total field, which is why gravimeters are among the most carefully temperature-controlled instruments in field geoscience. When you see a survey map contoured in milligals, the numbers are not small because the effect is trivial; they are small because the baseline they sit on is enormous.

Mixed Time Bases: km/h/s and mph/s

Automotive and rail engineering frequently quote acceleration with one time unit in the velocity and a different one in the rate, as in kilometres per hour per second. This is not sloppiness. It is genuinely more readable for a human, because the velocity half of the expression matches the speedometer. But it does mean the conversion factor is not a round number: one km/h/s is 1000 divided by 3600, or about 0.2778 m/s², and one mph/s is exactly 0.44704 m/s².

The trap is treating a zero-to-sixty time as a constant acceleration. A car that reaches 60 mph in 6 seconds has an average acceleration of 10 mph/s, about 4.47 m/s² or 0.456 g. Its instantaneous acceleration is nowhere near constant: it peaks in first gear, drops at every shift, and falls away as aerodynamic drag grows with the square of speed. Averaging is fine for comparing vehicles and useless for predicting the force on a component at a specific moment. If you also need to move between velocity units, the speed converter covers km/h, mph, knots and metres per second.

Reading g in Vehicle, Aviation and Sensor Specifications

Expressing acceleration in multiples of g is a shorthand that carries real information, because it tells you directly how the resulting inertial force compares to the object's own weight. A car pulling 1.0 g of lateral acceleration in a corner is generating a sideways force equal to its full weight. A passenger aircraft in a routine turn sits near 1.2 g. Accelerometer datasheets state a full-scale range in g precisely because the number is intuitive for anyone estimating structural loads.

Two details are easy to miss. First, a stationary accelerometer resting on a bench reads 1 g upward, not zero, because it measures proper acceleration rather than coordinate acceleration; the reading only falls to zero in free fall. Second, a full-scale range of ±16 g does not mean the device is accurate to that level, and shock events routinely exceed the range briefly, clipping the trace. Reading the sensor spec correctly requires separating the range, the resolution and the noise density, which are three different numbers.

Full Acceleration Conversion Table

Each factor below converts one unit of the named quantity into metres per second squared. Values marked exact are defined constants and are not rounded anywhere in this tool.

Common Mistakes to Avoid

• Using 9.81 or 9.8 as though it were exact — the defined value is 9.80665 m/s², and rounding it early introduces an error of up to one part in a thousand that compounds through a multi-step calculation.
• Confusing Gal with gallon — the capital-G Gal is an acceleration unit of 0.01 m/s² and has nothing to do with volume; volume belongs in the volume converter.
• Treating an average acceleration as an instantaneous one — a zero-to-sixty figure hides a peak that can be twice the average.
• Squaring the time unit twice — converting hours to seconds in a km/h/s value means dividing by 3600 once, not 3600 squared, because only one of the two time units is in hours.
• Ignoring direction — acceleration is a vector, so adding a 3 m/s² forward acceleration to a 4 m/s² lateral one gives 5 m/s², not 7.

Related Free Tools From Arb Digital

Acceleration sits in the middle of a chain of related quantities, and the rest of that chain has its own converters. Change velocity units with the speed converter, handle distance with the length converter, work with durations in the time converter, and turn mass times acceleration into newtons or pounds-force with the force converter. Very large and very small factors are easier to read through the scientific notation converter, and the general-purpose unit converter covers everything else in one place.

Frequently Asked Questions

This converter is a reference and planning aid. For safety-critical, structural, or metrological work, verify every factor against the current SI Brochure and your own instrument calibration records.