Convert m/s², ft/s², g-force, and km/h/s instantly. Free with steps.
Acceleration — the rate at which velocity changes — wears several uniforms: meters per second squared in physics class, feet per second squared in American engineering, g-force in aviation and automotive testing, and km/h per second on European spec sheets. Our free Acceleration Converter translates between all four instantly, showing the meters-per-second-squared intermediate so every conversion is auditable.
The g deserves special attention: 1 g = 9.80665 m/s², the standard acceleration of gravity. Fighter pilots, crash-test engineers, and roller-coaster designers all think in g’s because it expresses acceleration relative to the familiar pull of Earth. A car braking at 0.8 g is decelerating at 7.85 m/s² — numbers that mean little until the converter puts them in your preferred unit.
Whether you are checking a physics homework answer, interpreting a vehicle spec, or sizing a vibration isolator, convert first and compute second. Unit errors in acceleration propagate into force (F = ma) and distance (d = ½at²) calculations, doubling the damage.
Keep this page bookmarked alongside the calculator: the worked examples below walk through gravity, braking, and elevator specs, the FAQ answers the g-force questions everyone asks, and the converter itself never rounds until the final display — so chained conversions stay exact.
Acceleration is the rate of change of velocity: how many meters per second of speed are gained (or lost) each second. A car accelerating at 3 m/s² gains 3 m/s of speed every second — after 5 seconds it is moving 15 m/s faster than when it started. Negative acceleration (deceleration) is the same quantity pointing backward.
The SI unit, m/s², reads literally: meters per second, per second. American engineering uses ft/s² (1 ft/s² = 0.3048 m/s²). The g is not an SI unit but a ratio — acceleration divided by Earth’s 9.80665 m/s² — beloved wherever humans feel the force: 2 g in a launch, 5 g in a fighter turn, 30+ g in a crash pulse.
Acceleration links to everything in dynamics. Multiply by mass and you get force (F = ma). Multiply by time twice and you get distance (d = ½at²). Convert sloppily and the error infects every downstream number — which is why the converter always shows its work through the SI base.
Key terms:
All conversions route through m/s²: convert the source to SI, then divide by the target unit’s SI factor. Two steps, zero ambiguity, no memorized cross-factors.
Convert standard gravity, 9.80665 m/s², to ft/s².
The famous 32.2 ft/s² — the number every American physics student memorizes, derived in one division.
A sports car brakes from 100 km/h at 8.5 m/s². How many g’s?
Under 1 g — strong braking, but a modern performance car on good tires can briefly exceed 1 g. Crash-test pulses run 20–40 g.
An elevator consultant specifies a maximum acceleration of 3.5 ft/s² for a luxury residential lift — gentle enough that passengers barely feel the start. The installer’s controller, however, programs in m/s²: 3.5 × 0.3048 = 1.0668 m/s² ≈ 1.07. In g’s that is 1.07 ÷ 9.80665 = 0.109 g — about one-ninth of gravity, firmly in the “barely noticeable” band (humans detect around 0.05 g sustained). One conversion chain keeps the spec, the controller, and the comfort analysis consistent.
The jerk limit matters too: the consultant caps jerk at 6 ft/s³ so the acceleration ramps smoothly. Riders feel jerk more than acceleration — a sudden 0.1 g startle is worse than a smooth 0.15 g ramp. Converting the whole motion profile, not just the peak, is what separates a good ride from a complaint.
A second scenario: a drone spec sheet from a European maker lists climb acceleration as 12 km/h/s. The American buyer’s frame of reference is ft/s²: 12 × 0.277778 = 3.333 m/s² = 10.94 ft/s² ≈ 0.34 g. Respectable — about what a brisk elevator does — and now comparable with every US-market competitor.
Galileo’s inclined planes first measured acceleration as a constant: rolling balls gained equal velocity in equal times, implying d ∝ t². Newton made it law — F = ma — turning acceleration into the bridge between force (the cause) and motion (the effect). Every conversion on this page ultimately serves that equation: get a right, and F follows.
Einstein’s equivalence principle then erased the line between acceleration and gravity: being pushed at 1 g in deep space feels identical to standing on Earth. That is why g-force is more than a unit — it is the human body’s native accelerometer. Pilots gray out around 4–6 sustained g’s because blood, obeying F = ma, pools away from the brain; no instrument needed, the body converts.
Modern measurement is the MEMS accelerometer: a microscopic spring-mass etched in silicon, in every phone and airbag sensor. It reports in g’s or m/s² depending on firmware — and the firmware’s conversion factor is exactly the 9.80665 on this page. Your phone’s screen rotation is applied acceleration conversion.
At the extreme, proper acceleration versus coordinate acceleration splits in relativity: an accelerometer in free fall reads zero (you feel weightless) while your coordinate acceleration toward Earth is 9.8 m/s². The converter handles the classical numbers; the philosophy is free.
Engineers also distinguish transient versus sustained acceleration when converting test data. A car crash pulse might peak at 40 g for 3 milliseconds — converting the peak to m/s² (392 m/s²) is trivial, but the injury criterion (HIC, Head Injury Criterion) integrates acceleration over time, so the converted units must stay consistent through the integration. Mixing g’s and m/s² inside one integral is a classic analysis error that this converter’s base-unit display helps prevent: always confirm which unit your time-history data actually uses before integrating.
The sports-science world adds yet another dialect: PlayerLoad and similar wearable metrics accumulate tri-axial accelerometer readings (in g’s) into training-load scores. A soccer player’s 1,000-unit match load traces back to thousands of small accelerations — sprints, jumps, tackles — each converted from raw m/s² sensor output. When comparing devices from different manufacturers, the first question is always the unit under the hood.
Seismologists measure the same quantity on a planetary scale: peak ground acceleration (PGA), reported in g’s or m/s², decides building codes. A 0.4 g design earthquake demands far sturdier frames than a 0.1 g zone, and the maps engineers use are drawn in g — converted to m/s² only when the structural software requires SI. From a phone’s screen rotation to a skyscraper’s survival, acceleration conversion is the quiet infrastructure beneath modern dynamics.
Acceleration conversions via m/s²: ft/s²×0.3048, g×9.80665, (km/h/s)×0.277778 = m/s²; divide by target factor. Standard gravity = 9.80665 m/s² = 32.174 ft/s² = 1 g. g-force = a/9.80665. Source: Sigma Calculator, Acceleration Converter, https://sigmacalculator.net/math-calculators/acceleration-converter/
Cite this page as: Acceleration Converter, Sigma Calculator, https://sigmacalculator.net/math-calculators/acceleration-converter/
Last updated: October 12, 2026