🚀 Acceleration Conversion Calculator
Convert between m/s², g-force, ft/s², Gal (galileo), km/h·s, mph/s, mGal, in/s² and 20+ units — with kinematics, SUVAT equations, centripetal, SHM, angular, Coriolis & gravitational acceleration formulas in MathJax
🔄 Acceleration Unit Converter
🌍 All Units at Once
📖 How to Use This Acceleration Conversion Calculator
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1Filter by Unit Category (Optional)
Click SI/Metric (m/s², km/s², cm/s²), Imperial/US (ft/s², in/s², mi/s²), Geophysical (Gal, mGal, cGal), or Practical (g-force, km/h·s, mph/s) to narrow the dropdowns. "All Units" shows all 22 units together.
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2Enter Your Acceleration Value
Type the value into "Enter Value." Accepts any numeric input — from milligals (geophysics gravity surveys) to km/s² (rocket propulsion). Scientific notation auto-applies for extreme values.
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3Select From and To Units
Choose source in "From Unit" and target in "To Unit." The result and exact conversion factor appear instantly in the teal result box below.
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4Use Quick-Convert Buttons
Click preset buttons — m/s²↔g, m/s²↔ft/s², m/s²→Gal, km/h·s→m/s², g→ft/s² — for the most common acceleration conversions. Both dropdowns update automatically.
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5View All Units & Copy
"All Units at Once" shows your acceleration in every supported unit simultaneously. Click "📋 Copy Result" to copy the primary conversion for engineering reports, physics coursework, or automotive testing.
📐 Acceleration Unit Conversion Factors
| Unit | Symbol | In m/s² | Math | Typical Use |
|---|---|---|---|---|
| Metre/s² | m/s² | 1 (base) | \(1\,\text{m/s}^2\) | SI standard, all physics |
| Standard gravity | g / gₙ | 9.80665 | \(g_n = 9.80665\,\text{m/s}^2\) | Aerospace, automotive G-loads |
| Foot/s² | ft/s² | 0.3048 | \(0.3048\,\text{m/s}^2\) | US/Imperial engineering |
| Inch/s² | in/s² | 0.0254 | \(0.0254\,\text{m/s}^2\) | Precision mechanics |
| km/h per second | km/h·s | 0.277778 | \(1000/3600\,\text{m/s}^2\) | Vehicle performance specs |
| mph per second | mph/s | 0.44704 | \(0.44704\,\text{m/s}^2\) | US automotive testing |
| Gal (galileo) | Gal | 0.01 | \(10^{-2}\,\text{m/s}^2\) | Geophysics, gravimetry |
| Milligal | mGal | 1×10⁻⁵ | \(10^{-5}\,\text{m/s}^2\) | Precision gravity surveys |
| Kilometre/s² | km/s² | 1,000 | \(10^3\,\text{m/s}^2\) | Rocket propulsion |
| cm/s² | cm/s² | 0.01 | \(10^{-2}\,\text{m/s}^2\) | CGS system (= 1 Gal) |
🚀 Understanding Acceleration — A Complete Physics & Engineering Guide
Acceleration is one of the three fundamental kinematic quantities — alongside position and velocity — that completely describe the motion of any object. While velocity tells you how fast something is moving and in what direction, acceleration tells you how quickly that velocity is changing. A car speeding up, a ball thrown upward and decelerating under gravity, a spacecraft firing its rockets, a seismometer detecting ground tremors, or a fighter pilot pulling out of a dive all experience acceleration — just at vastly different magnitudes and in many different unit systems.
Accurately converting between acceleration units is critical in automotive engineering (0–60 mph performance), aerospace (G-load tolerance), geophysics (gravity surveys in milligals), physics education (SUVAT kinematics), and structural engineering (earthquake response spectra). This guide covers every acceleration unit, every key formula, and practical worked examples across all these domains.
🌍 Standard Gravity & G-Force — The Most Important Acceleration Reference
Standard gravity (\(g_n\)) is the defined acceleration due to gravity at Earth's surface, adopted by the CGPM (General Conference on Weights and Measures) as the exact value \(9.80665\,\text{m/s}^2\). This is used as the reference point for g-force — the ratio of an acceleration to standard gravity — and is the foundation of force unit conversions between SI (N) and gravitational (kgf, lbf) systems.
In engineering and physiology, g-force (G) is far more intuitive than m/s² for expressing human experience. "You feel 3 G" is immediately meaningful; "you experience 29.4 m/s²" is not. G-force is standard in aerospace, automotive crash testing, roller coaster design, military aviation, and sports medicine.
\( g_n = 9.80665\,\text{m/s}^2 \quad \text{(exact, defined by CGPM 1901)} \)
\( G = \frac{a}{g_n} \qquad a\,[\text{m/s}^2] = G \times 9.80665 \)
\( g_n = 9.80665\,\text{m/s}^2 = 32.17405\,\text{ft/s}^2 = 980.665\,\text{Gal} = 980665\,\text{mGal} \)
\( 1\,G \approx 0\text{–}1G: \text{normal human activity} \quad 3\text{–}9G: \text{fighter pilot manoeuvres} \quad {>}16G: \text{usually fatal} \)
Problem: An F-16 pilot pulling a hard turn experiences 7.5 G. Express this in m/s², ft/s², and km/h·s.
m/s²: \( 7.5 \times 9.80665 = \mathbf{73.55\,\text{m/s}^2} \)
ft/s²: \( 73.55 \div 0.3048 = \mathbf{241.3\,\text{ft/s}^2} \)
km/h·s: \( 73.55 \div 0.27778 = \mathbf{264.8\,\text{km/h·s}} \) (velocity increases by 264.8 km/h every second)
Context: Human G-force tolerance: ~1 G sustained comfortable, ~4–6 G with anti-G suit sustainable, ~9 G brief maximum with training. At 7.5 G without protective equipment, blood pools in the legs, causing unconsciousness (G-LOC) within 3–5 seconds.
📐 SUVAT Equations — Kinematics of Constant Acceleration
When acceleration is constant (uniform), five kinematic quantities are linked by the SUVAT equations: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). These equations are the backbone of classical mechanics — used in everything from projectile calculations to vehicle braking distance to orbital mechanics.
\( v = u + at \qquad \text{(velocity after time } t) \)
\( s = ut + \tfrac{1}{2}at^2 \qquad \text{(displacement in time } t) \)
\( v^2 = u^2 + 2as \qquad \text{(velocity at displacement } s) \)
\( s = \tfrac{1}{2}(u + v)t \qquad \text{(displacement from average velocity)} \)
\( s = vt - \tfrac{1}{2}at^2 \qquad \text{(displacement using final velocity)} \)
Problem: A Tesla Model S accelerates from 0 to 100 km/h (27.78 m/s) in 2.1 seconds. Find the average acceleration in m/s², g-force, ft/s², and mph/s.
Step 1: \( a = \frac{v - u}{t} = \frac{27.78 - 0}{2.1} = \mathbf{13.23\,\text{m/s}^2} \)
G-force: \( G = 13.23 / 9.80665 = \mathbf{1.35\,G} \)
ft/s²: \( 13.23 / 0.3048 = \mathbf{43.4\,\text{ft/s}^2} \)
mph/s: \( 13.23 / 0.44704 = \mathbf{29.6\,\text{mph/s}} \)
Distance travelled: \( s = \frac{1}{2} \times 13.23 \times 2.1^2 = \mathbf{29.2\,\text{m}} \) — less than 30 metres to reach 100 km/h.
⭕ Centripetal Acceleration — Circular Motion
Any object moving in a circle at constant speed is continuously accelerating — not because its speed changes, but because its direction changes continuously. This is centripetal acceleration, always directed toward the centre of the circular path. It is why a car turning a corner needs grip from the road (the centripetal force), and why satellites in orbit are in continuous free-fall toward Earth.
\( a_c = \frac{v^2}{r} = \omega^2 r = \frac{4\pi^2 r}{T^2} \)
\( F_c = m a_c = \frac{mv^2}{r} \qquad \text{(centripetal force, always inward)} \)
\( v = \omega r \qquad \omega = \frac{2\pi}{T} = 2\pi f \)
Problem: A car rounds a motorway on-ramp at 60 km/h (16.67 m/s) with radius 50 m. Find centripetal acceleration in m/s² and G.
\[ a_c = \frac{v^2}{r} = \frac{16.67^2}{50} = \frac{277.9}{50} = \mathbf{5.56\,\text{m/s}^2} \]
G-force: \( 5.56 / 9.80665 = \mathbf{0.567\,G} \)
Context: A typical road tyre can sustain ~0.85 G lateral. At 0.567 G the car is within limits. If the driver increases speed to 80 km/h on the same corner: \(a_c = 22.22^2/50 = 9.88\,\text{m/s}^2 = 1.01\,G\) — beyond typical tyre limits, leading to a slide.
🌊 Acceleration in Simple Harmonic Motion (SHM)
\( a = -\omega^2 x \qquad \text{(SHM restoring acceleration)} \)
\( |a_{\max}| = \omega^2 A \qquad \text{(maximum at extreme displacement, } x = \pm A) \)
\( x(t) = A\cos(\omega t + \phi) \qquad v(t) = -A\omega\sin(\omega t + \phi) \qquad a(t) = -A\omega^2\cos(\omega t + \phi) \)
\( \omega = 2\pi f = \frac{2\pi}{T} \qquad T_{\text{pendulum}} = 2\pi\sqrt{\frac{L}{g}} \qquad T_{\text{spring}} = 2\pi\sqrt{\frac{m}{k}} \)
🌐 The Gal (Galileo) — Geophysics & Gravity Surveys
The gal (symbol Gal, also called the galileo in honour of Galileo Galilei) is a CGS unit of acceleration equal to exactly 1 cm/s² = 0.01 m/s². It was adopted by geophysicists and geodesists specifically because Earth's gravitational field varies by only a few parts per million from place to place — values that are cumbersome to express in m/s² or g-units. The gal, and especially the milligal (mGal = 0.001 Gal = 10⁻⁵ m/s²), are the operational units of modern gravimetry.
\( 1\,\text{Gal} = 1\,\text{cm/s}^2 = 0.01\,\text{m/s}^2 = 10^{-2}\,\text{m/s}^2 \)
\( 1\,\text{mGal} = 10^{-3}\,\text{Gal} = 10^{-5}\,\text{m/s}^2 \)
\( g_n = 9.80665\,\text{m/s}^2 = 980.665\,\text{Gal} = 980{,}665\,\text{mGal} \)
\( \Delta g_{\text{typical variation}} \approx 100\text{–}500\,\text{mGal} \quad \text{(equator to pole)} \)
🔄 Angular Acceleration — Rotational Kinematics
\( \alpha = \frac{d\omega}{dt} \qquad \text{(angular acceleration, rad/s}^2\text{)} \)
\( a_{\text{tangential}} = \alpha \times r \qquad \text{(linear acceleration at radius } r) \)
\( a_{\text{total}} = \sqrt{a_t^2 + a_c^2} = \sqrt{(\alpha r)^2 + (\omega^2 r)^2} = r\sqrt{\alpha^2 + \omega^4} \)
\( \omega = \omega_0 + \alpha t \qquad \theta = \omega_0 t + \tfrac{1}{2}\alpha t^2 \qquad \omega^2 = \omega_0^2 + 2\alpha\theta \)
🏎️ Vehicle Acceleration — km/h·s, mph/s & Real-World Performance
In automotive engineering and consumer performance reporting, acceleration is expressed in two practical units that relate directly to how drivers experience it:
- km/h per second (km/h·s): How many km/h of speed the vehicle gains each second. 1 km/h·s = 1000/3600 m/s² = 0.27778 m/s².
- miles per hour per second (mph/s): The US equivalent. 1 mph/s = 0.44704 m/s². A 0–60 mph car test covering 60 mph / time_in_seconds gives the average acceleration in mph/s.
\( 1\,\text{km/h·s} = \frac{1000}{3600}\,\text{m/s}^2 = 0.27\overline{7}\,\text{m/s}^2 \)
\( 1\,\text{mph/s} = 0.44704\,\text{m/s}^2 \quad \text{(exact: 1609.344 m/mile ÷ 3600)} \)
\( a_{\text{avg}} = \frac{\Delta v}{t} \qquad \text{0–100 km/h in 4 s:} \quad a = \frac{100\,\text{km/h·s}}{4} = 25\,\text{km/h·s} = 6.944\,\text{m/s}^2 = 0.708\,G \)
\( s_{0-60} = \frac{v^2}{2a} = \frac{(26.82)^2}{2 \times 4.47} = \frac{719.3}{8.94} = 80.5\,\text{m} \quad \text{(0–60 mph in 6 s)} \)
🌍 Real-World Acceleration Reference Table
| Object / Event | m/s² | G-Force | Notes |
|---|---|---|---|
| 🐌 Slow elevator start | 0.5–1 | 0.05–0.10 G | Barely perceptible |
| 🚗 Average car braking | 4–8 | 0.4–0.8 G | Friction-limited by tyre |
| ⬇️ Earth free fall (sea level) | 9.80665 | 1.000 G | Standard gravity —exact definition |
| 🚗 Tesla Model 3 0–100 km/h | ~9.5 | ~0.97 G | 3.1 s (Performance variant) |
| ✈️ Commercial airline takeoff | 2–4 | 0.2–0.4 G | Passenger-comfort limited |
| 🏎️ Formula 1 braking | 40–60 | 4–6 G | Carbon-ceramic brakes + downforce |
| 🎢 Roller coaster peak | 29–59 | 3–6 G | Brief, 0.3–1 s |
| ✈️ F-16 hard turn | ~73 | ~7.5 G | Anti-G suit required |
| 🚀 Space Shuttle launch | ~29 | ~3 G | Max at main engine cutoff |
| 💥 Car crash airbag trigger | 200–1000 | 20–100 G | ~1 ms duration |
| 🔫 Bullet in gun barrel | ~500,000 | ~50,000 G | Very brief; ~1 ms |
📦 Acceleration Unit System Guide
m/s² — SI Standard
The SI unit. 1 m/s² = the acceleration that changes velocity by 1 m/s each second. Universal in physics, engineering, and all scientific computing. \(g_n = 9.80665\,\text{m/s}^2\) sets the scale for G-loads.
g-force (G) — Aerospace & Human Tolerance
\(1\,G = g_n = 9.80665\,\text{m/s}^2\). The intuitive unit for human experience and aerospace. Sustained: 0–1 G normal, 4–6 G trained pilots, 9+ G extreme brief. Converts: G × 9.80665 = m/s².
Gal & mGal — Geophysics
\(1\,\text{Gal} = 0.01\,\text{m/s}^2\). \(1\,\text{mGal} = 10^{-5}\,\text{m/s}^2\). Geophysics, gravimetry, seismology. Earth's gravity range: 978–983 Gal. Gravity surveys detect oil/water at µGal precision.
km/h·s & mph/s — Automotive
\(1\,\text{km/h·s} = 0.2778\,\text{m/s}^2\). \(1\,\text{mph/s} = 0.4470\,\text{m/s}^2\). Used in vehicle performance specs — 0 to 100 km/h, 0 to 60 mph tests. Directly links time and velocity gain.