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Acceleration Calculator

Calculate acceleration from velocity, time, distance, or force and mass. Supports m/s², g-force, ft/s², and Gal units with step-by-step solutions.

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Acceleration m/s²
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About

Acceleration quantifies the rate of change of velocity per unit time. Miscalculating a in engineering contexts leads to structural overloads, incorrect braking distances, or failed launch trajectories. This tool computes acceleration across four standard kinematic and dynamic formulas: from initial and final velocities with time or displacement, from net force and mass via Newton's Second Law, and from displacement with initial velocity over time. Results are cross-converted into m/s2, ft/s2, g-force, km/h/s, and Gal (cm/s2). All calculations assume constant (uniform) acceleration. For non-uniform or angular acceleration problems, this linear model will not apply.

Pro tip: when working with real vehicle data, account for reaction time before braking begins. The tool uses the standard kinematic equations valid in classical mechanics. At relativistic speeds (appreciable fractions of c), Newtonian formulas break down and Lorentz transformations are required.

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Formulas

The calculator implements four kinematic and dynamic equations for constant acceleration.

Mode 1 - From velocities and time:

a = v − ut

Mode 2 - From velocities and distance:

a = v2 − u22d

Mode 3 - Newton's Second Law:

a = Fm

Mode 4 - From distance, initial velocity, and time:

a = 2(d − ut)t2

where a = acceleration, v = final velocity, u = initial velocity, t = time elapsed, d = displacement, F = net force in N, m = mass in kg. Unit conversions use: 1 g = 9.80665 m/s2, 1 ft/s2 = 0.3048 m/s2, 1 Gal = 0.01 m/s2, 1 km/h/s = 0.27778 m/s2.

Reference Data

QuantityDescriptionTypical ValueUnit
Free fall on EarthStandard gravitational acceleration9.80665m/s2
Free fall on MoonLunar surface gravity1.625m/s2
Free fall on MarsMartian surface gravity3.72076m/s2
Free fall on JupiterJovian surface gravity24.79m/s2
Free fall on VenusVenusian surface gravity8.87m/s2
Free fall on SaturnSaturnian surface gravity10.44m/s2
Car (0-100 km/h in 8 s)Typical sedan acceleration3.47m/s2
Sports car (0-100 km/h in 3 s)High-performance vehicle9.26m/s2
Fighter jet catapult launchAircraft carrier steam catapult31m/s2
Space Shuttle at launchPeak during ascent ≈ 3 g29.4m/s2
Human tolerance (sustained)Trained pilot in g-suit, eyeballs-in88.3 (9 g)m/s2
Bullet in barrelRifle projectile acceleration9.8 × 105m/s2
Hard disk read headMicro-electromechanical5,500m/s2
Cheetah (0-100 km/h in 3 s)Fastest land animal sprint9.3m/s2
Electron in CRTCathode ray tube beam4 × 1014m/s2
1 GalCGS unit of acceleration0.01m/s2
1 g-forceStandard gravity equivalent9.80665m/s2
1 ft/s2Imperial acceleration unit0.3048m/s2
1 km/h/sVelocity change per second0.27778m/s2
Braking deceleration (dry road)Typical emergency braking−9.8m/s2

Frequently Asked Questions

Deceleration is simply negative acceleration. If the final velocity v is less than the initial velocity u, the calculator returns a negative value for a. A result of −5 m/s2 means the object is slowing down at 5 m/s2. The sign convention follows the standard physics convention where positive is in the direction of initial motion.
Both modes assume constant acceleration but use different known quantities. Mode 1 uses a = (v − u) / t, while Mode 2 uses a = (v2 − u2) / (2d). If your measured time or distance contains errors, the results diverge. Cross-checking with both modes is a standard validation technique in experimental physics.
The calculator uses the exact standard gravity constant gn = 9.80665 m/s2 as defined by the 3rd CGPM (1901). This is a conventional value. Actual gravitational acceleration varies from approximately 9.764 m/s2 at the equator to 9.832 m/s2 at the poles due to Earth's oblate shape and centrifugal effects.
No. All four formulas assume constant acceleration over the interval. For variable acceleration, you need the instantaneous form a(t) = dv/dt, which requires calculus-based integration of velocity data. If your acceleration changes significantly during the interval, break it into smaller constant-acceleration segments and compute each separately.
Division by zero is mathematically undefined. If t = 0 in Mode 1 or Mode 4, or d = 0 in Mode 2, the calculator will display an error message instead of a result. Physically, zero elapsed time with a velocity change implies infinite acceleration, which is non-physical in classical mechanics.
Use the km/h/s output directly. For example, if a car accelerates from 0 to 100 km/h in 8 s, enter u = 0 and v = 27.778 m/s (since 100 km/h = 27.778 m/s). The result in km/h/s will read 12.5, meaning the vehicle gains 12.5 km/h every second.