Acceleration Calculator

Acceleration is calculated as the change in velocity divided by the time taken: a = (v − u) / t, where v is the final velocity, u is the initial velocity, and t is the elapsed time. The result is in metres per second squared (m/s²).

A negative acceleration (also called deceleration) means the object is slowing down in the positive direction — its velocity is decreasing over time. For example, a car braking from 30 m/s to 10 m/s in 5 seconds has an acceleration of −4 m/s².

The SI unit of acceleration is the metre per second squared (m/s²). It means the velocity changes by that many metres per second for every second that passes. Standard gravitational acceleration at Earth's surface is approximately 9.81 m/s² (more precisely 9.80665 m/s² by definition).

Average acceleration is the total change in velocity divided by the total time interval — this is what the formula a = (v − u)/t computes. Instantaneous acceleration is the rate of velocity change at a single moment in time (the derivative dv/dt). They are equal only when acceleration is constant throughout the interval.

Yes. If you know the initial velocity, final velocity, and displacement, you can use the kinematic equation a = (v² − u²) / (2d). If you know the net force acting on an object and its mass, Newton's second law gives a = F / m. This calculator uses the time-based form as the primary method.

If you know the displacement d, initial velocity u, and time t, rearrange the kinematic equation: a = 2(d − u·t) / t². For example, a car starting from rest (u = 0) that travels 100 m in 10 s has acceleration a = 2×100/100 = 2 m/s².

G-force expresses acceleration as a multiple of standard gravity g = 9.80665 m/s². An acceleration of 9.80665 m/s² is 1 g, 19.613 m/s² is 2 g, and so on. To convert an acceleration in m/s² to g, divide by 9.80665.

Acceleration is a vector quantity — it has both magnitude and direction. In one-dimensional problems (like this calculator), direction is captured by the sign: positive acceleration means speeding up in the positive direction, negative means decelerating or moving faster in the negative direction.

Enter the initial velocity as 0, the final velocity in m/s (divide km/h by 3.6 to convert — e.g. 100 km/h ≈ 27.78 m/s), and the time in seconds. The result is the average acceleration in m/s². Divide by 9.80665 to express it in g-forces.

If u = v, the change in velocity is zero, so the acceleration is exactly 0 m/s². The object is moving at a constant speed — neither speeding up nor slowing down.

Division by zero (t = 0) is mathematically undefined — you cannot compute a rate of change over no time interval. The calculator enforces a minimum of 0.001 seconds to prevent this.

This formula assumes constant (uniform) acceleration over the interval and Newtonian (non-relativistic) mechanics. It gives AVERAGE acceleration, not instantaneous acceleration when the rate of speed change varies. At speeds approaching the speed of light, relativistic mechanics must be used instead.

Velocity is the rate at which an object changes its position — how fast it is moving and in which direction — measured in metres per second (m/s). Acceleration is the rate at which velocity itself changes over time, measured in metres per second squared (m/s²). An object can have a high velocity yet zero acceleration (constant-speed straight-line motion), or low velocity with high acceleration (a stationary car that suddenly floors the throttle).

According to Newton's second law, F = m × a, so for a fixed applied force, acceleration is inversely proportional to mass: a = F / m. Double the mass of an object and you halve its acceleration (assuming the same net force). This is why a loaded lorry accelerates far more slowly than a sports car with the same engine output — the extra mass resists the change in motion.