Acceleration Calculator

The standard formula is a = (v - u) / t, where a is acceleration in m/s², v is final velocity in m/s, u is initial velocity in m/s, and t is time in seconds. This can be rearranged to find final velocity (v = u + at) or time (t = (v - u) / a). It is the first of the five SUVAT kinematic equations for uniform acceleration.

The SI unit of acceleration is metres per second squared (m/s²). This means the velocity changes by that many m/s every second. Acceleration is also commonly expressed in g (multiples of standard gravity, 9.80665 m/s²) or ft/s² in some engineering contexts. A car accelerating at 3 m/s² gains 3 m/s of speed every second.

Deceleration is simply negative acceleration, which means the object is slowing down. If a car brakes from 20 m/s to 0 m/s in 4 seconds, the acceleration is (0 - 20) / 4 = -5 m/s². There is no separate formula for deceleration; you just get a negative result. Speed (magnitude of velocity) decreases when acceleration opposes the direction of motion.

1 m/s² = 1 / 9.80665 g, which is approximately 0.102 g. Conversely, 1 g = 9.80665 m/s². The g unit is useful in aviation and motorsport because humans feel acceleration as a fraction of gravity. A jet fighter pulling 6 g is accelerating at 6 x 9.80665 = 58.84 m/s².

Uniform (constant) acceleration means the rate of change of velocity is the same at every instant. All SUVAT equations, including a = (v - u) / t, assume uniform acceleration. Free fall near Earth's surface (ignoring air resistance) is the classic example: every object accelerates at g = 9.8 m/s² regardless of mass. Non-uniform acceleration requires calculus.

If you know distance (s), initial velocity (u), and time (t), use the SUVAT equation: a = 2(s - ut) / t². If the object starts from rest (u = 0), this simplifies to a = 2s / t². For example, a car starting from rest covers 50 m in 5 s: a = 2 x 50 / 5² = 4 m/s². The Kinematics Calculator at /science/physics/kinematic-equations-calculator/ handles all five SUVAT equations.

The standard value is g = 9.80665 m/s² (exactly, by definition of the standard). In practice, g varies slightly with latitude and altitude: 9.78 m/s² at the equator and 9.83 m/s² at the poles. For most physics problems and this calculator, g = 9.8 m/s² is used. On the Moon g is about 1.62 m/s², on Mars about 3.72 m/s².

By Newton's second law, F = ma, so a = F / m. A net force of 100 N acting on a 20 kg object produces an acceleration of 5 m/s². This formula gives instantaneous acceleration for a given net force; it does not require uniform acceleration. For force-based calculations, use the Force Calculator at /science/physics/force-calculator/.

Yes. A negative acceleration value (also called deceleration or retardation) means the object is slowing down (when it is already moving in the positive direction) or speeding up in the negative direction. The sign of acceleration is determined by the direction you define as positive. There is nothing physically special about a negative value, which is a sign convention.

Average acceleration = (v - u) / t over a time interval. Instantaneous acceleration is the limit of average acceleration as the time interval approaches zero, equal to the derivative dv/dt. For uniform acceleration they are equal. For variable acceleration (e.g. a car engine producing different power at different speeds), only instantaneous acceleration equals dv/dt at each moment.

Use the SUVAT equation s = ut + 0.5at². For a car starting from rest (u = 0) and accelerating at 4 m/s² for 5 seconds: s = 0 x 5 + 0.5 x 4 x 25 = 50 m. This calculator shows displacement automatically for every calculation. Alternatively, use s = (u + v) / 2 x t if you know initial and final velocities.

100 km/h = 27.78 m/s. Using a = (v - u) / t with u = 0, v = 27.78 m/s, t = 8 s: a = 27.78 / 8 = 3.47 m/s² = 0.354 g. Most family cars fall in the 2.5 to 4 m/s² range. Sports cars can exceed 10 m/s² (about 1 g), and dragsters can reach 30 m/s² (about 3 g).