How do you calculate acceleration?

Subtract the initial velocity from the final one and divide by the time that passed: a = (vf - vi)/t. Going from 0 to 20 m/s in 5 s is a change in velocity of 20 m/s over 5 s, which is 4 m/s². The line of arithmetic is printed under the answer with your own figures in it, so a number typed into the wrong field is easy to spot.

Does slowing down always mean negative acceleration?

Deceleration means acceleration opposite to velocity. For positive motion, 28 m/s to 0 m/s in 4 s gives -7 m/s². For negative motion, -20 m/s to -10 m/s in 2 s gives +5 m/s². Negative acceleration can also speed an object up: -10 m/s to -20 m/s in 2 s gives -5 m/s². Magnitude of a gives the nonnegative size separately.

How do I find final velocity from acceleration and time?

Set Solve for to vf and enter the initial velocity, the acceleration and the time: vf = vi + a t. Starting at 5 m/s with 2 m/s² for 3 s ends at 11 m/s. The vi and t switches run the same relation backwards, so the initial velocity comes out of vi = vf - a t and the elapsed time out of t = (vf - vi)/a.

Is this average acceleration or instantaneous acceleration?

It is average acceleration across the entered interval. The straight plot assumes constant acceleration; under that assumption the average is also the instantaneous value. The tool cannot differentiate a velocity function or read an uploaded graph.

What is 0 to 100 km/h in 4 seconds in m/s squared?

6.94444444444 m/s². The arithmetic runs in SI, so 100 km/h becomes 27.7777777778 m/s first, and a note under the answer shows that conversion. Pick km/h/s in the acceleration menu and the same answer is written as 25 km/h/s.

Can I work in mph, feet per second or g?

Yes. Velocities take m/s, km/h, cm/s, km/s, ft/s, mph or knots, time takes seconds, milliseconds, minutes or hours, and the acceleration is shown in m/s², cm/s², ft/s², km/h/s, mph/s or g. Every factor is a definition rather than a measurement: a foot is 0.3048 m, a mile per hour is 0.44704 m/s, and standard gravity is 9.80665 m/s² exactly, which makes 4 m/s² equal to 0.407886485191 g. Velocity and time selections define the units of your inputs; Acceleration in sets the output unit when solving a, or the input unit in the other modes.

Why can the elapsed time not be zero?

Because a velocity cannot change in no time at all: dividing by zero has no answer, and returning an infinity would be a wrong result that looks like a right one. The tool says so and asks for a time above zero. A negative time is refused the same way, with the reason: time is a length rather than a direction, and the direction belongs in the velocities.

What happens when the velocity changes direction?

The acceleration carries straight through it, and the page marks the instant of the reversal. Something moving at 28 m/s that is moving at -14 m/s six seconds later has an acceleration of -7 m/s² the whole way, with the velocity passing through zero at 4 s. That crossing is marked on the velocity-time line and named in a note, because it is the point a magnitude-only calculator hides.

Does it work out stopping distance or braking distance?

This page solves a = (vf - vi)/t and its rearrangements. It accepts no distance, force, mass, radius or angle inputs, and does not calculate stopping distance or vehicle safety figures.

How precise are the results, and are my numbers stored anywhere?

The arithmetic is ordinary double precision, the same as a spreadsheet, and figures are shown to twelve significant figures, with whole numbers below 1e15 written in full and very large or very small values in exponent form. Nonfinite results, nonzero values lost to zero during parsing or conversion, and nonzero velocity changes too small next to an endpoint to resolve are refused by name. Try a different output unit or representable figures. Entries longer than 200 characters are refused by length instead of being cut down. Everything stays in this browser: the last set you typed is remembered locally so the page opens where you left it, and if storage is blocked the calculator still works, it simply forgets.

How do I calculate acceleration in g or convert g to velocity?

To express a result in g, select a under Solve for, enter both velocities and elapsed time, then set Acceleration in to g. To use 1 g, select vf, set Acceleration in to g, enter acceleration 1, and supply initial velocity and elapsed time. Standard g is 9.80665 m/s²; it is a unit reference, not a calculation of local gravity.

How does integrating constant acceleration give velocity?

For constant acceleration, the integral over an elapsed time t is a t, so final velocity is vf = vi + a t. Select vf under Solve for and enter initial velocity 5 m/s, acceleration 2 m/s² and time 3 s: the result is 11 m/s. This operation integrates a numerical constant only; it does not accept acceleration functions or sampled acceleration-time data.

Can I calculate acceleration without the final velocity?

Calculating a here requires both endpoint velocities and elapsed time. The vf mode calculates a missing final velocity when you already know acceleration; it cannot calculate that acceleration without another independent relation. This page has no displacement or force input.

Acceleration Calculator

Enter three values to solve acceleration, initial velocity, final velocity or elapsed time on one signed axis. The result includes numeric working, acceleration magnitude and a straight velocity-time plot assuming constant acceleration. Use a minus sign for the opposite direction and choose units for velocity, time and acceleration.

Acceleration4 m/s²0 → 20 m/s in 5 s · a = (vf - vi)/t · constant acceleration

Solve for

Initial velocity

Final velocity

Velocity in

Acceleration in

Elapsed time

Time in

Enter both velocities and the time between them. The answer is the average acceleration across that interval, signed: a velocity that falls gives a negative number.

a: 4 m/s²

Magnitude of a: 4 m/s²

Change in v: 20 m/s

Time: 5 s

Solving: a

a = (20 m/s − 0 m/s) ÷ 5 s = 4 m/s²

Velocity against time, drawn straight because the acceleration is taken as constant across the interval. 4 m/s² is the average acceleration over 5 s: it is the instantaneous acceleration at every moment inside that interval only if the acceleration really held constant.

The speed rises from 0 m/s to 20 m/s, so the acceleration points the same way as the motion: 4 m/s².

That is 0.407886485191 g, taking standard gravity as 9.80665 m/s² exactly.

Three cases, worked

One speeding up, one slowing down, and a final velocity solved forwards.

0 to 20 m/s in 5 ssolve a
4 m/s²
28 to 0 m/s in 4 sslowing down
-7 m/s², sign kept
vi 5 m/s, a 2 m/s², t 3 ssolve vf
11 m/s

Accuracy. Exact arithmetic on a = (vf - vi)/t in the units you choose is represented with double-precision rounding. Results retain direction, with the sign preserved so slowing down reads as negative for positive velocity and positive for negative velocity. It assumes the acceleration is constant across the interval, which the page states in the plot's caption. This is a kinematics exercise and produces no stopping distance, reaction allowance or vehicle safety figure.

Common questions

How do you calculate acceleration?: Subtract the initial velocity from the final one and divide by the time that passed: a = (vf - vi)/t. Going from 0 to 20 m/s in 5 s is a change in velocity of 20 m/s over 5 s, which is 4 m/s². The line of arithmetic is printed under the answer with your own figures in it, so a number typed into the wrong field is easy to spot.
Does slowing down always mean negative acceleration?: Deceleration means acceleration opposite to velocity. For positive motion, 28 m/s to 0 m/s in 4 s gives -7 m/s². For negative motion, -20 m/s to -10 m/s in 2 s gives +5 m/s². Negative acceleration can also speed an object up: -10 m/s to -20 m/s in 2 s gives -5 m/s². Magnitude of a gives the nonnegative size separately.
How do I find final velocity from acceleration and time?: Set Solve for to vf and enter the initial velocity, the acceleration and the time: vf = vi + a t. Starting at 5 m/s with 2 m/s² for 3 s ends at 11 m/s. The vi and t switches run the same relation backwards, so the initial velocity comes out of vi = vf - a t and the elapsed time out of t = (vf - vi)/a.
Is this average acceleration or instantaneous acceleration?: It is average acceleration across the entered interval. The straight plot assumes constant acceleration; under that assumption the average is also the instantaneous value. The tool cannot differentiate a velocity function or read an uploaded graph.
What is 0 to 100 km/h in 4 seconds in m/s squared?: 6.94444444444 m/s². The arithmetic runs in SI, so 100 km/h becomes 27.7777777778 m/s first, and a note under the answer shows that conversion. Pick km/h/s in the acceleration menu and the same answer is written as 25 km/h/s.
Can I work in mph, feet per second or g?: Yes. Velocities take m/s, km/h, cm/s, km/s, ft/s, mph or knots, time takes seconds, milliseconds, minutes or hours, and the acceleration is shown in m/s², cm/s², ft/s², km/h/s, mph/s or g. Every factor is a definition rather than a measurement: a foot is 0.3048 m, a mile per hour is 0.44704 m/s, and standard gravity is 9.80665 m/s² exactly, which makes 4 m/s² equal to 0.407886485191 g. Velocity and time selections define the units of your inputs; Acceleration in sets the output unit when solving a, or the input unit in the other modes.
Why can the elapsed time not be zero?: Because a velocity cannot change in no time at all: dividing by zero has no answer, and returning an infinity would be a wrong result that looks like a right one. The tool says so and asks for a time above zero. A negative time is refused the same way, with the reason: time is a length rather than a direction, and the direction belongs in the velocities.
What happens when the velocity changes direction?: The acceleration carries straight through it, and the page marks the instant of the reversal. Something moving at 28 m/s that is moving at -14 m/s six seconds later has an acceleration of -7 m/s² the whole way, with the velocity passing through zero at 4 s. That crossing is marked on the velocity-time line and named in a note, because it is the point a magnitude-only calculator hides.
Does it work out stopping distance or braking distance?: This page solves a = (vf - vi)/t and its rearrangements. It accepts no distance, force, mass, radius or angle inputs, and does not calculate stopping distance or vehicle safety figures.
How precise are the results, and are my numbers stored anywhere?: The arithmetic is ordinary double precision, the same as a spreadsheet, and figures are shown to twelve significant figures, with whole numbers below 1e15 written in full and very large or very small values in exponent form. Nonfinite results, nonzero values lost to zero during parsing or conversion, and nonzero velocity changes too small next to an endpoint to resolve are refused by name. Try a different output unit or representable figures. Entries longer than 200 characters are refused by length instead of being cut down. Everything stays in this browser: the last set you typed is remembered locally so the page opens where you left it, and if storage is blocked the calculator still works, it simply forgets.
How do I calculate acceleration in g or convert g to velocity?: To express a result in g, select a under Solve for, enter both velocities and elapsed time, then set Acceleration in to g. To use 1 g, select vf, set Acceleration in to g, enter acceleration 1, and supply initial velocity and elapsed time. Standard g is 9.80665 m/s²; it is a unit reference, not a calculation of local gravity.
How does integrating constant acceleration give velocity?: For constant acceleration, the integral over an elapsed time t is a t, so final velocity is vf = vi + a t. Select vf under Solve for and enter initial velocity 5 m/s, acceleration 2 m/s² and time 3 s: the result is 11 m/s. This operation integrates a numerical constant only; it does not accept acceleration functions or sampled acceleration-time data.
Can I calculate acceleration without the final velocity?: Calculating a here requires both endpoint velocities and elapsed time. The vf mode calculates a missing final velocity when you already know acceleration; it cannot calculate that acceleration without another independent relation. This page has no displacement or force input.

Exact arithmetic on a = (vf - vi)/t in the units you choose is represented with double-precision rounding. Results retain direction, with the sign preserved so slowing down reads as negative for positive velocity and positive for negative velocity. It assumes the acceleration is constant across the interval, which the page states in the plot's caption. This is a kinematics exercise and produces no stopping distance, reaction allowance or vehicle safety figure.