Acceleration Calculator
Acceleration is a vector, and this page keeps it one. Give it two velocities and the time between them and it returns a = (vf - vi)/t with the sign attached: 0 to 20 m/s in 5 s is 4 m/s², a change in velocity of 20 m/s spread over 5 s, and 28 to 0 m/s in 4 s is -7 m/s², negative because it points against the motion and not because slowing down is some other quantity. The same relation runs three more ways, so an initial velocity of 5 m/s pushed at 2 m/s² for 3 s ends at 11 m/s, and the initial velocity or the elapsed time come back out of the other three figures. Velocities take m/s, km/h, cm/s, km/s, ft/s, mph or knots, time takes seconds, milliseconds, minutes or hours, and the answer can be read in m/s², cm/s², ft/s², km/h/s, mph/s or g, so 0 to 100 km/h in 4 s comes back as 6.94444444444 m/s² and the 4 m/s² above is also 0.407886485191 g against standard gravity of 9.80665 m/s². Beside the answer a velocity-time line is drawn straight, with the constant-acceleration assumption written next to it, because what this arithmetic gives is the average acceleration across the interval rather than a reading at one instant. Where the two velocities lie either side of zero the object reverses, and the page names the moment it happens: 28 m/s to -14 m/s over 6 s is -7 m/s² with the velocity passing through zero at 4 s. Figures are shown to twelve significant figures, and nothing here is a distance: it is a kinematics exercise, not a stopping figure.
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.
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. Every line below is computed by the code that answers the calculator above, so the examples and the tool can never disagree.
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.
- Is deceleration just negative acceleration?
- Yes, and this calculator treats it that way rather than as a separate mode. An object going from 28 m/s to 0 m/s in 4 s has an acceleration of -7 m/s²: the minus sign says it points against a velocity that was positive. Enter both velocities as negative and the arithmetic mirrors, so -10 m/s to -20 m/s in 2 s is -5 m/s² and the object is speeding up, not slowing down. A note under the answer says which of the two is happening.
- 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 the average acceleration across the interval you entered, which is what (vf - vi)/t means. Under the constant acceleration the method assumes, that average is also the value at every instant inside the interval, and the velocity-time line is straight for the same reason. If the real motion varied in between, the average stays right and the instantaneous value is not something these three figures can recover. That sentence sits beside the plot with your own numbers in it.
- 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. Choosing a unit changes the display and never the arithmetic.
- 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?
- No, and that is deliberate. This page computes velocities, an acceleration and the time between them, and nothing it prints is a distance. Turning those figures into how far a vehicle travels would make it a road-safety number, which is outside what this tool is built to answer.
- 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 written in full and very large or very small values in exponent form. A subtraction that runs past what a double can hold, or a quotient too small to tell from zero, is refused by name rather than shown as an infinity. 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.
Exact arithmetic on a = (vf - vi)/t in the units you choose, with the sign preserved so slowing down reads as negative rather than as a magnitude. It assumes the acceleration is constant across the interval, which the page states beside the plot. This is a kinematics exercise and produces no stopping distance, reaction allowance or vehicle safety figure.