Math & Science
Acceleration Calculator
Acceleration from a change in speed — with g-force and the distance covered alongside.
Acceleration Calculator
About the Acceleration Calculator
Acceleration is how fast a velocity changes. Subtract the starting speed from the finishing speed, divide by the time it took, and that is your answer in metres per second squared. This calculator does that, and solves the same equation backwards for whichever quantity you are missing.
Give it any three of initial velocity, final velocity, time and acceleration, and it returns the fourth. Alongside the answer it reports the g-force — the acceleration as a multiple of Earth's gravity — and the distance covered during the change, using s = ut + ½at².
Negative results are kept as negatives rather than hidden. A car braking has negative acceleration, and that sign carries real information about direction, so the tool preserves it.
How to use the Acceleration Calculator
- Choose which variable to solve for.
- Enter the other three in metres per second and seconds.
- Optionally add a mass to get the force needed.
- Select Calculate.
- The g-force figure puts the number in context — 1 g is gravity at sea level.
The acceleration formula (acceleration equation)
a = (v − u) ÷ t
u = initial velocity, v = final velocity, t = time taken. Units: m/s².
Two companion equations come from the same motion, and the calculator applies them automatically:
s = ut + ½at² (distance travelled)
F = ma (force needed, from Newton's second law)
Worked example
A car goes from rest to 27 m/s (about 60 mph) in 6.5 seconds.
a = (27 − 0) ÷ 6.5 = 4.15 m/s²
As a fraction of gravity: 4.15 ÷ 9.80665 = 0.42 g.
Distance covered: s = 0 × 6.5 + ½ × 4.15 × 6.5² = 87.7 metres.
4.15 m/s² — 0.42 g — 87.7 m travelled
What g-force means
One g is standard gravity, defined exactly as 9.80665 m/s². Expressing an acceleration in g gives it a sense of scale, because everyone has a body-level intuition for what gravity feels like.
| Situation | Approx. acceleration | In g |
|---|---|---|
| Passenger lift starting | 1 m/s² | 0.1 g |
| Family car, 0–60 mph in 9 s | 3.0 m/s² | 0.31 g |
| Sports car, 0–60 mph in 4 s | 6.7 m/s² | 0.68 g |
| Hard emergency braking | 8 m/s² | 0.8 g |
| Free fall (no air resistance) | 9.81 m/s² | 1.0 g |
| Roller coaster peak | 39 m/s² | 4 g |
| Fighter pilot, sustained limit | 88 m/s² | 9 g |
Sitting still, you already feel 1 g — the ground pushing up. The unpleasant sensation in a fast lift or a hard corner is the change from that baseline, not the total.
Negative acceleration
A negative value means the acceleration points opposite to the direction you called positive. In everyday terms that usually means slowing down, and people call it deceleration. Physics keeps one word and lets the sign do the work.
The sign only means "slowing" when the object is moving in the positive direction. A ball thrown upward has negative acceleration throughout its flight — gravity always pulls down — yet it speeds up on the way back. Sign describes direction, not whether something is getting faster.
Converting 0–60 times to acceleration
Car figures are usually quoted as 0–60 mph or 0–100 km/h. Convert the speed to metres per second first, then divide by the time.
- 60 mph = 26.82 m/s. Divide 26.82 by the quoted seconds.
- 100 km/h = 27.78 m/s. Divide 27.78 by the seconds.
A 0–60 time of 5.0 seconds gives 26.82 ÷ 5 = 5.36 m/s², or 0.55 g. Real acceleration is not constant — it is strongest in the low gears — so this is an average across the run, not the peak.
Common mistakes
- Mixing units. Convert km/h to m/s before dividing, or the answer is out by a factor of 3.6.
- Using distance instead of velocity change. The formula needs a change in speed, not how far the object went.
- Assuming acceleration is constant. These equations only hold for uniform acceleration. Real vehicles vary throughout the run.
- Dropping the sign. Direction matters, especially in problems with more than one stage of motion.
For steady speed rather than a change in it, use the velocity calculator. For the energy a moving object carries, try the kinetic energy calculator.
The four constant acceleration formulas
When acceleration stays the same, physics uses four equations, often called the SUVAT equations. Each one leaves out one of the five quantities, so pick the one that skips the value you do not know.
| Equation | Leaves out |
|---|---|
| v = u + at | distance (s) |
| s = ut + ½at² | final speed (v) |
| v² = u² + 2as | time (t) |
| s = ½(u + v)t | acceleration (a) |
Here u is the starting speed, v the final speed, a acceleration, t time and s distance.
Acceleration formula with distance and time
No speeds, just a distance and a time? If the object starts from rest, rearrange s = ½at²:
a = 2s ÷ t² (starting from rest)
a = 2(s − ut) ÷ t² (starting speed u)
A car covers 100 m from a standstill in 8 s. a = 2 × 100 ÷ 8² = 200 ÷ 64 = 3.1 m/s².
Acceleration due to gravity formula
Near Earth's surface, a falling object speeds up by about 9.81 m/s² (32.2 ft/s²), if you ignore air resistance. That value is called g. Drop a stone for 3 seconds and it reaches v = 9.81 × 3 = 29.4 m/s. Enter 0 as the starting speed and 3 s as the time above to check it.
Centripetal acceleration formula
Anything moving in a circle is accelerating towards the centre, even at a steady speed, because its direction keeps changing.
a = v² ÷ r = ω²r
A car taking a bend of radius 50 m at 20 m/s (45 mph) has a centripetal acceleration of 20² ÷ 50 = 8 m/s² — about 0.8 g. This is also called radial acceleration.
Angular acceleration and instantaneous acceleration
- Angular acceleration: α = change in angular velocity ÷ time. A fan going from 0 to 30 rad/s in 5 s has α = 6 rad/s².
- Instantaneous acceleration formula: the slope of the velocity time graph at one moment, a = dv/dt. With constant acceleration it equals the average acceleration.
Other ways to use this calculator
People search for this tool under several names. Each one is the same calculation with a different input.
- Average acceleration calculator — enter the starting speed, final speed and time; the answer is the average acceleration over that interval.
- Acceleration solver — choose what to solve for — acceleration, final speed, starting speed or time — and leave that box empty.
- Acceleration due to gravity calculator — set the acceleration to 9.81 m/s² and solve for speed or time in a fall without air resistance.
- Acceleration calculator for physics homework — every result shows the formula used, so you can copy the working.
- Physics acceleration — the formula is a equals v minus u over t: final speed minus starting speed, divided by time.
- Average acceleration formula — total change in velocity ÷ total time, even if the speed changed unevenly.
- Deceleration calculator — enter a final speed lower than the starting speed; the negative answer is the deceleration.
- G force calculator — divide the acceleration in m/s² by 9.81 to express it in g.
Frequently asked questions
Acceleration equals the change in velocity divided by the time taken: a = (v − u) ÷ t. A car reaching 27 m/s from rest in 6.5 seconds accelerates at (27 − 0) ÷ 6.5 = 4.15 m/s². The unit is metres per second squared, meaning the speed grows by that many metres per second every second. Convert any km/h or mph figures to m/s first.
G-force expresses an acceleration as a multiple of standard gravity, defined exactly as 9.80665 m/s². An acceleration of 4.15 m/s² is 0.42 g. It is a useful scale because everyone has a physical feel for gravity: a family car pulls about 0.3 g, hard braking around 0.8 g, and a fighter pilot may sustain 9 g.
It means the acceleration points opposite to whichever direction you chose as positive. Usually that describes slowing down, which people call deceleration. But the sign is about direction, not speed — a ball thrown upward has negative acceleration for its whole flight because gravity always acts downward, even though it speeds up on the way back down.
Convert the speed to metres per second, then divide by the time. 60 mph is 26.82 m/s, so a 5.0-second 0–60 gives 26.82 ÷ 5 = 5.36 m/s², or 0.55 g. For 0–100 km/h use 27.78 m/s instead. Bear in mind this is the average over the run — real acceleration peaks in the lower gears and tails off.
Average acceleration = change in velocity ÷ time taken, or a = (v − u) ÷ t. A car going from 0 to 27 m/s in 9 seconds has an average acceleration of 3 m/s².
If the object starts from rest, use a = 2s ÷ t². Covering 100 m in 8 s from a standstill gives 200 ÷ 64 = 3.1 m/s². If it already had a speed u, use a = 2(s − ut) ÷ t².
Sources and further reading
- NIST — Standard acceleration of gravity — the exact value 9.80665 m/s² used for g-force
- NIST — Guide for the Use of the International System of Units — SI units for acceleration, velocity and force
- Acceleration — Encyclopaedia Britannica — definitions and the equations of uniform motion