What the Acceleration Calculator does
This calculator works out acceleration - how quickly speed changes - from a change in speed over a time, from a distance and a time, from two speeds and a distance, or from a force and a mass. A car that goes from 0 to 100 km/h in 8 seconds accelerates at 3.47 m/s², about 0.35 g.
Any one value can be the unknown: leave out the time, the final speed, the distance, the force or the mass, and the page solves for it instead. Units are mixed freely - km/h, mph, knots, feet, miles, pounds, pound-force - and the answer is given in m/s², g, ft/s² and "km/h per second", with the equivalent 0-100 km/h and 0-60 mph times.
How to use it
- Pick the formula that matches what you know: speeds and a time, a distance and a time, two speeds and a distance, or a force and a mass.
- Choose what to solve for. Acceleration is the default; you can solve for time, distance, final or initial speed, force or mass instead.
- Fill in the remaining values and choose a unit for each. Use a negative acceleration for braking, or simply enter a final speed lower than the initial one.
- Read the answer, the SI working underneath it, and the acceleration in other units. Change Show acceleration in to quote it in g or ft/s².
Reading the results
Acceleration is the change in velocity per second. 3.47 m/s² means the car gains 3.47 m/s - 12.5 km/h - every second. A negative value is deceleration: the object loses that much speed each second.
"g" compares the figure with standard gravity, 9.80665 m/s². A family car pulls about 0.3 g when accelerating hard and up to about 1 g when braking hard on dry roads; a dropped object accelerates at 1 g until air resistance builds up.
The 0-100 km/h and 0-60 mph times are what the same constant acceleration would give. Real cars accelerate faster at low speed and slower near the top of a gear, so published times are averages too.
The force-mass formula is Newton's second law. It gives the acceleration of the net force: if friction or drag oppose the push, subtract them first.
Worked example: a car braking from 72 km/h to a stop in 40 metres
72 km/h is 72 ÷ 3.6 = 20 m/s. The final speed is 0 and the distance 40 m, so the speeds-and-distance formula applies: a = (v² − u²) / 2s.
a = (0² − 20²) / (2 × 40) = −400 / 80 = −5 m/s². The minus sign says the car is slowing down; in g that is 5 ÷ 9.80665 ≈ 0.51 g, typical of firm braking.
The time taken follows from a = (v − u)/t: t = (0 − 20) / (−5) = 4 seconds. Switch the formula to change in speed over time, solve for time, and the calculator confirms 4 s.
Formulas and scoring rules
- From a change in speed
a = (v − u) / tu = initial speed, v = final speed, t = time.- From distance and time
s = ut + ½at² → a = 2(s − ut) / t²Solving for t takes the smallest positive root of ½at² + ut − s = 0.- From two speeds and a distance
v² = u² + 2as → a = (v² − u²) / 2s- Newton's second law
F = ma → a = F / m- In g
a(g) = a(m/s²) / 9.80665Standard gravity, fixed by the CGPM in 1901.- Time to a speed
t = v / a; 0-100 km/h: t = 27.778 / a; 0-60 mph: t = 26.8224 / a1 mph = 0.44704 m/s and 1 km/h = 1/3.6 m/s exactly. Results are rounded to four decimal places for display.
Speed, velocity and the sign of acceleration
Strictly, acceleration is the rate of change of velocity, which has a direction. In a straight line that direction is just a sign: positive one way, negative the other. That is why a braking car has a negative acceleration even though it is still moving forwards, and why a ball thrown upwards has an acceleration of −9.8 m/s² both on the way up and on the way down.
The equations here are the "SUVAT" equations taught in school physics, and they are exact only when acceleration is constant. For anything that speeds up unevenly they give the average acceleration over the interval, which is still the useful number for comparing cars, sprints or lifts.
Limitations: what the result does not prove
- Every formula assumes constant acceleration along a straight line. Curved paths, varying thrust and air resistance are not modelled.
- Speeds are treated as velocities along one line; enter a negative value for motion in the opposite direction.
- The force-mass mode uses the net force. It does not subtract friction, rolling resistance or drag for you.
- Results are physics estimates, not a substitute for vehicle test data or an engineering calculation.
Privacy: where your data goes
Everything you paste, type or drop is processed in this browser tab. It is not uploaded, logged, stored or sent to analytics. Session recording and tag-manager scripts are switched off on this page.
Standards and sources
- NIST SP 811 - Guide for the Use of the International System of Units - checked 19 Sep 2026
- NIST Handbook 44 Appendix C - General tables of units of measurement (mile, foot, pound)
- OpenStax University Physics Volume 1 - 3.4 Motion with constant acceleration
- OpenStax University Physics Volume 1 - 5.3 Newton's second law
Frequently asked questions
What is the formula for acceleration?
Acceleration equals the change in velocity divided by the time taken: a = (v − u) / t. A cyclist going from 2 m/s to 8 m/s in 3 seconds accelerates at (8 − 2) / 3 = 2 m/s². The unit is metres per second per second, written m/s².
How do I calculate acceleration from distance and time?
If it starts from rest, use a = 2s / t². Covering 100 m in 10 s from a standstill needs 2 × 100 / 10² = 2 m/s². If it was already moving at speed u, use a = 2(s − ut) / t²; the calculator handles both.
How do I find acceleration from force and mass?
Divide the net force by the mass: a = F / m. A 1,000 N push on a 1,250 kg car gives 0.8 m/s². Use newtons and kilograms, or pick pound-force and pounds and the page converts them.
What is 0 to 60 mph in m/s² or g?
60 mph is 26.8224 m/s, so divide that by the time. A 6-second 0-60 is 26.8224 / 6 = 4.47 m/s², or 0.46 g. Enter the speeds and time and the calculator also shows the equivalent 0-100 km/h time.
Can acceleration be negative?
Yes. Negative acceleration, often called deceleration, means the velocity is decreasing in the chosen direction. Braking from 30 m/s to 0 in 6 seconds is (0 − 30) / 6 = −5 m/s².
How many m/s² is 1 g?
Standard gravity, 1 g, is defined as exactly 9.80665 m/s², about 32.17 ft/s². Real gravity varies slightly with latitude and altitude, from about 9.78 at the equator to 9.83 at the poles, but the standard value is used for g ratings.
How far does something travel while accelerating?
Use s = ut + ½at². A stone dropped from rest falls ½ × 9.81 × 2² ≈ 19.6 m in 2 seconds, ignoring air resistance. Choose the distance-and-time formula and solve for distance.
Last reviewed by the A2Z.Tools team against the sources listed above.
