Acceleration is the rate at which velocity changes. This calculator finds it from whichever measurements you have: a speed change and the time it took, the net force on a known mass, or a distance covered in a known time. It also converts the answer to g-force and tells you how long a 0–60 mph run would take at that rate, which makes the number easier to picture.
How to use the acceleration calculator
- Pick a Method: change in velocity over time, net force and mass, or distance and time.
- For the velocity method, choose what to Solve for — acceleration, final velocity, initial velocity or time — and enter the other three values with their units (m/s, km/h, mph, ft/s or knots for speeds).
- For the force method, enter the Net force (F) and Mass (m). For the distance method, enter the Displacement (s), the Initial velocity (u) and the Time (t).
- Use Show the result in to read the answer in m/s², ft/s², g, km/h/s or mph/s. The result lists the other units, the g-force and the 0–60 mph time, and the steps show every substitution.
Speeds, forces and displacements may be negative to show direction. Mass and time must be greater than zero; a zero or negative value is rejected.
Acceleration formulas
Definition of average acceleration, with its three rearrangements:
v = u + aΔt · u = v − aΔt · Δt = (v − u) ÷ a
From Newton’s second law, using the net force:
From distance and time with constant acceleration, rearranging s = ut + ½at²:
The SI unit is the meter per second squared (m/s²): meters per second of speed gained every second. One g is defined as exactly 9.80665 m/s², the standard gravity adopted by the CGPM.
Worked example: 0 to 60 mph in 8 seconds
A family car reaches 60 mph from a standstill in 8.0 s.
60 mph = 26.8224 m/s, so a = (26.8224 − 0) ÷ 8 = 3.3528 m/s².
That is 11 ft/s² or about 12.07 km/h of speed gained each second, and 3.3528 ÷ 9.80665 ≈ 0.342 g.
The other methods work the same way. A net force of 3,000 N on a 1,200 kg car gives 3,000 ÷ 1,200 = 2.5 m/s² (about 0.255 g, or 0–60 mph in 10.73 s). A cart that starts at 5 m/s and covers 50 m in 4 s has a = 2 × (50 − 5 × 4) ÷ 4² = 3.75 m/s².
The sign of acceleration and “deceleration”
Acceleration is a vector. Along a straight line, choose one direction as positive and give every velocity and force a sign. Braking from 60 mph to 0 in 3 s gives a = (0 − 26.8224) ÷ 3 = −8.9408 m/s²: the minus sign says the acceleration points backward, opposite the motion, so the car slows. The calculator adds a note whenever the result is negative, and it shows the g-force as a magnitude (0.912 g here).
Negative does not always mean slowing down. If the car is reversing, its velocity is negative too, and a negative acceleration makes it go faster backward. “Deceleration” is the everyday word for acceleration that opposes the velocity, whatever the signs. The 0–60 mph line only appears for positive accelerations, since it describes speeding up in the positive direction.
Typical accelerations
| Situation | m/s² | g |
|---|---|---|
| Car, 0–60 mph in 8 s (average) | 3.35 | 0.34 |
| Sports car, 0–60 mph in 3 s (average) | 8.94 | 0.91 |
| Free fall at standard gravity | 9.80665 | 1 |
| Moon surface gravity (approx.) | 1.62 | 0.165 |
| Mars surface gravity (approx.) | 3.71 | 0.38 |
| Hard braking on dry pavement (approx.) | 7–9 | 0.7–0.9 |
| Space Shuttle ascent, design limit | about 29 | 3 |
Braking figures depend heavily on tires and road surface. The car rows are averages; peak acceleration in first gear is higher.
Related calculators
To find how far an object travels while accelerating, use the displacement calculator (s = ut + ½at²), or solve any three of the five motion variables with the SUVAT calculator. For the force side of the story, see the force calculator, and switch between g, ft/s² and m/s² with the acceleration converter.
Frequently asked questions
What is the formula for acceleration?
Average acceleration is the change in velocity divided by the time it took: a = (v − u) ÷ Δt. A car that goes from 0 to 60 mph (26.8224 m/s) in 8 seconds averages 26.8224 ÷ 8 = 3.3528 m/s².
How do I convert acceleration to g-force?
Divide the acceleration in m/s² by standard gravity, 9.80665 m/s². For 3.3528 m/s² that gives about 0.342 g. The calculator reports the magnitude, so braking at −8.94 m/s² shows as roughly 0.91 g.
Is deceleration the same as negative acceleration?
Only when the object is moving in the positive direction. Deceleration means the acceleration points against the velocity, so the object slows down. A car reversing (negative velocity) with negative acceleration is actually speeding up.
How do I get a 0–60 mph time from an acceleration?
Divide 60 mph, which is exactly 26.8224 m/s, by the acceleration in m/s². At 2.5 m/s² that is 10.73 seconds. It assumes the acceleration stays constant; real cars pull harder in low gears and fade near the top.
Why won't the calculator solve for time with my numbers?
Time must come out positive. If the velocity change (v − u) and the acceleration have opposite signs, the time would be negative, and with zero acceleration the velocity never changes, so no time can be found.