Acceleration calculator

How do I calculate acceleration?

a = (final speed − starting speed) ÷ time. A car going from 0 to 27 m/s in 9 seconds accelerates at 3 m/s².

What is 0 to 60 mph in 6 seconds in g?

60 mph is 26.82 m/s, so 26.82 ÷ 6 = 4.47 m/s², or 0.46 g.

What does negative acceleration mean?

Slowing down (deceleration): going from 30 to 10 m/s in 4 seconds is −5 m/s².

What is 1 g?

Standard gravity, 9.80665 m/s² — about 32.17 ft/s². Accelerations are often compared with it.

How far do I travel while accelerating?

At a steady acceleration, distance = average speed × time = (start + end) ÷ 2 × time: 0 to 27 m/s in 9 s covers 121.5 m.

Can something accelerate while its speed stays the same?

Yes. Acceleration is the rate of change of velocity, which is a vector, so it points in the direction of the change in velocity and can reflect a change in speed, in direction or both (OpenStax University Physics, Volume 1, section 3.3). A car taking a curve at a steady 50 mph is accelerating toward the inside of the curve. This calculator compares two speeds along a straight line, so it cannot see that; for motion on a circle use the centripetal force calculator.

How do I find acceleration from distance and time?

If the object starts from rest and speeds up steadily, the distance is s = ½at², so a = 2s ÷ t². A car that covers 100 m from a standing start in 8 s at a steady rate has a = 2 × 100 ÷ 8² = 3.125 m/s² (0.32 g) and ends at 25.0 m/s (55.9 mph). The kinematics calculator solves this and the other constant-acceleration cases.

How do I convert mph per second to m/s²?

Multiply by 0.44704, because 1 mph is exactly 0.44704 m/s. A car that gains 10 mph every second accelerates at 4.47 m/s² (14.67 ft/s², 0.456 g). To go the other way, divide m/s² by 0.44704.

The formula and what it assumes

Average acceleration is the change in velocity divided by the time it took: a = (v − v₀) ÷ t (OpenStax University Physics, Volume 1, section 3.3, Eq. 3.8). Velocity is a vector, so the result has a direction as well as a size, and its sign depends on which way you call positive. The number is an average over the whole interval; it equals the acceleration at every instant only when the acceleration is constant. The “Distance covered” line makes that assumption: distance = (v₀ + v) ÷ 2 × t (section 3.4, Eq. 3.10 and 3.11).

Worked example: 0 to 60 mph in 6 seconds

60 mph is 60 × 0.44704 = 26.82 m/s. The speed changes by 26.82 m/s in 6 s, so a = 26.82 ÷ 6 = 4.47 m/s², which is 14.67 ft/s² or 0.456 g. At that steady rate the car covers ½ × 26.82 × 6 = 80.5 m (264 ft) on the way to 60 mph. Take 10 seconds for the same speed gain and the acceleration drops to 2.68 m/s², or 0.274 g.

Common mistakes

Dividing a speed change in mph by seconds gives “mph per second”, not m/s²; convert the speeds first, or let the calculator do it from the “Speed in” menu. A negative answer means the acceleration points opposite to your positive direction, not necessarily that the object is slowing down: something moving in the negative direction that speeds up also has a negative acceleration, which is one reason OpenStax avoids the word “deceleration” (section 3.3). Finally, the result is an average: a car that launches harder than it finishes peaks well above the figure.

Sources: OpenStax University Physics, Volume 1, sections 3.3 (average acceleration, Eq. 3.8) and 3.4 (motion with constant acceleration, Eq. 3.10–3.14); the exact factors 0.44704 m/s per mph, 0.3048 m per foot and standard gravity 9.80665 m/s² are from NIST SP 811, Appendix B.8. Related: kinematics calculator, speed calculator, centripetal force calculator and force calculator.