Acceleration Calculator
Acceleration three ways — or any other variable — with g-force and 0–100 km/h times.
Velocity–time graph
How it was worked out
About the Acceleration Calculator
Calculate acceleration the way your problem gives it: from a change in velocity over a time, a = (v − u) ÷ t; from a distance covered in a time with a known starting speed, a = 2(s − ut) ÷ t²; or from the net force and mass, a = F ÷ m. Each method can also be solved for any of its other variables — the final speed, the starting speed, the time, the distance, the force or the mass.
Every value takes its own unit (km/h, mph, m/s, knots; seconds, minutes or hours; metres, feet or miles; N, kN, lbf, kgf; kg, g, lb), and the answer comes with its g-force equivalent and, for a car-like problem, the 0–100 km/h and 0–60 mph times — or the stopping time and distance when the acceleration is negative. A velocity–time graph and the full working are shown underneath.
How to use it
- Choose what you know: Δv and time, distance and time, or force and mass.
- Pick what to solve for — acceleration, or one of the other variables. The box for that value is marked calculated and fills in by itself.
- Type the other values and choose their units. Use the ± button for negative values: an acceleration is negative when the object slows down.
- Read the answer, its g-force and the 0–100 km/h figures, then check the working. Copy result copies the values and the working.
Examples
u = 0, v = 100 km/h, t = 8.5 s
a = 3.268 m/s² = 0.3332 g; 0–60 mph in 8.208 s
u = 100 km/h, v = 0, t = 3.5 s
a = −7.937 m/s² (0.8093 g), stopping in 48.61 m
s = 0.25 mi, u = 0, t = 12 s
a = 2s ÷ t² = 5.588 m/s² (0.5698 g), reaching 67.06 m/s (241.4 km/h)
500 lbf net force on 1,000 kg
2,224 N ÷ 1,000 kg = 2.224 m/s²
u = 0, v = 60 mph, a = 0.5 g
t = 26.82 m/s ÷ 4.903 m/s² = 5.470 s
s = 200 m, u = 10 m/s, a = 2 m/s²
t² + 10t − 200 = 0 → t = 10 s (the root −20 s is rejected)
Common uses
- Car performance: 0–100 km/h or 0–60 mph times, quarter-mile runs and braking.
- Physics homework on acceleration, deceleration and Newton’s second law, with working.
- Converting an acceleration into g-force for rides, aircraft or sport.
- Checking whether a measured time and distance imply a sensible acceleration.
The formulas
- From velocity and time:
a = (v − u) ÷ t, sov = u + a t,u = v − a tandt = (v − u) ÷ a. - From distance and time:
s = u t + ½ a t², soa = 2(s − u t) ÷ t²andu = (s − ½ a t²) ÷ t. Solving for t means solving the quadratic½ a t² + u t − s = 0; the calculator gives the first positive root. - From force and mass (Newton’s second law):
a = F ÷ m, with F the net force. 1 N is the force that gives 1 kg an acceleration of 1 m/s². - g-force:
a ÷ g₀with standard gravity g₀ = 9.80665 m/s². - 0–100 km/h:
t = 27.78 m/s ÷ aand distancev² ÷ 2a, for a constant acceleration.
The constant-acceleration formulas assume the acceleration does not change during the time considered; with a varying acceleration, the result is the average acceleration.
Typical accelerations
From OpenStax University Physics Volume 1, Table 3.2 (approximate values):
- Fast passenger train: 0.25 m/s²
- Elevator: 2 m/s²
- Cheetah: 5 m/s²
- Free fall near Earth’s surface without air drag: 9.8 m/s²
- Space shuttle launch (maximum): 29 m/s² (about 3 g)
- F-16 pulling out of a dive: 79 m/s² (about 8 g)
- Ejection-seat firing: 147 m/s² (about 15 g)
Sources
- OpenStax, University Physics Volume 1: §3.3 Average and Instantaneous Acceleration (Eq. 3.8 and Table 3.2), §3.4 Motion with Constant Acceleration (Eqs. 3.12–3.14 and Example 3.11) and §5.3 Newton’s Second Law.
- BIPM, 3rd CGPM (1901), Declaration on the unit of mass and on the definition of weight; conventional value of gₙ — g₀ = 980.665 cm/s².
- NIST, SP 811 Appendix B.8 — mph, ft/s², lbf and kgf conversion factors.
Limitations
- All formulas assume a constant acceleration over the time considered; for real cars the result is an average.
- The force method needs the net force — the total of all forces, after friction and drag are subtracted.
- Speeds near the speed of light need relativity; speeds above it are refused.
- Velocities are one-dimensional: positive in one direction, negative in the other.
Privacy
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Frequently asked questions
What is the formula for acceleration?
Acceleration is the change in velocity divided by the time it takes: a = (v − u) ÷ t, in metres per second squared (m/s²). A car going from 0 to 100 km/h (27.78 m/s) in 8.5 s accelerates at 27.78 ÷ 8.5 = 3.268 m/s².
How do I find acceleration from distance and time?
Use s = ut + ½at², rearranged to a = 2(s − ut) ÷ t². Starting from rest (u = 0) it is simply a = 2s ÷ t²: a quarter mile (402.3 m) in 12 s means 2 × 402.3 ÷ 144 = 5.588 m/s².
What does a negative acceleration mean?
That the acceleration points in the negative direction. If the object is moving in the positive direction, it is slowing down (decelerating): braking from 100 km/h to rest in 3.5 s is −7.937 m/s². If it is moving in the negative direction, it is speeding up.
How do I convert acceleration to g-force?
Divide by standard gravity, 9.80665 m/s². 3.268 m/s² is 0.3332 g, and 29 m/s² (a space-shuttle launch) is about 3 g.
How is the 0–100 km/h time worked out?
At a constant acceleration a, reaching 100 km/h (27.78 m/s) from rest takes t = 27.78 ÷ a seconds and covers 27.78² ÷ (2a) metres. Real cars accelerate harder at low speed, so treat this as the time at the average acceleration.
How are force, mass and acceleration related?
By Newton’s second law, F = ma: the net force equals the mass times the acceleration. A net force of 2,000 N on a 1,000 kg car gives 2 m/s²; the same force on a 2,000 kg van gives only 1 m/s².