Acceleration Calculator
Solve for acceleration, final velocity, initial velocity or time — in m/s², ft/s² or g — and see the rearranged formula used for whichever direction you picked.
a = (v − u) ÷ t
Acceleration
Formula used for this direction
a = (v − u) ÷ t
Your values
u = 0 m/s, v = 27 m/s, t = 10
Time cannot be zero — a velocity change over no time has no defined rate.
What Acceleration Actually Measures
Acceleration is the rate at which velocity changes. That word "rate" is what makes it a second-order quantity: velocity already measures how fast position changes, and acceleration measures how fast that changes. Hence the doubled-up unit, m/s² — metres per second, gained every second.
The core relationship is a = (v − u) ÷ t, where u is the starting velocity, v the ending velocity, and t the time between them. Because it is a single equation with four quantities, knowing any three gives you the fourth, which is why this calculator lets you solve in every direction rather than only for a. Rearranged, the same relationship gives v = u + a·t, u = v − a·t, and t = (v − u) ÷ a.
A second form appears when you know distance instead of final speed: a = 2(d − u·t) ÷ t². It comes from rearranging d = u·t + ½·a·t², and it is the form you want for problems phrased as "covered this far in this long" rather than "reached this speed".
Worked example — a car merging onto a motorway
A car accelerates from a standstill to 60 mph in 6.5 seconds. First convert: 60 mph is exactly 26.82 m/s, because a mile per hour is defined as exactly 0.44704 m/s.
a = (26.82 − 0) ÷ 6.5 = 4.127 m/s²
Expressed in g, that is 0.4208 g — about 42.08% of the acceleration you would feel falling freely, which is why a brisk launch presses you into the seat but does not hurt.
A second example at a very different scale. A commuter train pulls away from rest and reaches 27 m/s in 10 seconds:
a = (27 − 0) ÷ 10 = 2.7 m/s² — roughly a third of the car's, which is why you can stand up safely on a train but not in a launching car.
And the same formula going the other way. That train braking from 27 m/s to a stop in 3.2 seconds:
a = (0 − 27) ÷ 3.2 = -8.438 m/s² — negative, because the velocity is decreasing. Nothing about the formula changes.
Common mistake
Dividing distance by time squared directly. If a car covers 135 m in 10 s from rest, the acceleration is not 135 ÷ 100 = 1.35 m/s². The correct form is a = 2(d − u·t) ÷ t² = 2.7 m/s² — exactly double the naive answer. The factor of two comes from the ½ in d = u·t + ½·a·t², and forgetting it is the single most common error in introductory kinematics.
Gravity Across the Solar System
Surface gravity is just an acceleration, so the same formula applies anywhere. The last column uses t = (v − u) ÷ a to work out how long a dropped object would take to reach 100 km/h (27.78 m/s) under each body's gravity, ignoring any atmosphere.
| Body | Surface gravity | Relative to Earth | Time to 100 km/h |
|---|---|---|---|
| Mercury | 3.7 m/s² | 0.377× | 7.51 s |
| Venus | 8.9 m/s² | 0.908× | 3.12 s |
| Earth | 9.8 m/s² | 0.999× | 2.83 s |
| Moon | 1.6 m/s² | 0.163× | 17.4 s |
| Mars | 3.7 m/s² | 0.377× | 7.51 s |
| Jupiter | 23.1 m/s² | 2.36× | 1.2 s |
| Saturn | 9 m/s² | 0.918× | 3.09 s |
| Uranus | 8.7 m/s² | 0.887× | 3.19 s |
| Neptune | 11 m/s² | 1.12× | 2.53 s |
| Pluto | 0.7 m/s² | 0.0714× | 39.7 s |
Surface gravity figures from the NASA NSSDC Planetary Fact Sheet, fetched 2026-09-19. NASA publishes these rounded to two significant figures. Earth appears as NASA's measured 9.8 m/s²; the exactly defined standard gravity used elsewhere on this site is 9.80665 m/s² from NIST, which is a defined constant rather than a measurement.
Keep going
- Acceleration is the rate a velocity changes, so the two formulas are rearrangements of each other; the velocity calculator solves the same relationship for the speed rather than the rate. Velocity Calculator
- Newton's second law says the acceleration you just found was produced by a force equal to mass times that acceleration; the force calculator takes it from there. Force Calculator
Frequently Asked Questions
What is the formula for acceleration?
a = (v − u) ÷ t: the change in velocity divided by the time that change took. If a car goes from rest to 27 m/s in 10 seconds, its acceleration is (27 − 0) ÷ 10 = 2.7 m/s². When you know distance rather than final speed, the alternative form is a = 2(d − u·t) ÷ t².
Can acceleration be negative?
Yes, and it means the velocity is decreasing — braking rather than speeding up. The formula handles it automatically: a car slowing from 27 m/s to rest in 10 seconds gives (0 − 27) ÷ 10 = −2.7 m/s². The sign tells you the direction of the change, not that anything is wrong. Physicists rarely say 'deceleration'; they just use a negative acceleration.
Why is acceleration measured in m/s² rather than m/s?
Because it measures how fast a speed changes, not the speed itself. Each second, the velocity changes by some number of metres per second — so the units are metres per second, per second, which compresses to m/s². An acceleration of 2.7 m/s² means the object gains 2.7 m/s of velocity every second it accelerates.
What does acceleration in 'g' mean?
It expresses acceleration as a multiple of standard gravity, which NIST defines as exactly 9.80665 m/s². So 2 g is about 19.6 m/s². Pilots, drivers and engineers use g because human tolerance is easier to reason about in those terms — sustained acceleration above roughly 5 g causes most untrained people to lose consciousness.
Does a heavier object accelerate more slowly under the same force?
Yes. Newton's second law rearranges to a = F ÷ m, so for a fixed force, acceleration falls as mass rises — double the mass and you halve the acceleration. This is separate from free fall, where heavier objects do not fall faster, because gravity scales the force with the mass and the two effects cancel exactly.
Why does this calculator refuse to solve for time when acceleration is zero?
Because there is no answer. At zero acceleration the velocity never changes, so if your start and end speeds differ, no amount of time will get you from one to the other. Dividing by zero acceleration is the arithmetic signalling a physically impossible question rather than a computational failure.
Related Calculators
- Velocity Calculator — Motion & Kinematics
- Free Fall Calculator — Motion & Kinematics
- Projectile Motion Calculator — Motion & Kinematics
- Force Calculator — Forces & Rotation