Acceleration Calculator finds how fast velocity changes from two speeds and a time, from a distance, or from force and mass, and shows results in m/s², ft/s², g and mph per second.
Choose the formula that fits your known values. Set the mass in the panel to get the net force.
Mass and Result Units
Step-by-Step Working
- Known values: vi = 0 mph, vf = 60 mph, Δt = 4 s
- In SI units: vi = 0 m/s, vf = 26.8224 m/s, Δt = 4 s
- a = (vf − vi) ÷ Δt = (26.8224 − 0) ÷ 4 = 6.7056 m/s²
- Net force for m = 1500 kg: F = m × a = 1500 × 6.7056 = 10058.4 N
- Result: acceleration a = 6.7056 m/s²
Velocity and Distance Over Time
| Time (t) | Velocity (v) | Distance (d) |
|---|---|---|
| 0 s | 0 mph | 0 ft |
| 1.00 s | 15.00 mph | 11.00 ft |
| 2.00 s | 30.00 mph | 44.00 ft |
| 3.00 s | 45.00 mph | 99.00 ft |
| 4.00 s | 60.00 mph | 176.00 ft |
Four Formulas in the Acceleration Calculator
Acceleration is the rate at which velocity changes. Its symbol is a, and its SI unit is the meter per second squared, m/s². The Acceleration Calculator finds it from four different sets of known values, chosen in the Formula menu.
| Formula | You know | Equation |
|---|---|---|
| Speed Difference | Initial velocity, final velocity, time | a = (vf − vi) ÷ Δt |
| Distance Traveled | Initial velocity, distance, time | a = 2(Δd − viΔt) ÷ Δt² |
| Mass and Force | Net force and mass | a = F ÷ m |
| Velocity and Distance | Initial velocity, final velocity, distance | a = (vf² − vi²) ÷ (2Δd) |
The first three are the formulas most often listed for acceleration. The fourth covers the common case where no time is given. All four assume the acceleration stays constant, so the result is the average acceleration over the interval.
This tool belongs to the Dynamics and Statics Calculators, the group that deals with forces and the motion they cause. It runs in a phone browser, so no app is needed, and every result can be copied or printed.
Acceleration From Velocity and Time
To find acceleration from two speeds, subtract the initial velocity from the final velocity and divide by the time taken. This is the average acceleration formula, and it is the one most questions need.
$$a = \frac{v_f – v_i}{\Delta t}$$
The Acceleration Calculator opens with a car going from 0 to 60 mph in 4 seconds. It converts 60 mph to 26.82 m/s, then divides by 4. The acceleration is 6.71 m/s², which is 22 ft/s², 15 mph per second or 0.68 g. The car covers 176 ft in that time.
The sign of the answer carries the direction. OpenStax University Physics gives a racehorse that goes from rest to 15 m/s due west in 1.8 seconds. With west as negative, enter −15 m/s and the result is −8.33 m/s², the textbook answer.
That horse is speeding up, even though its acceleration is negative. An object slows down only when acceleration and velocity have opposite signs. The note under the results says which case applies, and it flags any motion that reverses direction.
Acceleration From Distance
Two of the formulas work as an acceleration calculator with distance. Distance Traveled is for when the final speed is unknown. It needs the starting velocity, the distance covered and the time.
$$a = \frac{2(\Delta d – v_i \Delta t)}{\Delta t^2}$$
A car that starts from rest and covers 53.645 m in 4 seconds has an acceleration of 2 × 53.645 ÷ 16 = 6.71 m/s². It is the same 0 to 60 mph run as before, seen from the distance side. The second card adds the final velocity, 60 mph.
Velocity and Distance is for when the time is unknown. It finds acceleration using speed and distance alone, which suits braking and runway problems. Enter the two velocities and the distance between them.
$$a = \frac{v_f^2 – v_i^2}{2 \Delta d}$$
A car that brakes from 60 mph to a stop in 40 m has an acceleration of −8.99 m/s², or 0.92 g of deceleration. The stop takes 2.98 seconds. For problems with two unknowns at once, the SUVAT Calculator solves the full set of constant-acceleration equations.
Acceleration From Mass and Force
Newton’s formula for acceleration comes from his second law, F = m × a. Divide the net force on an object by its mass. The net force is what remains after friction, drag and every other force have been added up.
$$a = \frac{F}{m}$$
Enter 10,058.4 N and 1,500 kg, and the Acceleration Calculator returns 6.71 m/s² again. The second card shows the trade-off. The same force on double the mass gives 3.35 m/s², and double the force on the same mass gives 13.41 m/s².
The other three formulas run this law in reverse. Set the mass in the lower section and the last card gives the accelerating force. The 1,500 kg car needs a net force of 10,058.4 N, or 2,261.22 lbf, to reach 60 mph in 4 seconds. Its weight is 14,709.98 N, so the push is about two thirds of its weight.
Car Acceleration: 0 to 60 and Beyond
Car reviews quote acceleration as a time to 60 mph or 100 km/h. The third card turns any result into those terms. At a steady 6.71 m/s², a car reaches 100 mph in 6.67 seconds, covers a quarter mile in 10.95 seconds and travels 1,100 ft in its first 10 seconds.
These figures assume the acceleration never fades. A real car pulls hardest at low speed and loses acceleration as drag builds and the gears get taller. The Quarter Mile Calculator estimates real elapsed times from weight and power.
For a negative result the same card switches to braking. It shows the time to stop from 60 mph or 100 km/h and the stopping distances from two speeds, without any reaction time. Enter a final velocity below the initial one to see it.
Units of Acceleration and How Fast 1 g Is
Acceleration is a velocity unit divided by a time unit. The SI unit is m/s², and ft/s² is common in US engineering. Drivers often use mph per second or km/h per second, which read directly as speed gained each second.
One g is standard gravity, defined as exactly 9.80665 m/s². That equals 32.174 ft/s², 21.94 mph per second or 35.3 km/h per second. A car pulling a steady 1 g would reach 60 mph in 2.74 seconds. Result Units in the Acceleration Calculator switches the main answer between all five units.
Position, Velocity and Acceleration Over Time
The three quantities form a chain. Velocity is how fast position changes, and acceleration is how fast velocity changes. With constant acceleration, velocity grows in a straight line and distance grows with the square of the time.
| Time | Velocity | Distance |
|---|---|---|
| 0 s | 0 mph | 0 ft |
| 1 s | 15 mph | 11 ft |
| 2 s | 30 mph | 44 ft |
| 3 s | 45 mph | 99 ft |
| 4 s | 60 mph | 176 ft |
This is the Velocity and Distance Over Time table from the Acceleration Calculator for the 0 to 60 mph run. Velocity rises by the same 15 mph every second. Distance does not. Half of the 176 ft is covered only after 2.83 seconds, well past the halfway point in time.
To turn acceleration into speed, multiply it by the time and add the starting velocity, vf = vi + a × Δt. The Displacement Calculator handles the position side when the motion has several legs.
Zero, Sideways and Missing-Value Cases
Is acceleration zero at maximum speed?
Yes, when the speed holds steady at its peak. A falling object at terminal velocity and a car at top speed both have zero acceleration, because the forces on them balance. A ball at the top of a throw is the opposite case. Its velocity is zero for an instant, but its acceleration is still a full 1 g downward.
How can something accelerate without changing speed?
By changing direction. Velocity includes direction, so a car rounding a bend at a steady speed is accelerating toward the center of the curve. That centripetal acceleration is v² ÷ r. At 20 m/s on a curve of 50 m radius it is 8 m/s², or 0.82 g. The Magnitude of Acceleration Calculator combines components like these.
Can you calculate acceleration with only velocity?
No. A single velocity says nothing about how quickly it is changing. You need two velocities plus either the time between them or the distance covered. Without any speed at all, use the Mass and Force formula in the Acceleration Calculator, or Distance Traveled with a start from rest.