Velocity Calculator
Velocity is how fast position changes. Solve it three ways: as displacement divided by time, as a final velocity from a starting velocity and acceleration (v = u + at), or as the average across several legs of a journey. Every result is shown in m/s, km/h, mph and ft/s, with units converted for you.
Formula
Worked example
100 m in 10 s: v = 100 ÷ 10 = 10 m/s (that is 36 km/h, or about 22.4 mph). From rest at 3 m/s² for 5 s: v = 0 + 3 × 5 = 15 m/s, covering 37.5 m.
What velocity actually measures
Velocity is the rate at which an object changes its position. In one dimension it is the displacement, the signed straight-line change from the starting point, divided by the time taken. Because displacement carries a direction, velocity is a vector quantity: 10 m/s east is a different velocity from 10 m/s west. This calculator reports average velocity, the single steady value that would produce the same displacement over the same interval. The instantaneous velocity at any given moment can be higher or lower, which is why a sprinter who covers 100 m in 10 s averages 10 m/s even though their top speed is faster.
Three ways to find velocity
This tool covers the three situations you meet most often. The first divides a displacement by the time taken, the textbook v = Δx ÷ Δt. The second starts from a known initial velocity and a constant acceleration and applies v = u + a·t, the first equation of motion, and it also reports the distance covered using u·t + ½·a·t². The third averages a journey made of several legs by adding all the distances and dividing by the total time, which is the correct way to combine legs: you cannot simply average the individual leg speeds, because each leg is weighted by how long it lasted, not how far it went.
Velocity versus speed
People use "speed" and "velocity" interchangeably in everyday talk, but in physics they differ in one important way. Speed is the total distance travelled divided by time and is always positive; velocity is the displacement divided by time and keeps track of direction. If you jog 400 m around a track and finish where you started, your average speed over that lap is non-zero but your average velocity is zero, because your displacement is zero. For motion in a straight line that never reverses, the two values match in magnitude, which is why the worked example above gives the same number you would get from a speed calculation.
Keeping the units consistent
The formula only works when every quantity shares a coherent system, so this tool converts displacement to metres, time to seconds, speeds to metres per second and acceleration to metres per second squared before computing, then expresses the result in four common units. To convert by hand, multiply a metres-per-second value by 3.6 to get kilometres per hour, or divide km/h by 3.6 to go back. To reach miles per hour, divide the km/h figure by 1.609344; to reach feet per second, divide m/s by 0.3048. Mixing units is the most common source of error, so always reduce both quantities to the same base before computing.
Common velocities for reference
| Motion | m/s | km/h | mph |
|---|---|---|---|
| Brisk walk | 1.4 | 5 | 3.1 |
| Cyclist (casual) | 5 | 18 | 11.2 |
| Usain Bolt (100 m avg) | 10.4 | 37.6 | 23.3 |
| Highway car | 27.8 | 100 | 62.1 |
| Commercial jet (cruise) | 250 | 900 | 559.2 |
Approximate average velocities, rounded for comparison.
Frequently asked questions
What is the formula for velocity?
Average velocity equals displacement divided by elapsed time: v = Δx ÷ Δt. Δx is the change in position (a vector) and Δt is the time interval. Express displacement in metres and time in seconds to get velocity in metres per second.
How do I find final velocity from acceleration?
Use the first equation of motion: v = u + a·t, where u is the initial velocity, a is the constant acceleration, and t is the time. Starting from rest (u = 0) at 3 m/s² for 5 s gives v = 0 + 3 × 5 = 15 m/s. Switch this calculator to the acceleration mode to do it automatically and also see the distance covered.
How do I average velocity over several legs of a trip?
Add up the distance of every leg and divide by the total time of the whole trip. Do not average the individual leg speeds, because each leg is weighted by its duration. For example, 100 m in 10 s then 200 m in 40 s is 300 m in 50 s, which is 6 m/s, not the simple average of 10 and 5 m/s.
What is the difference between velocity and speed?
Speed is distance ÷ time and is always positive; velocity is displacement ÷ time and includes direction, so it can be negative or zero. For straight-line motion that never reverses, the magnitude of velocity equals the speed.
How do I convert m/s to km/h, mph or ft/s?
Multiply metres per second by 3.6 to get kilometres per hour. Divide that km/h value by 1.609344 to reach miles per hour, or multiply m/s by about 2.237 directly. To get feet per second, divide m/s by 0.3048.