Velocity Calculator
What the velocity calculator does
The velocity calculator divides displacement by elapsed time to give average velocity. Enter the displacement in metres and the time in seconds, press Calculate Velocity, and the result appears in metres per second. Because it works from displacement rather than distance, the answer is a vector quantity: a negative displacement gives a negative velocity, which simply means motion in the opposite direction to the one you chose as positive.
The formula
v = Δx / Δt
where Δx is the change in position (final position minus initial position) and Δt is the time taken. In SI units the result is m/s. If you know the distance travelled along a path rather than the straight-line change in position, you are calculating speed, and the speed calculator is the right tool.
Velocity versus speed
| Velocity | Speed | |
|---|---|---|
| Type | Vector (magnitude and direction) | Scalar (magnitude only) |
| Based on | Displacement | Distance travelled |
| Can be negative | Yes | No |
| Round trip | Zero average velocity | Non-zero average speed |
A runner who completes one lap of a 400 m track in 60 s has an average speed of 6.67 m/s but an average velocity of zero, because the finish line is the start line.
Worked examples
A car on a straight road. It moves 1500 m east in 75 s. v = 1500 / 75 = 20 m/s east, which is 72 km/h.
A lift. It travels from the 12th floor to the 2nd floor, a displacement of −35 m, in 28 s. v = −35 / 28 = −1.25 m/s. The sign shows it is moving down.
A satellite in low Earth orbit. It covers 40,000 km in 5,400 s along a circle. Its speed is about 7.4 km/s, but its average velocity over a full orbit is zero. This is the clearest case where the two quantities differ.
Converting the result
| m/s | km/h | mph | knots |
|---|---|---|---|
| 1 | 3.6 | 2.237 | 1.944 |
| 10 | 36 | 22.4 | 19.4 |
| 30 | 108 | 67.1 | 58.3 |
| 100 | 360 | 224 | 194 |
Multiply m/s by 3.6 for km/h and by 2.237 for mph. The speed converter handles other units.
Average versus instantaneous velocity
This calculator gives the average velocity over the whole interval. If an object speeds up or slows down, its instantaneous velocity at a given moment can be quite different. For uniformly accelerated motion, average velocity equals the mean of the initial and final velocities, vavg = (v0 + v)/2, and the change in velocity is a × t. The acceleration converter and projectile motion calculator cover those cases.
Common mistakes
- Mixing units. Kilometres with seconds gives km/s, not m/s. Convert displacement to metres first.
- Entering minutes as seconds. 2.5 minutes is 150 s.
- Using path length for displacement. A winding road of 10 km may have a straight-line displacement of only 6 km.
- Dropping the sign. Direction is the whole point of velocity. Decide which direction is positive before you start.
Related tools
The pace to speed converter is useful for runners who think in minutes per kilometre. The kinetic energy to velocity converter works backwards from energy and mass, and the centripetal force calculator uses velocity as an input for circular motion. For trip planning, see the flight time calculator and time calculator.
External references
Frequently asked questions
Can velocity be negative?
Yes. A negative value means the displacement is opposite to the direction you chose as positive. Speed is never negative.
What is the velocity if the displacement is zero?
Zero, regardless of how far the object travelled along the way. Its average speed can still be large.
Does this calculator handle acceleration?
No. It returns average velocity over the interval. For changing velocity use the kinematics tools linked above.
How do I get velocity in km/h?
Multiply the result by 3.6. For example, 15 m/s is 54 km/h.
Why does the result show many decimal places?
The calculator does not round for you. Quote the answer to the same number of significant figures as your least precise measurement.