Formula and Method for Velocity
Velocity is the rate of change of position with respect to time, and unlike speed, it includes direction. Over a time interval, the average velocity is v = Δx / Δt, where Δx is the displacement (final position minus initial position, x1 − x0) and Δt is the elapsed time. This calculator takes your initial and final position, subtracts to find displacement, divides by the elapsed time, and converts the result into meters per second, kilometers per hour, and miles per hour.
Velocity vs. speed
- Speed is a scalar: it has magnitude only and is always zero or positive — it's the rate at which total distance traveled accumulates.
- Velocity is a vector: it has magnitude and direction, shown here as the sign of the result. A positive velocity means position increased over the interval; a negative velocity means position decreased. Speed is simply the magnitude, |v|.
- Displacement vs. distance: average velocity uses displacement (straight-line change in position), not total distance traveled. An object that returns to its starting point has zero displacement — and zero average velocity — even though it covered real distance.
Converting between velocity units
- To km/h: multiply m/s by 3.6, since 1 km/h = 1000 m / 3600 s ≈ 0.2778 m/s, so 1 m/s = 1 / 0.2778 ≈ 3.6 km/h.
- To mph: multiply m/s by 2.23694, using 1 mile = 1609.344 m and 1 hour = 3600 s.
- Mixed units: keep position values in one consistent distance unit and convert the elapsed time to a single time unit before comparing results across scenarios.
Frequently Asked Questions
What is the difference between velocity and speed?
Speed is a scalar (magnitude only) and is always zero or positive, while velocity is a vector that also carries direction, shown as a positive or negative sign. Average speed is total distance traveled divided by time; average velocity is displacement (straight-line change in position) divided by time. For a round trip that returns to the starting point, average velocity is zero even though average speed is not.
What is the formula for average velocity?
Average velocity is v = Δx / Δt, where Δx is the displacement (final position minus initial position) and Δt is the elapsed time. For example, moving from x = 0 m to x = 100 m in 10 s gives v = 100/10 = 10 m/s.
Can velocity be negative, and what does that mean?
Yes. A negative velocity simply means the object moved in the direction you defined as negative — for example, if you set right as positive, a negative velocity means net motion to the left. The sign depends entirely on your choice of coordinate system, not on the object going backward in any absolute sense.
How do I convert a velocity to km/h or mph?
Multiply a velocity in meters per second by 3.6 to get kilometers per hour, or by 2.23694 to get miles per hour. For example, 10 m/s equals 36 km/h and about 22.37 mph.