What this calculator does
Average velocity and average speed sound interchangeable, and for a straight one-way trip they give the same number. They part ways once a journey doubles back on itself: average speed is total distance travelled divided by total time, while average velocity is net displacement (how far you end up from where you started, in a straight line) divided by total time.
This calculator makes that distinction concrete with a there-and-back journey: an outbound leg and a return leg along the same line, each with its own distance and speed. If the return leg covers the same distance as the outbound leg, you finish back where you started, and average velocity works out to exactly zero, even though the average speed is clearly not zero.
The formula
Time for each leg is that leg's distance divided by its speed, and total time is the two added together. Average speed is total distance (both legs added) divided by total time. Net displacement is outbound distance minus return distance, treating the return direction as negative along the same line; average velocity is that net displacement divided by total time.
| Term | Meaning |
|---|---|
| Average speed | Total distance travelled divided by total time, always zero or positive, and independent of direction. |
| Average velocity | Net displacement divided by total time; can be zero, positive or negative depending on where you end up relative to where you started. |
| Net displacement | The straight-line difference between your start and end position, here calculated as outbound distance minus return distance. |
The inputs explained
| Field | What to enter |
|---|---|
| Distance, leg 1 (outbound) (km) | The distance covered on the first (outbound) leg of the journey. |
| Speed, leg 1 (km/h) | The average speed maintained on that outbound leg. |
| Distance, leg 2 (return, same line) (km) | The distance covered on the return leg, back along the same line. Use the same value as leg 1 for a full round trip. |
| Speed, leg 2 (km/h) | The average speed maintained on the return leg. |
When to use it
A daily commute
Driving 10 km to work and 10 km home again covers 20 km of ground, but ends the day back at the same front door: average speed is a meaningful number for fuel and time planning, while average velocity for the whole round trip is zero.
A training run that turns back partway
A run that goes out 5 km and only returns 3 km before stopping (perhaps picked up by a lift) leaves a net displacement of 2 km from the start, giving a small but non-zero average velocity alongside a much larger average speed.
Explaining the difference for a physics problem
Setting the return leg's distance equal to the outbound leg is the clearest way to see the concept: the average speed stays clearly positive while average velocity drops to exactly zero, which is the classic textbook illustration of why the two are not the same quantity.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Average velocity as the return leg gets closer to a full round trip
A fixed 10 km outbound leg, with the return distance varied from a short partial return up to the full 10 km.
| Return distance | Average velocity | Average speed | Net displacement |
|---|---|---|---|
| 0 km | 50.00 km/h | 50.00 km/h | 10.00 km |
| 2 km | 32.00 km/h | 48.00 km/h | 8.00 km |
| 4 km | 20.00 km/h | 46.67 km/h | 6.00 km |
| 6 km | 11.43 km/h | 45.71 km/h | 4.00 km |
| 8 km | 5.00 km/h | 45.00 km/h | 2.00 km |
| 10 km | 0.00 km/h | 44.44 km/h | 0.00 km |
How average speed and average velocity respond to the same distances at different speeds
A fixed 10 km outbound and 10 km return, across a range of return speeds.
| Return speed | Average velocity | Average speed |
|---|---|---|
| 20 km/h | 0.00 km/h | 28.57 km/h |
| 30 km/h | 0.00 km/h | 37.50 km/h |
| 40 km/h | 0.00 km/h | 44.44 km/h |
| 50 km/h | 0.00 km/h | 50.00 km/h |
| 60 km/h | 0.00 km/h | 54.55 km/h |
| 80 km/h | 0.00 km/h | 61.54 km/h |
Questions
Why is average velocity zero for a round trip even though the car clearly moved?
Velocity is defined by displacement, the straight-line distance and direction from start to finish, not by the path taken to get there. A round trip finishes exactly where it started, so displacement is zero no matter how much ground was actually covered, which makes average velocity zero too.
Is average velocity ever negative?
Yes. If the return leg does not fully retrace the outbound leg (for example, you overshoot the starting point and keep going past it in the return direction), net displacement flips sign, and average velocity comes out negative, reflecting the direction of net travel.
Is this the same as the speed, distance and time calculator elsewhere on the site?
No. That calculator handles a single straight-line leg of a journey, where average speed and average velocity are the same figure. This calculator is specifically for a two-leg out-and-back journey, where the two quantities can differ, which is the entire point of distinguishing speed from velocity.
What if the outbound and return legs are not along exactly the same line?
This calculator assumes the return leg retraces the outbound line, which covers most everyday round-trip cases such as a commute or an out-and-back run. A journey that returns by a genuinely different path needs the actual straight-line distance between the start and end points to work out true displacement.
For a single-leg journey where speed and velocity are the same figure, see the speed, distance and time calculator. For acceleration and stopping distance on a single leg, see the acceleration calculator.