Speed and velocity are used interchangeably in conversation and mean different things in physics. The difference comes down to one word: direction.
The definitions
- Average speed = total distance ÷ total time. A scalar : magnitude only.
- Average velocity = displacement ÷ total time. A vector : magnitude and direction.
Distance is how far you travelled. Displacement is how far you ended up from where you started, in a straight line. Those are the same number only if you moved in a straight line and never turned back.
The lap example
Run one lap of a 400 m track in 80 seconds.
- Average speed = 400 m ÷ 80 s = 5 m/s
- Average velocity = 0 m ÷ 80 s = 0 m/s
You finished exactly where you started, so displacement is zero, so average velocity is zero : despite obviously having moved. This is the example that makes the distinction click for most people, and it is not a trick. It is what the definitions say.
A second example: the return trip
You drive 30 km east in 30 minutes, then 30 km back west in 30 minutes.
- Total distance: 60 km. Total time: 1 hour. Average speed = 60 km/h.
- Displacement: 0 km. Average velocity = 0 km/h.
Change the trip so you drive 30 km east then 10 km back west, still in an hour:
- Distance 40 km, so average speed = 40 km/h
- Displacement 20 km east, so average velocity = 20 km/h east
Note that the velocity answer is incomplete without "east". A velocity without a direction is not a velocity.
Which one does a speedometer show?
Speed. A car speedometer and a GPS speedometer both report magnitude only : they do not care which way you are pointing. Our GPS speedometer shows instantaneous speed, plus a session average that is average speed, computed as total distance over elapsed time.
A GPS receiver does internally know your direction of travel, which is how navigation apps show a heading. But the number on a speed readout is the scalar.
Instantaneous vs average
Both speed and velocity come in instantaneous and average forms. Instantaneous speed is the reading right now; average speed covers an interval. The same applies to velocity. Mixing these up causes as many errors as confusing speed with velocity in the first place.
Where it actually matters
In everyday life, almost nowhere : which is why the words blur together. It matters in physics problems, in navigation where displacement determines whether you arrive, and in any calculation involving acceleration, since acceleration is defined as the rate of change of velocity, not speed.
That last point has a consequence people find surprising: an object moving in a circle at constant speed is accelerating continuously, because its direction : and therefore its velocity : is always changing.
The takeaway
Speed is distance over time and ignores direction. Velocity is displacement over time and requires one. If your journey ends where it began, your average velocity is zero no matter how fast you went. For the formula side of average speed, see the average speed formula.