Distance is how much ground you covered. Displacement is how far you ended up from where you began, and in which direction. One measures the journey; the other measures only its result.
The comparison table
| Distance | Displacement | |
|---|---|---|
| Definition | Total length of the path actually travelled | Straight line from the starting point to the final point |
| Quantity | Scalar — size only | Vector — size and direction |
| Depends on the route? | Yes | No, only on the two end points |
| Sign | Never negative | Positive, negative or zero |
| Can it decrease as you keep moving? | No, it only grows | Yes, when you head back toward the start |
| For a closed path | Equals the length of the loop | Zero |
| SI unit | metre (m) | metre (m) |
The one line worth memorising: the size of the displacement is never more than the distance. The two are equal only when the body moves along a straight line without turning back.
Example 1 — the 3-4-5 walk
A girl walks 4 m east and then 3 m north.
- Distance = 4 + 3 = 7 m. Add the legs as they were walked.
- Displacement = the straight line from her first position to her last. The two legs are at right angles, so by Pythagoras it is √(4² + 3²) = √25 = 5 m, pointing north of east.
Seven metres of walking, five metres of result. The missing two metres are the price of not going in a straight line.
Example 2 — half a circle
A cyclist rides half-way round a circular track of radius 7 m.
- Distance is half the circumference: π × 7, which is 22 m if you take π as 22/7.
- Displacement is the straight line across the circle — the diameter — so 14 m.
Complete the lap and the distance becomes 44 m while the displacement drops to zero, because the cyclist is back at the starting point.
Example 3 — out and back on a straight road
A car drives 60 km from town A to town B and then 20 km back toward A.
- Distance = 60 + 20 = 80 km.
- Displacement = 60 − 20 = 40 km from A, toward B.
This is where the sign matters. If "toward B" is taken as positive, the first leg is +60 km and the second is −20 km. Displacements along a line are added with their signs; distances are added without them.
Why physics needs both
A car's odometer records distance. It is what you pay fuel for, and it never runs backward. A map's "as the crow flies" figure is the size of a displacement.
The split carries straight into the next pair of ideas. Speed is built from distance and velocity is built from displacement, which is exactly why a round trip can have a healthy average speed and an average velocity of zero. That is worked through in the difference between speed and velocity.
Where marks are lost
- Adding at right angles. For legs that are perpendicular, the displacement comes from Pythagoras, not from adding the two numbers.
- Forgetting the direction. "5 m" is a distance. "5 m, north of east" is a displacement. A displacement written without a direction is incomplete.
- Calling the diameter the distance. On a circular path the body travels along the arc. The diameter is the displacement after half a turn.
- Assuming zero displacement means no motion. It only means the body finished where it started.
Quick check
A boy runs once round a square field of side 10 m and stops at the corner he started from. What are the distance and the displacement? Then answer again for the moment he reaches the corner diagonally opposite.
Full lap: distance 40 m, displacement 0. At the opposite corner he has run two sides, so the distance is 20 m, and the displacement is the diagonal, 10√2 ≈ 14.1 m.