Distance and displacement

What you need to know

• Distance is the total length of the path travelled — it is a scalar (magnitude only, no direction).
• Displacement is the straight-line distance from start to finish, including the direction — it is a vector.
• A displacement answer must state both magnitude (e.g. 40 m) and direction (e.g. north, or at 30° east of north).
• A scalar has magnitude only; a vector has both magnitude and direction — this is the key conceptual split.

The big picture

Distance tells you how far an object has travelled along its path — it is always a positive number and has no direction. Displacement is different: it is the straight-line distance from start to finish, but it also includes the direction of that line. Because distance has magnitude only it is a scalar quantity, while displacement has both magnitude and direction making it a vector. Knowing this distinction is the foundation of all AQA motion topics.

From distance to displacement — how they differ

Follow one object moving through space and watch how the two quantities behave differently at each stage.

1. 1

   The object starts moving

   At the moment the object leaves its starting point, both distance and displacement are zero. They are about to diverge — distance will track every metre of path, displacement will track only the straight-line gap.

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2. 2

   Object travels along a curved or winding path

   Distance increases with every metre of path travelled, regardless of direction. Displacement, however, is only the straight-line distance from the start to the current position — it can be much smaller than distance if the path has turned.

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3. 3

   Object changes direction

   When the object turns back towards its start, distance keeps growing (it never decreases). But the straight-line gap between start and current position — the displacement magnitude — shrinks. Direction of displacement also changes as the object turns.

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4. 4

   Object returns to the starting point

   When the object arrives back at its start, displacement = 0 m because the straight-line distance from start to finish is zero. Distance = the full length of the path taken. This one scenario proves that distance and displacement are fundamentally different quantities.

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5. 5

   Recording the answer correctly

   Distance is recorded as a magnitude only (e.g. 400 m) — no direction needed, because it is a scalar. Displacement must always be recorded as a magnitude AND a direction (e.g. 250 m north-east) — because it is a vector. Missing the direction loses marks.

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Stop and predict

Commit to an answer before you reveal — this is how the concept sticks.

A student walks 300 m from home to a shop, then walks 300 m back home. Which row correctly gives their distance and displacement for the whole journey?

Tap any cell to reveal it. Tap a column header to read one property down every item.

Memory hook

Think of a satnav (displacement) vs a trip meter (distance). The satnav shows 'head north 3 km' — direction included. The trip meter just adds up every metre you drove.

Check yourself

A runner completes exactly one lap of a 400 m track. Without looking — what is her distance travelled, and what is her displacement?