Both distance and displacement tell you how far something has moved — but they answer slightly different questions. Distance asks “how much ground did you cover?” while displacement asks “how far are you from where you started, and in which direction?” Getting this difference clear now makes the rest of motion much easier.
📘 What you need to know
Distance: the total length of the path travelled. It only has a size (a number + unit), so it’s a scalar.
Displacement: a straight line from start to finish, with a direction. It has size and direction, so it’s a vector.
Scalar = size only (e.g. distance, speed). Vector = size and direction (e.g. displacement, velocity).
Both are measured in metres (m) in SI units.
Displacement can be zero even after a long journey — if you finish back where you began.
Displacement can also be negative, because direction matters (e.g. 5 m left instead of 5 m right).
Distance — the path you actually walked
Distance is simply how far you travelled in total, following every twist and turn of your path. It doesn’t care which way you went — only the total length counts. Because there’s no direction attached, distance is a scalar.
Think about jogging once around a running track and stopping exactly where you started. You’ve clearly moved — your legs are tired! That “how far did my feet travel” amount is the distance.
Displacement — the straight-line shortcut
Displacement ignores the route completely. Draw an arrow straight from your starting point to your finishing point: the length of that arrow is the size of the displacement, and the way it points is the direction. Because it carries a direction, displacement is a vector.
In words
displacement = how far you are from the start + the direction
The dashed trail winding past the trees and pond is the distance (the real route). The straight green arrow is the displacement — start → finish, with direction.
A quick everyday example
Imagine walking from home to school. The distance is the full length of every street you follow, including all the corners you turn. The displacement is a single straight arrow from your front door to the school gate — straight through any buildings, parks or rivers in between. The displacement is almost always shorter than the distance.
One-line summary: distance = whole path (scalar). Displacement = straight line start → finish, with direction (vector).
Why displacement can be zero
Here’s the part students often find strange. Run a full lap of a 400 m track and finish on the starting line: you’ve covered a distance of 400 m, but your displacement is 0 m — because the straight arrow from start to finish has no length when start and finish are the same point.
A full lap: lots of distance covered, but you end up exactly where you started — so the displacement is zero.
A handy way to remember it: distance is what your shoes feel; displacement is what a bird flying straight overhead would measure between your start and end points.
Spotting scalars and vectors
This distance/displacement pair is your first example of a bigger idea that runs through all of physics. Some quantities only need a size; others need a size and a direction.
🧭 How to decide: scalar or vector?
Ask “does direction matter here?” If yes → vector. If no → scalar.
Distance: “I walked 3 km” makes sense without a direction → scalar.
Displacement: “I’m 3 km north-east of home” needs the direction → vector.
Same logic later separates speed (scalar) from velocity (vector).
Worked examples
WE 1
Walking around a rectangular garden
A professor walks once around her rectangular garden along the path A → B → C → D → A. The long sides are 15 km and the short sides are 9 km. At the end of the walk, find (a) the total distance travelled and (b) the displacement.
The walk goes all the way round the rectangle and returns to corner A.
(a) Distance — add up every side15 + 9 + 15 + 9distance = 48 km(b) Displacement — start and finish are both Ashe ends exactly where she began, so the straight arrow has no lengthdisplacement = 0 km
WE 2
Athletes on a 400 m track
Some runners race 300 m around a 400 m oval track, all starting from the same line. At the end, they are 100 m (in a straight line) from where they began. State their (a) distance and (b) displacement.
(a) Distance = the path they randistance = 300 m(b) Displacement = straight line, start → finishgiven as 100 m from the startdisplacement = 100 m (in that direction)if they had run the full 400 m lap, the displacement would be 0 m.
WE 3
There and back again
A student walks 8 m east to a shop, then walks 8 m back west to the exact spot they started. Find the (a) total distance and (b) displacement.
(a) Distance — add both parts of the trip8 m + 8 mdistance = 16 m(b) Displacement — back at the start8 m east then 8 m west cancel outdisplacement = 0 m
WE 4
A right-angled walk
A hiker walks 3 km north, then turns and walks 4 km east. Find the (a) distance walked and (b) the size of the displacement.
(a) Distance — add the two legs3 km + 4 kmdistance = 7 km(b) Displacement — straight line, use Pythagorasd = √(3² + 4²) = √(9 + 16) = √25displacement = 5 km (north-east)the straight-line displacement is shorter than the 7 km actually walked.
💡 Top tips
Always give displacement a direction (e.g. “5 km north-east”, “100 m to the right”). A displacement with no direction is only half an answer.
Returned to the start? Displacement is 0 — no matter how far you walked.
Check the units are metres in SI; convert km, cm or mm if needed.
For an L-shaped or right-angled path, the straight-line displacement often needs Pythagoras.
⚠ Common mistakes
Treating them as the same thing: distance and displacement only match when the motion is in one straight line with no turning back.
Forgetting the direction on displacement — that’s what makes it a vector.
Adding displacements like plain numbers: 8 m east + 8 m west is 0 m, not 16 m. Direction decides whether they add or cancel.
Thinking a bigger journey means a bigger displacement — a full loop has lots of distance but zero displacement.
Up next: Speed & Velocity — the same scalar-vs-vector idea, but now applied to how fast you’re moving rather than how far.
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