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Distance vs displacement: what's the difference?

Highlighted from a real textbook passage. Explained by Clicked.

Used in a sentence

University Course Reader · STEM

After the full circuit the runner's displacement was zero, though she had covered another 3 miles.

The reader highlighted one word in a textbook passage. Clicked broke down the physics term “displacement” into plain English:

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Overview

Distance is the total length of the path something travels. Displacement is the straight line from where it started to where it ended, with a direction. Drive between two towns 8 miles apart on the map, along a road that winds for 12, and your distance is 12 miles. Your displacement is 8 miles east, because the second town lies 8 miles east of the first. Distance says how far you went. Displacement says how far you got, and which way.
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Overview

Distance is how far you actually travelled. Displacement is how far you ended up from where you started, and which way. Jog a loop round the park, back to your doorstep, and your watch says 3 miles. That is distance, and it is why your legs ache. Your displacement is zero, because you are standing exactly where you set off. Distance is what you did. Displacement is where it left you. 😎

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Detail

Distance is the total length of the path something travels. Displacement is the straight line from where it started to where it ended, and it has a direction. Two towns face each other across a bay, 5 miles apart. You can cross by ferry, straight over the water, or drive round the shore on 30 miles of road. Either way you start in one town and finish in the other, so either way your displacement is 5 miles, north across the bay. Your distance is 5 miles by ferry and 30 by road, because distance counts every mile you cover, whichever way it points. Displacement depends only on where you start and finish; distance depends on the route in between. So displacement can never be larger than distance, because a straight line is the shortest route there is, and the two match only when you travel straight and never turn back. And a round trip has a displacement of zero: drive there and back and you finish where you started, with 60 miles of distance to show for it. The same split runs into speed and velocity. You cover the 30 miles of road in an hour, so your average speed is 30 miles an hour. Your average velocity is your displacement over that hour, 5 miles an hour heading north. That heading is what makes displacement a vector, and distance, with no direction, a scalar.
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Detail

Distance is how far you actually travelled, and displacement is how far you ended up from where you started, and in which direction. You leave your hotel in a strange city to find the cathedral, and you get lost. Two hours of wrong turns later you are standing in front of it, and your phone says you have walked 6 miles. That is your distance, and every wrong turn is in it. The cathedral turns out to be 300 yards from the hotel door, straight up the street. That is your displacement, 300 yards up the street. Every step went into the distance. Only two spots go into the displacement, the hotel door and the cathedral steps, and the line between them. Somewhere in those two hours you walked away from the cathedral for a while, so your distance kept growing while your displacement shrank. Distance only ever increases. Displacement can increase, shrink or land on zero, and it carries a direction, which distance never does. Average speed is your 6 miles divided by the two hours, 3 miles an hour. Average velocity is your displacement divided by the same two hours, 150 yards an hour, up the street. Distance is the walk. Displacement is where the walk left you. 😎

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Analogy

Distance is the way you walk to a shop, and displacement is the way a crow flies there. Set off from your front door to a shop half a mile away and the streets bend, so you walk a mile and a half. That is your distance, every yard of it, whichever way each street pointed. A crow leaves your roof and flies straight to the shop, half a mile in the direction the shop lies. The crow's flight is your displacement. It shows how far your finish lies from your start, and which way. Walk a longer way round and your distance increases, but the crow flies the same half mile, so your displacement stays the same.
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Analogy

How far you swim is distance, and where you climb out compared with where you got in is displacement. Forty lengths of a 25-yard pool add up to a thousand yards, and your shoulders know every one of them. Climb out at the end you dived in from and your displacement is zero, because you finished exactly where you started. Climb out at the far end instead, after thirty-nine lengths, and your displacement is 25 yards, shallow end to deep end, while your distance is 975 yards. Every length counts towards distance. Displacement asks one thing only: where did you get out, compared with where you got in. 😎
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AI explanations may contain errors · Not professional advice

Formal definition — The same term, explained the usual way

Distance is a scalar quantity equal to the total length of the path traversed by a moving body, irrespective of direction; it is non-negative and never decreases along a journey. Displacement is a vector quantity equal to the change in position of the body, defined by the straight-line separation between its initial and final positions and the direction from one to the other. Its magnitude is less than or equal to the distance travelled, with equality only for straight-line motion in a single direction, and it is zero for any journey that returns to its starting point. Both are measured in units of length (SI: the metre). Average speed is distance divided by elapsed time; average velocity is displacement divided by elapsed time.

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