Distance Between Points

x₁

y₁

x₂

y₂

Advanced options

z₁

z₂

Result

Distance in the plane5
Distance in space5
Midpoint(2.5; 4)
Δx3
Δy4
Manhattan distance7

Pythagoras in coordinates

Distance in the plane and in space, the midpoint of the segment, and the Manhattan distance along a street grid.

The distance formula is Pythagoras in disguise: the coordinate differences are the legs and the distance is the hypotenuse. In three dimensions a third term joins the sum under the root and the logic is unchanged.

Manhattan distance is shown alongside — the sum of the absolute coordinate differences. That is how far you actually walk on a rectangular street grid, and it matters more than the straight line in routing problems.

What this calculator shows

Distance in the plane and in three dimensions
The coordinates of the midpoint
The coordinate differences and the Manhattan distance

What to keep in mind

The coordinate system is rectangular with equal scaling on each axis.
This does not work for distances on the Earth's surface — those need the haversine formula and its allowance for curvature.

FAQs

How do I find the midpoint?

Average each coordinate: the midpoint x is (x₁+x₂)/2 and likewise for y. The pair is printed ready to use.

What is Manhattan distance?

The sum of the absolute coordinate differences — travel along a grid with no diagonals. Named after Manhattan's street layout and widely used in pathfinding algorithms.

Can I use this between cities?

No, the Earth is not flat. Geographic coordinates need the haversine formula, which accounts for the curvature.

How do I work in three dimensions?

Fill in z₁ and z₂ under the advanced settings. The formula is the same with one more squared difference under the root.

Worked example

From (1, 2) to (4, 6)

Input: x₁=1, y₁=2, x₂=4, y₂=6

Output: Distance exactly 5

Note: The differences are 3 and 4 — a Pythagorean triple again. Manhattan distance is 7: walking the grid takes longer than flying straight.

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Distance Between Points

Result

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