Distance Between Points

Written byOleh Soloninupdated 27 September 2026

x₁

y₁

x₂

y₂

Advanced options

z₁

z₂

Result

Distance in the plane5
Workingd = √((4 − 1)² + (6 − 2)²) = √25 = 5
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.

How to use

Enter the coordinates of the first point; leave z at zero for a flat problem.
Enter the coordinates of the second point.
Read the distance in the plane and in space, the midpoint and the coordinate differences.

The distance formula is Pythagoras in disguise

The coordinate differences are the legs of a right triangle and the distance is its hypotenuse: from (1, 2) to (4, 6) the legs are 3 and 4, so the distance is 5. Space adds a third leg and one more term under the root.

The sign of the differences never matters, because they are squared. Swapping the two points leaves the distance unchanged, and the slope too: both differences change sign together, so their ratio stays the same.

Worked out with this calculator in the plane.
Point A	Point B	Differences	Distance
(1, 2)	(4, 6)	3 and 4	5
(0, 0)	(5, 12)	5 and 12	13
(0, 0)	(1, 1)	1 and 1	1.4142

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.

What is the distance between (1, 2) and (4, 6)?

Five. The differences are 3 and 4, their squares are 9 and 16, and the square root of 25 is 5.

Does swapping the points change the answer?

No. The differences are squared, so their signs disappear and the distance is the same in both directions.

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

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