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Distance Between Two Points Calculator

Computes the straight-line (Euclidean) distance between two points in the plane, their midpoint, the coordinate differences and the Manhattan distance.

When to use

You have two (x, y) coordinates and need the distance between them or the point halfway between them.

Do not use when: You need the slope or equation of the line through the points (use slope) or the third side of a right triangle from two sides (use pythagorean).

Formula

distance = √((x₂ − x₁)² + (y₂ − y₁)²); midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2); manhattan = |x₂ − x₁| + |y₂ − y₁|

Inputs

Parameter	Type	Required	Description
`x1`	number	yes	x-coordinate of the first point.
`y1`	number	yes	y-coordinate of the first point.
`x2`	number	yes	x-coordinate of the second point.
`y2`	number	yes	y-coordinate of the second point.

Outputs

Output	Type	Description
`distance`	number	√((x₂ − x₁)² + (y₂ − y₁)²).
`midpoint_x`	number	(x₁ + x₂) / 2.
`midpoint_y`	number	(y₁ + y₂) / 2.
`midpoint`	string	The midpoint as a coordinate pair, e.g. '(2, 4)'.
`delta_x`	number	x₂ − x₁.
`delta_y`	number	y₂ − y₁.
`manhattan_distance`	number	\|Δx\| + \|Δy\|: the grid (taxicab) distance.

Example

(0, 0) to (3, 4): {"x1":0,"y1":0,"x2":3,"y2":4} → {"distance":5,"midpoint_x":1.5,"midpoint_y":2,"midpoint":"(1.5, 2)","delta_x":3,"delta_y":4,"manhattan_distance":7}

(1, 2) to (4, 6): {"x1":1,"y1":2,"x2":4,"y2":6} → {"distance":5,"midpoint_x":2.5,"midpoint_y":4,"midpoint":"(2.5, 4)","manhattan_distance":7}

GET https://tttkmbb.com/api/v1/calculate/distance-2d?x1=0&y1=0&x2=3&y2=4

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/distance-2d (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/distance-2d · Markdown: https://tttkmbb.com/math/distance-2d.md · JSON definition: https://tttkmbb.com/math/distance-2d.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="distance-2d"
OpenAPI operationId: calculate_distance_2d
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Euclidean distance (reference)
Wikipedia – Midpoint (reference)
Wolfram MathWorld – Distance (reference)

FAQ

Does the order of the points matter?

Not for the distance or midpoint. Δx and Δy are signed (second minus first), so they flip sign if the points are swapped.

Can I use this for GPS coordinates?

Only for very short distances. Latitude/longitude lie on a sphere; use the haversine formula for geographic distances.

Related calculators

Slope Calculator — Slope and equation of the line through the points.
Pythagorean Theorem Calculator — The distance formula is the Pythagorean theorem applied to Δx and Δy.
Right Triangle Calculator — Full right-triangle solver.