Distance Calculator
Distance and Midpoint Between Two Points works out Distance and Euclidean distance from x₁, y₁ and x₂. The default figures on this page give distance of 5.000000; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
6 steps
- Δx = 3 − 0 = 3; Δy = 4 − 0 = 4
- d = √(Δx² + Δy²)
- d² = (3)² + (4)² = 25
- d = √25 = 5
- Midpoint = (1.5, 2)
- Slope of the segment = Δy / Δx = 4 / 3 = 1.3333333333
Its 4 worked examples are re-run on every release, last on 15 September 2026. What changed
What the Distance and Midpoint Between Two Points calculates
Computes the distance and midpoint between two points in the Cartesian plane or in 3D space, using the Euclidean, Manhattan, Chebyshev or Minkowski metric.
How to use this Distance and Midpoint Between Two Points
Enter x₁, y₁, x₂ and y₂. Distance updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Distance, Euclidean distance and Manhattan distance.
The method follows Euclid, Elements, Book I, Proposition 47 (Pythagorean theorem) — basis of the distance formula, NIST Dictionary of Algorithms and Data Structures — Manhattan distance, Chebyshev distance and Weisstein, Eric W. "Distance." MathWorld — Minkowski / L^p metric.
3-4-5 right triangle: (0,0) to (3,4) example
With x₁: 0, y₁: 0, x₂: 3, y₂: 4, the calculator returns Distance: 5, Midpoint x: 1.5, Midpoint y: 2. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Distance, Euclidean distance and Manhattan distance. The inputs you can vary are x₁, y₁, x₂, y₂, z₁ (optional) and z₂ (optional).
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How can I calculate the distance between two locations?
Computes the distance and midpoint between two points in the Cartesian plane or in 3D space, using the Euclidean, Manhattan, Chebyshev or Minkowski metric. Open “How this is worked out” beside the result to see each step for your own figures.
How do I calculate distance?
It needs x₁, y₁, x₂, y₂, z₁ (optional) and z₂ (optional). Nothing else is required, and the figures stay in your browser.
How can I calculate the distance between two cities?
The result gives Distance, Euclidean distance, Manhattan distance, Chebyshev distance, Minkowski distance and Distance squared, each labelled with its unit so the figure can be read on its own.
Can I Measure a distance with my phone?
Computes the distance and midpoint between two points in the Cartesian plane or in 3D space, using the Euclidean, Manhattan, Chebyshev or Minkowski metric. On the figures this page opens with — x₁ 0, y₁ 0 and x₂ 3 — the distance is 5. Put your own figures in their place and the working updates beside the result.
What information do I need for the Distance and Midpoint Between Two Points?
You need x₁, y₁, x₂, y₂, z₁ (optional), z₂ (optional), Distance metric and Minkowski order p. The page opens with default figures that give distance of 5.000000, so you can see the scale before entering your own.
What does this Distance and Midpoint Between Two Points show?
It shows Distance, Euclidean distance, Manhattan distance, Chebyshev distance, Minkowski distance, Distance squared, Δx (run) and Δy (rise), with the working and any warnings for your entries.