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Distance Calculator

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Enter two coordinate points to find the straight-line distance between them.

Distance Calculator

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Distance
13

The formula

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Example

From (2, 3) to (7, 15): distance = √((7-2)² + (15-3)²) = √(25 + 144) = √169 = 13.

Step-by-step guide

  1. Enter the coordinates of your first point (x₁, y₁).
  2. Enter the coordinates of your second point (x₂, y₂).
  3. Read the straight-line distance between them.

Why this is just the Pythagorean theorem in disguise

The distance formula isn't a separate rule to memorize - it's the Pythagorean theorem applied directly to coordinate geometry. The horizontal difference (x₂ - x₁) and vertical difference (y₂ - y₁) between two points form the two legs of a right triangle, and the straight-line distance between the points is exactly the hypotenuse of that triangle. This is also why the example above (2,3) to (7,15) gives a clean whole number - the horizontal and vertical differences, 5 and 12, form a classic Pythagorean triple with a hypotenuse of exactly 13.

Common mistakes

Subtracting coordinates in the wrong order and forgetting to square the result - since squaring removes any negative sign, the order of subtraction (x2-x1 vs x1-x2) doesn't actually affect the final answer, but skipping the squaring step does.
Adding the differences before squaring instead of squaring each one separately first - the formula requires squaring each difference individually, then summing the squares.

Frequently asked questions

Does this work for negative coordinates?

Yes - the formula works correctly regardless of whether coordinates are positive or negative, since squaring the differences eliminates any sign issues.

Can this be extended to 3D coordinates?

Yes - the same pattern extends naturally by adding a squared z-difference term inside the square root, following the same underlying geometric logic in three dimensions.

Is this the same as distance on a map (accounting for curvature)?

No - this calculates straight-line ("as the crow flies") distance on a flat plane. Real-world distances over large areas of the Earth's curved surface use different formulas that account for that curvature.

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