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Distance Between Two Points

Find the Euclidean distance between two coordinates.

How it is calculated

The straight-line (Euclidean) distance between points (x1, y1) and (x2, y2) is d = √((x2 − x1)² + (y2 − y1)²). The horizontal difference and the vertical difference are the two legs of a right triangle and d is its hypotenuse.

Coordinates can be negative or decimal, and the order of the points does not matter because the differences are squared. The answer is in the same unit as your coordinates (the tool has no units of its own) and is displayed rounded to two decimals. It measures flat, plane distance only, not distance along roads or on the curved Earth.

Worked example

Find the distance from (1, 2) to (4, 6). The horizontal difference is 4 − 1 = 3 and the vertical difference is 6 − 2 = 4. Squares: 9 and 16, which sum to 25. The square root of 25 gives a distance of 5.00 units.

Try this example →

Common mistakes

  • Subtracting x from y within the same point instead of comparing x with x and y with y.
  • Forgetting to take the square root and reporting 25 instead of 5.
  • Entering latitude and longitude in degrees and expecting a real distance on Earth; degrees are not equal-length units, so a great-circle formula is needed.
  • Mixing units between axes, such as x in metres and y in kilometres.

Sources

About this calculator

This calculator finds the straight-line (Euclidean) distance between two points on a plane, using the coordinates of each point and the Pythagorean theorem — treating the horizontal and vertical gaps between the points as the two legs of a right triangle and the direct distance as its hypotenuse. Entering the x and y coordinates of both points returns that direct distance instantly.

This calculation underlies a wide range of practical and technical uses: in geometry and coordinate-plane coursework, students use it to verify distance calculations done by hand; in programming and game development, it's a routine building block for collision detection, pathfinding and physics simulations where objects' positions are tracked as coordinates; and in mapping, CAD and design work, it's used to measure the direct distance between two points on a grid or drawing without accounting for any obstacles along the way.

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Comments (1)

  • Editorial team

    This is straight-line distance on a flat grid, with both points in the same unit and the answer in that unit too. It suits pixel positions, graph-paper coordinates and CAD or game maps. Do not feed it latitude and longitude: a degree of longitude is shorter than a degree of latitude away from the equator, so the flat formula gives wrong distances. Are you working with pixels, a map grid or a drawing, and would you want a 3D version?

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