What is the distance formula?

The distance between two points is the square root of the change in x squared plus the change in y squared. It is the Pythagorean theorem applied to the horizontal and vertical gaps between the points.

Does the order of the points matter?

No. Because the differences are squared, swapping the two points gives the same distance. Distance is always positive or zero.

Can it handle negative coordinates?

Yes. Enter negative values freely. The formula uses the difference between the coordinates, so negatives are handled correctly.

Distance Formula Calculator

This distance formula calculator finds the straight-line distance between two points on a coordinate plane. The distance formula is one of the most useful results in coordinate geometry, and it is simply the Pythagorean theorem in disguise: the gap between two points is the hypotenuse of a right triangle whose other two sides are the horizontal and vertical distances between them. So the distance is the square root of the change in x squared plus the change in y squared. You enter the x and y coordinates of the first point and the second point, and the calculator returns the distance along with the individual changes in x and y, which are the legs of that right triangle, so you can see exactly how the answer is built. The order of the points does not matter, since the differences are squared before being added, and negative coordinates are handled correctly. This is a core skill in school and university geometry, and it has real applications in mapping, navigation, computer graphics, game development and any field that works with positions on a grid. The result is exact within normal precision and updates the moment you change a coordinate. Enter the two points to see the distance between them straight away.

Point 1: x

Point 1: y

Point 2: x

Point 2: y

distance between the points

Change in x3

Change in y4

How it works

The calculator subtracts the x coordinates to get the change in x, and the y coordinates to get the change in y. It squares each, adds them, and takes the square root. This is the distance formula, which is the Pythagorean theorem with the changes in x and y as the two shorter sides.

Worked example

From the point 1, 2 to the point 4, 6, the change in x is 3 and the change in y is 4. The distance is the square root of 9 plus 16, which is the square root of 25, or 5.

Related calculators

Midpoint Calculator: the middle point.
Slope Intercept Calculator: line equations.
Hypotenuse Calculator: right triangle sides.
Pythagorean Theorem Calculator: a squared plus b squared.

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