How the Distance Formula Works
The distance formula is the Pythagorean theorem in disguise. The horizontal gap between two points is one leg of a right triangle, the vertical gap is the other leg, and the straight-line distance is the hypotenuse.
2D and 3D Versions
In 2D you square two differences; in 3D you square three. The pattern extends to any number of dimensions โ just keep adding squared coordinate differences under the square root.
Exact vs. Decimal Answers
Many distances are irrational (like โ50). Geometry classes often want the exact radical form, while applied problems want the decimal โ this tool shows both.
The same right-triangle idea powers our Pythagorean theorem calculator โ and you can check the arithmetic with the four-function calculator.