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 — just keep adding squared coordinate differences under the square root.
Exact vs. Decimal Answers
Many distances are irrational (like √50). Geometry classes often want the exact radical form, while applied problems want the decimal — this tool shows both.
The same right-triangle idea powers our Pythagorean theorem calculator — and you can check the arithmetic with the four-function calculator.