How to Calculate Distance
Distance measures how far apart two points or objects are. In geometry, the Euclidean distance formula gives the straight-line distance between two points on a coordinate plane. This distance calculator handles both 2D and 3D coordinates, and it also supports the simple speed-times-time formula used in physics and travel planning.
The Distance Formula
In two dimensions, the distance between points (x₁, y₁) and (x₂, y₂) is the square root of (x₂ - x₁)² plus (y₂ - y₁)². This formula is a direct application of the Pythagorean theorem: the horizontal and vertical differences form the legs of a right triangle, and the distance is the hypotenuse. In three dimensions, the formula simply adds a term for the z-coordinate difference.
Speed, Time, and Distance
For movement problems, distance equals speed multiplied by time. If you drive 60 miles per hour for 2 hours, you travel 120 miles. Rearranging the same relationship lets you find speed from distance and time, or time from distance and speed. This mode is handy for road trips, running training, and estimating delivery times.
Where Distance Calculations Are Used
The distance formula appears in map applications when measuring straight line distances between locations, in video games when checking how close two objects are, and in physics when analyzing motion. Surveyors and engineers use three-dimensional distances to plan structures and measure terrain.
Since the distance formula is built on the Pythagorean theorem, our Pythagorean theorem calculator is a natural companion for solving right-triangle problems.