Measure the straight-line separation between two points in a coordinate plane. The page traces how the inputs become distance before rounding.
The coordinate distance formula is the Pythagorean theorem applied to horizontal and vertical changes. Squaring removes direction and the final square root restores the original unit. For a connected concept in Distance Formula, see center of the segment.
The calculation treats x₁, y₁, x₂ and y₂ according to their labels, not as interchangeable values in distance formula.
Coordinate distance is used in analytic geometry, mapping on flat grids, screen layouts, and vector calculations. It represents the direct segment, not a route constrained to horizontal and vertical streets.
The order of points does not matter, but each coordinate must remain paired with its own point. On the Earth's curved surface, latitude and longitude require a spherical or ellipsoidal distance model instead. If the Distance Formula assumptions do not fit, consider right-triangle relation.
Save extra digits internally if distance will become an input to another calculation.
Between (−2, 4) and (5, −1), horizontal change is 7 and vertical change is −5. Distance is √(7² + (−5)²) = √74, approximately 8.6023. This Distance Formula example can be compared with directional steepness.
Subtract x-coordinates and y-coordinates, square both differences, add the squares, and take the nonnegative square root. Keep radical form if an exact result is requested.
Transfer x₁, y₁, x₂ and y₂ one at a time and keep their units visible in your notes. This page can validate numerical ranges, but only the reader can confirm that each value represents the intended quantity.
Translation and rotation preserve the distance. Doubling both coordinate differences doubles the result, while changing only one component follows a square-root rather than simple additive response. Trying a nearby input should follow this pattern; otherwise inspect the field assignment.
Attach units and the name distance whenever the answer leaves this page. A rounded value is suitable for presentation, while retained working digits are safer for a dependent calculation.
Euclidean distance follows the straight segment. Grid-walking or taxicab distance instead adds absolute horizontal and vertical changes and will generally be longer. That neighboring measure needs its own setup rather than a relabeled answer.
Copying only the decimal discards the setup. Pair the distance with x₁, y₁, x₂ and y₂ and the unit convention so another reader can reconstruct its meaning.
No. Geometric length is nonnegative.
No. Reversing the order negates both differences, but their squares stay the same.
No. It is Euclidean straight-line distance.
Both coordinate changes are zero, so the distance is zero.
The result uses the same coordinate unit; label it when the coordinates represent physical measurements.