Point to Line Distance Calculator
Find the perpendicular distance from a 2D point to a line, using standard form or two points on the line, with signed distance and closest point.
Point to line distance in 2D
English calculator intent focuses on the perpendicular distance from a point to a line on the coordinate plane. The most common input is line standard form, but two points on the line are also useful for geometry problems.
d is distance from point (x0, y0) to line Ax + By + C = 0.
Closest point and signed distance
- The ordinary distance is always nonnegative.
- Signed distance shows which side of the line the point is on for the chosen normal direction.
- The closest point is the foot of the perpendicular from the point to the line.
- Vertical and horizontal lines are handled by the same standard-form formula.
Examples
| Point | Line | Distance |
|---|---|---|
| (0, 0) | 3x + 4y - | 2 |
| (2, 5) | 0 | |
| (3, 1) | 4 |
Frequently Asked Questions
Sources and References
- Distance From Point to Line CalculatorCalculator Academy
- Distance between a line and a point calculatorMathPortal
- Point-Line Distance--2-DimensionalWolfram MathWorld
- Distance from a point to a lineWikipedia
Calculations are based on the listed reference sources. Links open in a new tab.
Related Tools
Find where two 2D lines intersect from standard form, slope-intercept form, or two points on each line. The calculator also detects parallel and coincident lines.
Calculate the slope of a line from two points, an angle, or standard-form coefficients. Shows undefined vertical slope, angle, intercept, and perpendicular slope.
Calculate the Euclidean distance between two points in 2D or 3D coordinates, with midpoint, coordinate differences, Manhattan distance, Chebyshev distance, and angle.
Calculate the shortest distance from a point to a 3D line using a point and direction vector or two points on the line, with projection and closest point.