How to use the point to line distance calculator
Find the shortest distance from a point to a straight line Ax + By + C = 0. Enter coefficient a, coefficient b, constant c, point x-coordinate, point y-coordinate in the fields above; the distance from point to line, foot of perpendicular x are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “distance from point to line”, “perpendicular distance”, “line distance formula”, “calculate point to line distance”, “find distance from point to line”.
Formula
Variables
- A — Coefficient A
- B — Coefficient B
- C — Constant C
- px — Point x-coordinate
- py — Point y-coordinate
Worked example
With coefficient a = 3, coefficient b = 4, constant c = -12, point x-coordinate = 1, point y-coordinate = 2, the calculator gives distance from point to line ≈ 0.2; foot of perpendicular x ≈ 1.12.
Frequently asked questions
What is the point to line distance calculator used for?
Find the shortest distance from a point to a straight line Ax + By + C = 0. It helps with questions such as “distance from point to line”, “perpendicular distance”, “line distance formula”.
What is the formula for the point to line distance calculation?
Distance from point to line = abs(A × px+B × py+C) / √(A × A+B × B). Foot of perpendicular x = px-A × (A × px+B × py+C) / (A × A+B × B). Here A is coefficient a, B is coefficient b, C is constant c, px is point x-coordinate, py is point y-coordinate.
What inputs do I need for the point to line distance calculator?
You need coefficient a, coefficient b, constant c, point x-coordinate, point y-coordinate. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the point to line distance calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the point to line distance result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.