ClarityHow to use this tool
- Enter point x, point y, line a, line b, line c.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
The method, explained
Perpendicular distance = |a×x₀+b×y₀+c| / hypot(a,b). The denominator normalizes the line’s coefficient scale.
Using point x = 3, point y = 4, line a = 1, line b = -1, line c = 0, the result is 0.707106781. Change these example inputs to match your task; use the method above to check each step.
Understanding your result
Multiplying a, b and c by the same nonzero factor describes the same line. The numerator and denominator scale together, leaving the distance unchanged.
What to keep in mind
Distance to an infinite line; it is not distance to a bounded segment. Coordinates must use the same length unit. Use the indicated units consistently. Ideal shapes are assumed; dimensions must describe the same object. Display rounding does not increase measurement precision.
Common questions
Does scaling the line coefficients change the distance?
Multiplying a, b and c by the same nonzero factor describes the same line. The numerator and denominator scale together, leaving the distance unchanged.
How can I check the result?
Perpendicular distance = |a×x₀+b×y₀+c| / hypot(a,b). The denominator normalizes the line’s coefficient scale. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.
Methodology maintained by ClarityKit. How these tools are built and checked.