Point-to-Line Distance Calculator
Compute the perpendicular distance from a point to a line Ax+By+C=0.
Inputs
Distance
4.0000units
Step by step
Numerator |Ax₀ + By₀ + C|
|3×3 + 4×4 + -5|
= 20
Denominator √(A² + B²)
√(3² + 4²)
= 5.0000
Distance
d = 20 / 5.0000
= 4.0000
How it works
The perpendicular distance from point (x₀, y₀) to line Ax+By+C=0 is |Ax₀+By₀+C| / √(A²+B²).
Formula
Point-Line Distance
d = |Ax₀ + By₀ + C| / √(A² + B²)
- x₀,y₀
- The point
- A,B,C
- Line coefficients in Ax+By+C=0
Frequently Asked Questions
How do I convert y = mx + b to Ax + By + C = 0?
Rearrange: mx − y + b = 0, so A = m, B = −1, C = b.
Is the distance always positive?
Yes — distance is always non-negative. It equals zero only when the point lies on the line.