Point-to-Line Distance Calculator
Compute the perpendicular distance from a point to a line Ax+By+C=0.
About Point-to-Line Distance Calculator
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
Worked example
With the default values below, Point-to-Line Distance Calculator returns Distance of 4.0000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Point x
- 3
- Point y
- 4
- A (coefficient of x)
- 3
- B (coefficient of y)
- 4
- C (constant)
- -5
Results
- Distance
- 4.0000 units
Step by step
- 1Numerator |Ax₀ + By₀ + C|= 20
- 2Denominator √(A² + B²)= 5.0000
- 3Distance= 4.0000
Assumptions and limits
- The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.