What formula is used?

The perpendicular distance from point (x₀, y₀) to line Ax + By + C = 0 is d = |Ax₀ + By₀ + C| / √(A² + B²). This gives the shortest possible distance — the length of the perpendicular dropped from the point to the line.

What if I only have two points on the line?

Switch to Two-Point mode. The tool converts the two points (x₁, y₁) and (x₂, y₂) into standard form internally using A = y₂ − y₁, B = x₁ − x₂, C = x₂y₁ − x₁y₂, then applies the same formula.

Can the distance be zero?

Yes — if the point lies exactly on the line, Ax₀ + By₀ + C = 0, so the numerator is zero and the distance is 0.

What does it mean if A and B are both zero?

If A = 0 and B = 0 simultaneously, the equation Ax + By + C = 0 does not define a line (it collapses to a contradiction or a trivially false statement). The calculator will flag this as an invalid line.

Is the result always positive?

Yes. Distance is always non-negative. The absolute value in the numerator ensures the result is ≥ 0 regardless of which side of the line the point is on.

Distance Point To Line Calculator

Find the shortest (perpendicular) distance from a point to a line using either the standard form Ax + By + C = 0 or two points on the line.

Line Input Mode

Line: Ax + By + C = 0

Point (x₀, y₀)

x₀

y₀

Enter values and click Calculate Distance

Summary

This calculator finds the perpendicular (shortest) distance from any point to a straight line in 2D space. Supply the line in standard form Ax + By + C = 0, or define the line by entering two points and letting the tool derive the equation. The result includes step-by-step working so you can follow the formula.

How it works

Choose input mode: Standard Form (Ax + By + C = 0) or Two-Point Form.
Enter the coefficients A, B, C — or the coordinates of two points on the line.
Enter the coordinates of the point (x₀, y₀) you want to measure from.
Click Calculate to see the perpendicular distance with step-by-step work.
Review the perpendicular distance result, summary table, and step-by-step algebraic breakdown.

Use cases

Find how far a city coordinate is from a straight road or border line.
Verify geometry homework involving perpendicular distances.
Check the closest approach distance between a point and a line in a physics problem.
Compute tolerance margins in 2D CAD or graphics work.
Validate analytical geometry proofs and calculations.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu

Distance Point To Line Calculator

Use the Distance Point To Line Calculator

Step-by-Step Solution

Summary

Summary

How it works

Use cases

Frequently Asked Questions