Perpendicular Line Calculator

About the Perpendicular Line Calculator

Find the equation of the line perpendicular to y = mx + b that passes through a given point, using the negative reciprocal slope.

Also known as: perpendicular line equation, perpendicular slope, line perpendicular to another line.

How to use this calculator

1. Enter slope of given line m, point x, point y.
2. The result updates instantly as you type — press Calculate (or Enter) at any time.
3. Open “Step-by-step” to see how the answer was worked out.
4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

Worked example

Using the values pre-filled in the calculator above:

• Slope of given line m = 2
• Point x = 1
• Point y = 4

the calculator returns:

• Equation: y = -0.5x + 4.5
• Slope: -0.5

Working

1. Perpendicular slope = −1 / 2 = -0.5
2. b = 4 − -0.5 × 1 = 4.5