Perpendicular Line Equation Calculator

Work out perpendicular line equation instantly with clear inputs, formula shown and shareable results.

About Perpendicular Line Equation Calculator

Perpendicular lines have gradients whose product is −1, so the new gradient is the negative reciprocal −1/m. Substituting the given point then fixes the intercept.

Formula

Perpendicular gradient

m₁ · m₂ = −1, so m₂ = −1 / m₁

Worked example

With the default values below, Perpendicular Line Equation Calculator returns Equation of the perpendicular line of y = -0.25x + 7. Change any input above and every figure here is recalculated in your browser.

Inputs used

Gradient of the original line: 4
Point x₁ on the new line: 8
Point y₁: 5

Results

Equation of the perpendicular line: y = -0.25x + 7
Perpendicular gradient −1/m: -0.25000000
y-intercept: 7.00000000
Product of the gradients (should be −1): -1.00000000

Step by step

1Values used
2Perpendicular gradient
3Equation of the perpendicular line= y = -0.25x + 7
4Perpendicular gradient −1/m= -0.25000000
5y-intercept= 7.00000000
6Product of the gradients (should be −1)= -1.00000000

Assumptions and limits

The result is derived only from the 3 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 8 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

Perpendicular to gradient 4 through (8, 5)?

The new gradient is −0.25, so c = 5 + 2 = 7 and the line is y = −0.25x + 7.

What about horizontal and vertical lines?

They are perpendicular to each other, but the product rule breaks down because a vertical line has no defined gradient.