What is a perpendicular line?

Two lines are perpendicular when they intersect at a 90-degree angle. If the original line has slope m, the perpendicular slope is -1/m (the negative reciprocal).

What happens when the original line is horizontal (slope = 0)?

A line perpendicular to a horizontal line is vertical. Its equation is x = (x-coordinate of the given point), which cannot be written in slope-intercept form.

What happens when the original line is vertical?

A line perpendicular to a vertical line is horizontal. Its equation is y = (y-coordinate of the given point).

What is standard form (Ax + By + C = 0)?

Standard form expresses the line with integer or simplified coefficients as Ax + By + C = 0. It is useful when slope-intercept form is not possible (e.g., for vertical lines).

Can I enter decimal or fractional values?

Yes. You can enter decimal values for all inputs. The calculator displays results as fractions when the values are rational, and as decimals otherwise.

Perpendicular Line Calculator

Name: Perpendicular Line Calculator
Availability: InStock
Author: Nham Vu

Enter a line (y = mx + b or two points) and a point — get the equation of the perpendicular line through that point instantly.

Original Line Input

Slope (m)

Y-Intercept (b)

Perpendicular line passes through:

x₀

y₀

Enter values on the left and click Calculate

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Summary

Enter a line (y = mx + b or two points) and a point — get the equation of the perpendicular line through that point instantly.

How it works

Choose whether to define the original line using slope-intercept form (y = mx + b) or by two points.
Enter the required values for the original line.
Enter the coordinates of the point the perpendicular line must pass through.
Click "Calculate" — the tool computes the negative reciprocal of the slope.
The perpendicular line equation is shown in both slope-intercept and standard form.
Edge cases: a horizontal original line produces a vertical perpendicular, and vice versa.

Use cases

Geometry homework — find the line perpendicular to a given line at a specific point.
Verify textbook answers for perpendicular line problems.
Computer graphics — calculate normals to line segments.
Engineering drawings that require right-angle constructions.
Analytic geometry — check if two lines are perpendicular (slopes are negative reciprocals).
Build altitude lines in triangle geometry problems.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu