Perpendicular Line Calculator.

Find the line through a point perpendicular to a given slope.

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Set your values

Results update as you type.

02 / ANSWER

Given slope

Point x

Point y

Perpendicular slope

0.000000

Intercept

0.000000

Equation

y = -0.5x + 3.5

Results update automatically as you type.

Use Cases

Geometry homework and assignments

Quickly verify your answers when finding perpendicular lines in coordinate geometry problems. Enter the slope and a point to check if your derived equation is correct.

Example: Given slope 3 and point (2, 5), find the perpendicular line equation.

Frequently Asked Questions

How do I find a perpendicular line to a given slope?: Enter the slope of the original line and the coordinates of a point (x, y) through which the perpendicular line should pass. The calculator computes the negative reciprocal of the given slope to find the perpendicular slope, then uses the point to determine the y-intercept, giving you the equation of the perpendicular line.
What is the perpendicular slope of a given slope?: The perpendicular slope is the negative reciprocal of the given slope. For example, if the given slope is 2, the perpendicular slope is -1/2. If the given slope is -3/4, the perpendicular slope is 4/3. The calculator automatically computes this for you.
Can I use this calculator for vertical or horizontal lines?: Yes, but note that if the given slope is 0 (horizontal line), the perpendicular line will be vertical, which has an undefined slope. The calculator will indicate this. If the given slope is undefined (vertical line), the perpendicular line will be horizontal with slope 0. The calculator handles these cases appropriately.

Tips & Common Mistakes

Tips

Remember that the product of the slopes of two perpendicular lines is -1. Use this to check your result: multiply the given slope by the calculated perpendicular slope; it should equal -1.
If the given slope is a fraction, enter it as a decimal or use the fraction form if supported. Ensure you input the slope correctly to get an accurate perpendicular slope.
The point you enter is the point through which the perpendicular line passes. Double-check that the coordinates are correct, as they determine the y-intercept of the perpendicular line.
For vertical or horizontal lines, the calculator will handle the undefined or zero slope cases, but be aware that the equation may be in a different form (e.g., x = constant for vertical lines).

Common Mistakes to Avoid

Entering the slope as a fraction incorrectly: if you input a slope like 2/3 as 2.3 instead of 0.666..., the perpendicular slope will be wrong. Use the correct decimal or fraction format.
Confusing the point: the point you enter is on the perpendicular line, not the original line. Ensure you use the correct coordinates for the point through which the perpendicular line must pass.

Last updated: August 13, 2026

Frequently Asked Questions

How do I find a perpendicular line to a given slope?

Enter the slope of the original line and the coordinates of a point (x, y) through which the perpendicular line should pass. The calculator computes the negative reciprocal of the given slope to find the perpendicular slope, then uses the point to determine the y-intercept, giving you the equation of the perpendicular line.

What is the perpendicular slope of a given slope?

The perpendicular slope is the negative reciprocal of the given slope. For example, if the given slope is 2, the perpendicular slope is -1/2. If the given slope is -3/4, the perpendicular slope is 4/3. The calculator automatically computes this for you.

Can I use this calculator for vertical or horizontal lines?

Yes, but note that if the given slope is 0 (horizontal line), the perpendicular line will be vertical, which has an undefined slope. The calculator will indicate this. If the given slope is undefined (vertical line), the perpendicular line will be horizontal with slope 0. The calculator handles these cases appropriately.

Tips & Common Mistakes

Tips

Remember that the product of the slopes of two perpendicular lines is -1. Use this to check your result: multiply the given slope by the calculated perpendicular slope; it should equal -1.
If the given slope is a fraction, enter it as a decimal or use the fraction form if supported. Ensure you input the slope correctly to get an accurate perpendicular slope.
The point you enter is the point through which the perpendicular line passes. Double-check that the coordinates are correct, as they determine the y-intercept of the perpendicular line.
For vertical or horizontal lines, the calculator will handle the undefined or zero slope cases, but be aware that the equation may be in a different form (e.g., x = constant for vertical lines).

Common Mistakes to Avoid

Entering the slope as a fraction incorrectly: if you input a slope like 2/3 as 2.3 instead of 0.666..., the perpendicular slope will be wrong. Use the correct decimal or fraction format.
Confusing the point: the point you enter is on the perpendicular line, not the original line. Ensure you use the correct coordinates for the point through which the perpendicular line must pass.

Frequently Asked Questions

How do I find a perpendicular line to a given slope?

What is the perpendicular slope of a given slope?

Can I use this calculator for vertical or horizontal lines?

Tips & Common Mistakes

Tips

Remember that the product of the slopes of two perpendicular lines is -1. Use this to check your result: multiply the given slope by the calculated perpendicular slope; it should equal -1.
If the given slope is a fraction, enter it as a decimal or use the fraction form if supported. Ensure you input the slope correctly to get an accurate perpendicular slope.
The point you enter is the point through which the perpendicular line passes. Double-check that the coordinates are correct, as they determine the y-intercept of the perpendicular line.
For vertical or horizontal lines, the calculator will handle the undefined or zero slope cases, but be aware that the equation may be in a different form (e.g., x = constant for vertical lines).

Common Mistakes to Avoid

Entering the slope as a fraction incorrectly: if you input a slope like 2/3 as 2.3 instead of 0.666..., the perpendicular slope will be wrong. Use the correct decimal or fraction format.
Confusing the point: the point you enter is on the perpendicular line, not the original line. Ensure you use the correct coordinates for the point through which the perpendicular line must pass.