Perpendicular Line Calculator
Result
Perpendicular Line Calculator — free online calculator.
Formula
- Find the slope and y-intercept of the line perpendicular to a non-horizontal original line and passing through the given point. A horizontal original line has a vertical perpendicular and cannot be represented as y = mx + b; this version rejects m = 0.
- The main inputs are Original Line Slope, Point X-coordinate, Point Y-coordinate. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Perpendicular Line
- Original Line Slope: 2 m
- Point X-coordinate: 3 x₀
- Point Y-coordinate: 4 y₀
For original slope 2 through (3,4), perpendicular slope = −0.5 and y-intercept = 5.5, so y = −0.5x + 5.5.
Sample result: Calculating…
Frequently asked questions
What does the Perpendicular Line calculate?
Perpendicular Line Calculator — free online calculator.
Which values should I enter?
Enter Original Line Slope, Point X-coordinate, Point Y-coordinate using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: For original slope m ≠ 0: perpendicular slope = −1/m; through (x₀,y₀), intercept b = y₀ + x₀/m, so y = (−1/m)x + b..
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.