How to use the Pythagorean Theorem Calculator
Use the calculator to find one missing side from two known sides of a right triangle. Follow the fields shown for the selected solve mode.
- Select Hypotenuse to calculate Hypotenuse c from Leg a and Leg b.
- Select Missing leg to calculate the missing leg from Leg b and Hypotenuse c. The Leg a field is hidden in this mode.
- Enter the known side values, select Unit, and click Calculate. Changing the solve mode clears the current result.
- Click Reset to clear the inputs and result.
What the calculator calculates
For a right triangle with legs a and b and hypotenuse c, the calculator uses a² + b² = c². It applies c = sqrt(a² + b²) in Hypotenuse mode and a = sqrt(c² − b²) in Missing leg mode.
Inputs, units, and calculation rules
- Solve mode: select Hypotenuse or Missing leg.
- Enter a positive decimal-form number in each required field. Blank fields, malformed values, zero, and negative values are rejected.
- Each input must be no greater than
1e12. Larger values are rejected as too large to calculate. - Unit: choose Unitless (plain numbers), Millimeters (mm), Centimeters (cm), Meters (m), Kilometers (km), Inches (in), Feet (ft), Yards (yd), or Miles (mi). This only labels the result; use the same unit for every side.
Calculation rules and limitations
The calculator assumes an exact 90-degree angle and the same unit for every side. In Missing leg mode, the known leg must be shorter than the hypotenuse. It does not solve for angles, convert units, or verify that a real-world triangle is right-angled.
Review, copy, or download the result
After a successful calculation, review the missing side, the formula, and the intermediate steps. Use Copy result or Download result (.txt). If clipboard writing fails, the interface displays Could not copy - select and copy manually.
Page-level data activity
The side-length arithmetic runs locally in your browser. The page also loads analytics, records tool views on the server, and includes a subscription form that posts to /assets/subscribe.php; the entire page is not accurately described as sending nothing to a server.
Frequently Asked Questions
What is the Pythagorean theorem?
For a right triangle with legs a and b and hypotenuse c, the Pythagorean theorem states that a² + b² = c². It relates the two shorter sides to the longest side, which is opposite the right angle.
How do I find the hypotenuse?
Given both legs a and b, the hypotenuse is c = sqrt(a² + b²).
How do I find a missing leg?
Given the hypotenuse c and one leg b, the missing leg is a = sqrt(c² − b²). The known leg must be shorter than the hypotenuse for a real result.
Does this only work for right triangles?
Yes. The Pythagorean theorem only applies to right triangles - triangles with one 90-degree angle. This calculator assumes the triangle you describe is a right triangle.
What units does this calculator support?
You can label the sides as unitless or in millimeters, centimeters, meters, kilometers, inches, feet, yards, or miles. The calculator does not convert between units - it assumes all sides are already expressed in the same unit you select.