Pythagorean Theorem Calculator
Free, with no sign up. Calculations run on your device; your entries stay in this browser.
Enter exactly two measured sides of a right triangle and leave the third blank. Legs a and b meet at the right angle; the hypotenuse is opposite it. Each entered side must be from 0.000000001 to 1,000,000,000 (10⁻⁹ to 10⁹) in the same selected unit. The hypotenuse must be longer than either leg. Angles are in degrees and area in square units. Results use floating-point arithmetic and display up to 12 significant digits.
Your result
a² + b² = hypotenuse²; hypotenuse = √(a² + b²); missing leg = √(hypotenuse² − known leg²); area = ab/2; angle opposite a = atan2(a, b).
Primary source: OpenStax Prealgebra 2e, right triangles and the Pythagorean theorem.
Worked example
With a = 3 m and b = 4 m, the hypotenuse is √(9 + 16) = 5 m. Area = 3 × 4 / 2 = 6 m². The angles opposite a and b are about 36.8699° and 53.1301°, plus the 90° right angle.
How to use this tool
Enter your measured values and select Calculate to see the result, formula and details below.
Frequently asked questions
Can I find a leg from the hypotenuse?
Yes. Enter the hypotenuse and either leg, leaving the other leg blank. The calculator uses the square root of hypotenuse squared minus the known leg squared.
Does this work for every triangle?
This formula applies to right triangles. The entered legs must meet at 90°.
Why must I leave one field blank?
Exactly two sides determine the missing side. Filling all three or fewer than two fields gives an error.