Pythagorean Theorem Calculator
Find the missing side of a right triangle from the other two, plus its area, perimeter and the two acute angles.
In a right triangle the square on the hypotenuse equals the sum of the squares on the other two sides: a² + b² = c².
How the pythagorean theorem calculator works
In a right triangle the square on the hypotenuse equals the sum of the squares on the other two sides: a² + b² = c². Given two legs, c = √(a² + b²); given the hypotenuse and one leg, the other leg is √(c² − a²). The angles come from the tangent of the legs.
Formula: a² + b² = c²
Worked examples
| Inputs | Missing side | Note |
|---|---|---|
| legs 3 and 4 | 5 | hypotenuse 5 |
| leg 5, hypotenuse 13 | 12 | other leg 12 |
| legs 1 and 1 | 1.414214 | hypotenuse √2 |
FAQFrequently asked questions
What is the hypotenuse?
The longest side of a right triangle, opposite the right angle.
Does the theorem work for all triangles?
Only right triangles. For others use the law of cosines: c² = a² + b² − 2ab cos C.
What are Pythagorean triples?
Whole-number solutions: 3-4-5, 5-12-13, 8-15-17, 7-24-25 and their multiples.
How is this used in building?
The 3-4-5 rule checks a corner is square: measure 3 along one edge, 4 along the other; the diagonal should be exactly 5.
How do I find the angles?
tan A = opposite ÷ adjacent, so A = arctan(a/b); the other acute angle is 90° − A.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.