Pythagorean Theorem Calculator
Find the hypotenuse or a missing leg of a right triangle, plus its area, perimeter and angles.
The Pythagorean theorem
In any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.
a² + b² = c² c = √(a² + b²) b = √(c² − a²)
A triangle with legs 3 and 4 has a hypotenuse of √(9 + 16) = √25 = 5. This 3-4-5 triangle is the best-known Pythagorean triple.
Common Pythagorean triples
Whole-number solutions are called Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25 and 20-21-29. Any multiple of a triple, such as 6-8-10, is also a triple.
Real-world uses
- Construction: builders check a corner is square by measuring 3 ft along one wall, 4 ft along the other and confirming the diagonal is 5 ft.
- Screens: a TV's advertised size is its diagonal. A 16:9 screen 48 inches wide and 27 inches tall measures about 55 inches.
- Ladders: a 10 ft ladder with its base 3 ft from a wall reaches √(100 − 9) ≈ 9.5 ft up the wall.
- Distance on a map: the straight-line distance between two grid points is √(Δx² + Δy²).
The calculator also gives the two acute angles using the inverse tangent: angle A = arctan(a ÷ b).
Frequently asked questions
Does the Pythagorean theorem work for all triangles?
No, only for right triangles. For other triangles, use the law of cosines: c² = a² + b² − 2ab·cos(C).
How do I find a missing leg?
Subtract the square of the known leg from the square of the hypotenuse and take the square root: b = √(c² − a²).
Which side is the hypotenuse?
The hypotenuse is always the longest side and is opposite the right angle.
Last reviewed Oct 20, 2026. Results are estimates; check important decisions with a qualified professional.