Pythagorean Theorem Calculator
Pick which two sides of a right triangle you know — both legs, or a leg and the hypotenuse — and this calculator finds the missing side with the Pythagorean theorem, plus the acute angles, area and perimeter.
TheCalculators — Pythagorean Theorem Calculator
Printed thecalculators.com
Hypotenuse c
5
a = 3 · b = 4 · c = 5
- Hypotenuse c
- 5
- Leg a
- 3
- Leg b
- 4
- Hypotenuse c
- 5
- a²
- 9
- b²
- 16
- c²
- 25
- Angle α (opposite a)
- 36.87°
- Angle β (opposite b)
- 53.13°
- Area
- 6
- Perimeter
- 12
Step-by-step solution
- 1Pythagorean theorema² + b² = c²
- 2Substitute the known sidesc = √(a² + b²) = √(3² + 4²) = √25 = 5
- 3Anglesα = arcsin(a/c) = arcsin(0.6) = 36.87° · β = 90° − α = 53.13°
- 4Area & perimeterA = ½·a·b = 6 · P = a + b + c = 12
Integer right triangles like 3-4-5 or 5-12-13 are called Pythagorean triples.
Most useful next
Formula
a² + b² = c² → c = √(a² + b²), a = √(c² − b²), b = √(c² − a²)
Pro tips
- • The hypotenuse is always the longest side — if your leg computes longer than c, swap the inputs.
- • Memorize 3-4-5: any multiple (6-8-10, 9-12-15) is also a right triangle.
- • The two acute angles always add to 90°.
FAQ
Related Calculators
More Everyday tools you might need.
Right Triangle Calculator
Solve right triangles: sides, acute angles, area, perimeter and altitude.
CalculateTriangle Calculator
Solve any triangle: area, perimeter and angles from base & height or three sides (Heron).
CalculateDistance Calculator
Euclidean distance between two 2-D points, plus midpoint and slope, with full working.
Calculate