Pythagorean Theorem Calculator
Pythagorean theorem calculator: find the hypotenuse or a missing leg of a right triangle, plus its area and angle.
a² + b² = c²
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
In a right triangle the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c².
Enter any two sides to get the third. The calculator also gives the area (a·b/2) and the angle opposite side a.
Formula
a² + b² = c²
| Symbol | Quantity | Units |
|---|---|---|
| a | Leg a | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| b | Leg b | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| c | Hypotenuse c | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
Worked example
Given: a = 3 cm · b = 4 cm
c = √(a² + b²)
Result: c = 5 cm
Frequently asked questions
What is a 3-4-5 triangle?
The simplest Pythagorean triple: 3² + 4² = 9 + 16 = 25 = 5².
Does it work for triangles without a right angle?
No. For any triangle use the law of cosines, c² = a² + b² − 2ab·cos C.