Pythagorean Theorem Calculator
Enter any two sides of a right-angled triangle to find the third with a² + b² = c², along with both acute angles, the area and the perimeter.
Result
Enter your values and select Calculate to see the result.
How to use this calculator
- Enter two side lengths and leave the one to find empty.
- Side c is the hypotenuse — the longest side, opposite the right angle.
- When solving for a leg, the hypotenuse must be longer than the other leg.
Formula
a² + b² = c²
- Hypotenuse:
c = √(a² + b²) - Leg:
a = √(c² − b²) - Angles:
A = asin(a ÷ c)andB = 90° − A - Area:
½ × a × b
Worked example
The classic 3-4-5 triangle
a = 3, b = 4: c = √(9 + 16) = √25 = 5. The angles are about 36.87° and 53.13°.
A ladder against a wall
A 13 m ladder (c) with its foot 5 m from the wall (a) reaches b = √(169 − 25) = 12 m up the wall.
Assumptions and limitations
- The triangle must contain a 90° angle. For other triangles, use the Area calculator’s three-sides option.
- All sides must use the same unit.
Frequently asked questions
How can I check if a corner is square?
Measure 3 units along one side and 4 along the other. If the diagonal between the marks is exactly 5 units, the corner is a right angle.
Does it work for non-right triangles?
No. For other triangles use the law of cosines, c² = a² + b² − 2ab·cos(C).