Pythagorean theorem calculator
Find a missing side of a right-angled triangle, plus its area and perimeter.
Enter your values and press Calculate. Your inputs stay in the address, so you can switch language or share the link.
Formula
c² = a² + b²
How it works
In a right-angled triangle the square of the hypotenuse equals the sum of the squares of the two legs: c² = a² + b².
Worked example
The same calculation with the default values:
- Find The hypotenuse
- Side a (a leg) 3
- Side b (a leg, or the hypotenuse when finding a leg) 4
- c = √(3² + 4²) = √25 = 5
- area = ½ × 3 × 4 = 6
Result: Missing side: 5 · Area: 6 · Perimeter: 12
When finding a leg, side b is the hypotenuse and must be longer than side a.
Common mistakes
- Applying the theorem to a triangle that isn't actually right-angled - c² = a² + b² only holds for a right triangle; using it on any other triangle gives a meaningless result.
- Mixing up the hypotenuse with a leg - the hypotenuse (c) is always the side opposite the right angle and is always the longest side; solving for a leg uses subtraction (c² − a²), not addition.
- Forgetting to take the square root at the final step - the formula gives the square of the side length first; the actual length is the square root of that value.
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