Pythagorean Theorem Calculator
Calculate the missing side of a right triangle using the Pythagorean theorem.
A Pythagorean theorem calculator finds the missing side of a right triangle given the other two sides using a² + b² = c².
Examples
3-4-5 Triangle
5-12-13 Triangle
Finding a leg
Frequently Asked Questions
What is the Pythagorean theorem?
Does it work for all triangles?
What are Pythagorean triples?
Quick Tips
- •Double-check your inputs — small errors lead to incorrect results.
- •The hypotenuse (c) must always be the longest side of a right triangle.
- •Use decimal form for fractions when entering values.
A Pythagorean theorem calculator finds the missing side of a right triangle given the other two sides using a² + b² = c².
How to Use This Calculator
Select which side to solve for (a, b, or hypotenuse c). Enter the two known sides. The calculator will find the missing side and also compute the area and perimeter of the right triangle.
Understanding the Formula
a² + b² = c², where c is the hypotenuse (longest side opposite the right angle).
Examples
3-4-5 Triangle
3² + 4² = 9 + 16 = 25 = 5². The hypotenuse is 5.
5-12-13 Triangle
5² + 12² = 25 + 144 = 169 = 13². The hypotenuse is 13.
Finding a leg
If c = 10 and b = 6, then a = √(100 - 36) = √64 = 8.
Frequently Asked Questions
What is the Pythagorean theorem?
It states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
Does it work for all triangles?
No, the Pythagorean theorem only applies to right triangles (triangles with a 90-degree angle).
What are Pythagorean triples?
Sets of three positive integers (a, b, c) that satisfy a² + b² = c², such as (3, 4, 5), (5, 12, 13), and (8, 15, 17).
Assumptions & Limitations
- Assumes Euclidean geometry and a valid right triangle.
- Assumes exact input values; rounding in inputs propagates to results.
- Results may show floating-point approximations for irrational numbers.