What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides: a² + b² = c². It was formalized by ancient Greek mathematician Pythagoras.

What is a hypotenuse?

The hypotenuse is the longest side of a right triangle, always opposite the 90° right angle. In the formula a² + b² = c², c is the hypotenuse.

What are Pythagorean triples?

Pythagorean triples are sets of three positive integers (a, b, c) that satisfy a² + b² = c². Common examples: 3-4-5, 5-12-13, 8-15-17, 7-24-25.

Does this only work for right triangles?

Yes. The Pythagorean theorem applies only to right triangles (triangles with one 90° angle). For other triangles, use the law of cosines.

Can I use this for real-world problems?

Absolutely. The theorem is used in construction, navigation, carpentry, physics, and computer graphics to find distances, angles, and diagonal measurements.

Math

↵ to calculate

Pythagorean Theorem Calculator — Find Side Hypotenuse

Solve for any side of a right triangle using the Pythagorean theorem. Also calculates perimeter and area.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.

📌 Direct Answer & Summary

The Pythagorean theorem calculator solves for any missing side of a right triangle given the other two sides using the formula a² + b² = c². It also computes the triangle's perimeter and area.

Solve For

Hypotenuse (c) Side a Side b

What is Pythagorean Theorem Calculator — Find Side Hypotenuse?

The Pythagorean theorem calculator solves for any missing side of a right triangle given the other two sides using the formula a² + b² = c². It also computes the triangle's perimeter and area.

How to use it

1️⃣ Select which side you want to solve for: side a, side b, or hypotenuse c.
2️⃣ Enter the two known side lengths.
3️⃣ Click Calculate to find the missing side.
4️⃣ Results include the missing side, perimeter, and area of the triangle.
5️⃣ All side values must be positive numbers.

Formula

a² + b² = c². Solve for c: c = √(a²+b²). Solve for a: a = √(c²−b²). Solve for b: b = √(c²−a²). Perimeter = a + b + c. Area = (1/2) × a × b.

💡 See it in action — a real example

Known sides a=3, b=4, solve for c: c = √(9+16) = √25 = 5. Perimeter = 12. Area = (1/2)(3)(4) = 6. This is the classic 3-4-5 right triangle.

❓ Common questions

What is the Pythagorean theorem?: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides: a² + b² = c². It was formalized by ancient Greek mathematician Pythagoras.
What is a hypotenuse?: The hypotenuse is the longest side of a right triangle, always opposite the 90° right angle. In the formula a² + b² = c², c is the hypotenuse.
What are Pythagorean triples?: Pythagorean triples are sets of three positive integers (a, b, c) that satisfy a² + b² = c². Common examples: 3-4-5, 5-12-13, 8-15-17, 7-24-25.
Does this only work for right triangles?: Yes. The Pythagorean theorem applies only to right triangles (triangles with one 90° angle). For other triangles, use the law of cosines.
Can I use this for real-world problems?: Absolutely. The theorem is used in construction, navigation, carpentry, physics, and computer graphics to find distances, angles, and diagonal measurements.

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