Pythagorean Theorem Calculator

Calculate the hypotenuse (Side C) of a right-angled triangle instantly using the Pythagorean Theorem. Ideal for students, engineers, builders, architects, surveyors and anyone working with geometry.

✔ Find the hypotenuse • ✔ Right triangles • ✔ Step-by-step formula • ✔ Free calculator

What is the Pythagorean Theorem Calculator?

The Pythagorean Theorem Calculator calculates the length of the hypotenuse (the longest side) of a right-angled triangle using one of the most famous formulas in mathematics.

Simply enter the lengths of the two shorter sides, and the calculator instantly determines the missing third side with excellent precision.

The Pythagorean Theorem is widely used in mathematics, construction, engineering, architecture, surveying, navigation, physics and computer graphics.

What is the Pythagorean Theorem?

The Pythagorean Theorem states that in every right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Where:

• a = first side
• b = second side
• c = hypotenuse (longest side)

To calculate the hypotenuse:

How to use this calculator

1. Enter the length of Side A.
2. Enter the length of Side B.
3. Click Calculate.
4. The hypotenuse is calculated instantly.

All measurements should use the same unit (metres, centimetres, inches, feet, etc.).

Worked Examples

Example 1 — The Famous 3-4-5 Triangle

• Side A = 3
• Side B = 4
• 3² + 4² = 9 + 16 = 25
• √25 = 5

Result: Hypotenuse = 5

Example 2 — 5-12-13 Triangle

• Side A = 5
• Side B = 12
• 5² + 12² = 25 + 144 = 169
• √169 = 13

Result: Hypotenuse = 13

Example 3 — Ladder Against a Wall

A ladder stands 4 metres from a wall and reaches 3 metres up the wall.

• Distance from wall = 4 m
• Height = 3 m
• Ladder length = √(4² + 3²)
• Ladder length = 5 m

Builders regularly use the Pythagorean Theorem for safe ladder placement and construction work.

Common Pythagorean Triples

Side A	Side B	Hypotenuse
3	4	5
5	12	13
8	15	17
7	24	25
20	21	29
12	35	37
9	40	41

Real-World Applications

Interesting Facts

• The theorem is more than 2,500 years old.
• It is named after the Greek mathematician Pythagoras.
• It only applies to right-angled triangles.
• Thousands of Pythagorean triples exist.
• It remains one of the most widely used formulas in mathematics.

Common Mistakes

• Using the formula on triangles that are not right-angled.
• Forgetting to square both shorter sides.
• Adding side lengths instead of their squares.
• Forgetting to calculate the square root.
• Using different measurement units.

This calculator performs every calculation automatically, helping eliminate common mathematical mistakes.

Frequently Asked Questions

What is the hypotenuse?
The hypotenuse is the longest side of a right triangle and is always opposite the 90° angle.

Can I use decimal numbers?
Yes. The calculator supports both whole numbers and decimal values.

Can I use any units?
Yes. Use metres, centimetres, millimetres, inches or feet, provided both sides use the same unit.

Does this work for every triangle?
No. The Pythagorean Theorem only applies to right-angled triangles.

Why is the Pythagorean Theorem important?
It is one of the most fundamental formulas in mathematics and is used throughout engineering, science, architecture, surveying and construction.

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