Hypotenuse Calculator

Q: What is the formula for the hypotenuse?

The formula for the hypotenuse of a right triangle is c = √(a² + b²), where a and b are the two shorter sides, and c is the hypotenuse (the longest side). This formula is based on the Pythagorean theorem.

Formula: c = √(a² + b²)

Side A Side B

Hypotenuse Result

Triangle Visualization

Right triangle with sides a, b and hypotenuse c

Last Updated: 25-07-2026

📐 What is a Hypotenuse Calculator?

A Hypotenuse Calculator is a tool that helps you quickly find the longest side of a right triangle without manual calculation. You simply enter the two known sides (a and b), and it instantly calculates the hypotenuse (c) using the Pythagorean theorem.

Instead of solving square roots manually, this calculator gives you fast and accurate results, making it useful for students, engineers, and everyday problem-solving.

How to calculate the hypotenuse of a right triangle?

The hypotenuse is the longest side of a right triangle, located opposite the 90° angle. It is calculated using the Pythagorean theorem: c = √(a² + b²). Square the two shorter sides, add the results together, and then take the square root. For example, if a = 6 and b = 8: c = √(6² + 8²) = √100 = 10.

Where:

a = one side of the triangle
b = second side of the triangle
c = hypotenuse (longest side)

how to calculate hypotenuse of a right triangle example 6 8 10

🧮 Example 1 (Basic)

Find the hypotenuse when two sides are small numbers:

a = 6
b = 8

\[ c = \sqrt{6^2 + 8^2} \] \[ c = \sqrt{36 + 64} = \sqrt{100} = 10 \]

✅ Hypotenuse = 10

📘 Example 2 (Common Exam)

This is a popular Pythagorean triple used in exams:

a = 5
b = 12

\[ c = \sqrt{5^2 + 12^2} \] \[ c = \sqrt{25 + 144} = \sqrt{169} = 13 \]

✅ Hypotenuse = 13

🏗️ Example 3 (Real-Life Use)

A ladder is placed against a wall:

Height (a) = 9 m
Distance from wall (b) = 12 m

\[ c = \sqrt{9^2 + 12^2} \] \[ c = \sqrt{81 + 144} = \sqrt{225} = 15 \]

📏 Ladder length = 15 m

📐 Example 4 (Advanced)

Find the hypotenuse for larger values:

a = 7
b = 24

\[ c = \sqrt{7^2 + 24^2} \] \[ c = \sqrt{49 + 576} = \sqrt{625} = 25 \]

✅ Hypotenuse = 25

When Do You Need This Calculator?

This calculator is useful in many real-life situations:

📏 Measuring diagonal distance between two points
🏗️ Construction and civil engineering calculations
📡 RF and antenna alignment (distance estimation)
🎮 Game development and graphics positioning
📐 School and competitive exam problems

Steps to Calculate the Hypotenuse

Measure the two shorter sides.
Square both values.
Add the squares together.
Take the square root.
The result is the hypotenuse.

Common Hypotenuse Values

Side A	Side B	Hypotenuse
3	4	5
5	12	13
8	15	17
7	24	25
9	40	41

FAQ on Hypotenuse Calculator

1. What is the hypotenuse?

The hypotenuse is the longest side of a right triangle, opposite the 90° angle.

2. Can the hypotenuse be smaller than other sides?

No, the hypotenuse is always the longest side in a right triangle.

3. Does this formula work for all triangles?

No, it only works for right-angled triangles.

4. What is the formula for the hypotenuse?

The formula for the hypotenuse of a right triangle is: c = √(a² + b²)
where a and b are the two shorter sides, and c is the hypotenuse (the longest side). This formula is based on the Pythagorean theorem.

5. What is the hypotenuse of a 3-4-5 triangle?

In a 3-4-5 right triangle, the hypotenuse is 5. The sides form a Pythagorean triple because 3² + 4² = 5², making 5 the longest side of the triangle.

6. Why is the hypotenuse always the longest side?

The hypotenuse is always the longest side of a right triangle because it is opposite the 90° angle. According to the Pythagorean theorem, its length is greater than either of the other two sides.