Skip to main content
math

Hypotenuse Calculator

Calculate the hypotenuse of a right triangle given the two legs using c = √(a² + b²).

Reviewed by Chase FloiedUpdated

This free online hypotenuse calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Results

Hypotenuse

5 units

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Hypotenuse Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Hypotenuse Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Hypotenuse Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • Use the Hypotenuse Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • Use it to explore the behavior of mathematical functions across a range of inputs.

About This Calculator

The Hypotenuse Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate the hypotenuse of a right triangle given the two legs using c = √(a² + b²). The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.

About Hypotenuse Calculator

The hypotenuse is the longest side of a right triangle, located opposite the 90-degree angle. The hypotenuse calculator uses the Pythagorean theorem to find this length: c = √(a² + b²). This is one of the most practical calculations in geometry, used constantly in construction, navigation, and engineering. When you need to find the straight-line distance between two points that differ in both horizontal and vertical position, you are computing a hypotenuse. Carpenters use the 3-4-5 triangle to check for right angles, surveyors use it to calculate distances, and pilots use it to determine ground speed from airspeed and wind components. This calculator provides the result instantly for any pair of leg lengths.

The Math Behind It

The hypotenuse formula c = √(a² + b²) is a direct application of the Pythagorean theorem. The term 'hypotenuse' comes from the Greek 'hypoteinousa,' meaning 'stretching under.' In the coordinate plane, the distance between two points (x₁, y₁) and (x₂, y₂) is d = √((x₂−x₁)² + (y₂−y₁)²), which treats the horizontal and vertical differences as legs of a right triangle. The concept extends to higher dimensions and non-Euclidean spaces. The hypotenuse also relates to trigonometry: sin(θ) = opposite/hypotenuse and cos(θ) = adjacent/hypotenuse. Common Pythagorean triples where the hypotenuse is an integer include (3,4,5), (5,12,13), (8,15,17), (7,24,25), and all scalar multiples thereof. For isosceles right triangles (45-45-90), the hypotenuse is a√2 where a is the leg length. For 30-60-90 triangles, the hypotenuse is 2 times the shorter leg.

Formula Reference

Hypotenuse

c = √(a² + b²)

Variables: a, b = legs of the right triangle

Worked Examples

Example 1: TV screen diagonal

A TV screen is 48 inches wide and 27 inches tall.

Step 1:c = √(48² + 27²)
Step 2:c = √(2304 + 729)
Step 3:c = √3033

c ≈ 55.07 inches (a 55-inch TV)

Common Mistakes & Tips

  • !Forgetting to take the square root — a² + b² gives c², not c.
  • !Using the formula when the triangle is not a right triangle.
  • !Entering the hypotenuse as one of the legs when trying to find a missing leg.

Related Concepts

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Frequently Asked Questions

Can the hypotenuse be shorter than a leg?

No. The hypotenuse is always the longest side of a right triangle.

Is the diagonal of a rectangle the same as a hypotenuse?

Yes. The diagonal of a rectangle forms the hypotenuse of a right triangle with the length and width as legs.