Home / Calculators / Hypotenuse Calculator

Hypotenuse Calculator

Find the hypotenuse of a right triangle from its two legs — or a missing leg, or every side from one side and an angle. Get the exact square-root answer, both angles, the area and a diagram.

100% Private Exact √ answers Scaled diagram

Triangle

α is the angle opposite leg a. The other acute angle is β = 90° − α.
Hypotenuse c
—
—
Side a
—
Side b
—
Hypotenuse c
—
Angle α
—
Angle β
—
Area
—
Perimeter
—
Height to hypotenuse
—
Inradius / circumradius
—

Diagram

Working

—

How to find the hypotenuse

The hypotenuse is the longest side of a right triangle — the side opposite the 90° angle. The Pythagorean theorem says the square of the hypotenuse equals the sum of the squares of the other two sides (the legs):

c² = a² + b²  ⇒  c = √(a² + b²)

Example: with legs of 5 and 12, c = √(25 + 144) = √169 = 13. If you know the hypotenuse and one leg instead, rearrange it: b = √(c² − a²).

With an angle

a = c × sin α    b = c × cos α    c = a ÷ sin α = b ÷ cos α

Common Pythagorean triples

These whole-number right triangles appear constantly in homework and construction: 3-4-5, 5-12-13, 8-15-17, 7-24-25, 20-21-29 and 9-40-41 — plus any multiple of them, such as 6-8-10.

Frequently Asked Questions

It is the side opposite the right angle in a right triangle, and always the longest of the three sides. Only right triangles have a hypotenuse.

Square both legs, add the results and take the square root: c = √(a² + b²). For legs of 6 and 8, c = √(36 + 64) = √100 = 10.

Subtract the square of the known leg from the square of the hypotenuse and take the square root: b = √(c² − a²). The hypotenuse must be longer than the leg.

It is the exact value of a square root that is not a whole number. √50 = √(25 × 2) = 5√2 ≈ 7.0711. Teachers often ask for this simplified radical form; the decimal is shown next to it.

No, only for right triangles. For other triangles use the law of cosines: c² = a² + b² − 2ab·cos C, which reduces to the Pythagorean theorem when C = 90°.
Our Ecosystem

Strategic Partnerships for
Global Excellence

We collaborate with industry-leading specialists to deliver high-impact results. Through these trusted alliances, we expand our technical reach and ensure your project benefits from world-class expertise at every scale.

SEO Specialist Pakistan Logo

SEO Specialist Pakistan

A full-service power-house supporting regional and international clients. This collaboration scales our operational efficiency while maintaining the highest quality standards for strategy and content optimization.

SEO Specialist USA Logo

SEO Specialist USA

A leading SEO and digital growth partner dedicated to helping businesses dominate search results. Our expertise spans Technical SEO, Local SEO, Content Strategy, Link Building, and Conversion Optimization, empowering brands to increase visibility, attract qualified leads, and achieve long-term online success.

Coalition Technologies Logo

Coalition Technologies

A world-class SEO, PPC, and web design powerhouse. Through this collaboration we tap into advanced data-driven strategies and enterprise-grade resources that elevate campaign performance and deliver measurable growth at scale.

SEO Specialist Pakistan Logo

SEO Specialist Pakistan

A full-service power-house supporting regional and international clients. This collaboration scales our operational efficiency while maintaining the highest quality standards for strategy and content optimization.

SEO Service Canada Logo

SEO Service Canada

Our trusted Canadian partner extending high-performance search expertise across North American markets. This alliance strengthens our regional reach with localized strategy, technical precision, and proven ranking results for Canadian businesses.