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Hypotenuse Calculator (a² + b² = c²)

Solve a² + b² = c² step by step: find the hypotenuse from two legs, find a missing leg, or test whether three sides form a right triangle — with exact simplified radicals like 5√2, a scaled diagram, area and perimeter.

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Validating sides
Substituting into the theorem
Simplifying the square root
Done

Result

This page opens the Pythagorean theorem calculator in hypotenuse mode: enter the two legs of a right triangle and c = √(a² + b²) is computed with every substitution shown. The classic 3 and 4 give 9 + 16 = 25 and c = √25 = 5; legs of 5 and 5 give the irrational √50, which the calculator simplifies to the exact 5√2 before showing ≈ 7.0711.

Decimals are handled exactly by scaling to whole numbers first, so 1.5 and 2 produce precisely 2.5. Together with the missing side you get the area and perimeter of the triangle and a diagram drawn to your proportions with the right angle marked — a complete picture, not just one number.

The hypotenuse question appears anywhere a right angle does: the diagonal of a rectangle or screen, the length of a ladder against a wall, a roof slope from run and rise, the straight-line distance between two points on a grid. If the angle between your two known sides is not 90°, use the general triangle calculator on this site instead — the law of cosines handles any angle.

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Accepted Formats & Rules

  • Three modes: find the hypotenuse from two legs, find a missing leg from a leg and the hypotenuse, and check whether three sides make a right triangle.
  • Exact arithmetic on decimal inputs and exact simplified radicals (c = 5√2) next to rounded decimals.
  • Also computes the area and perimeter of the triangle and draws it with the right angle marked.

Key Benefits

✓ Every answer shows the full a² + b² = c² substitution, so the working is ready to copy into homework.
✓ Irrational results are given exactly — √50 is simplified to 5√2 by integer factorization — alongside the decimal value.
✓ Runs entirely in your browser: no sign-up, no uploads, instant results with a right-triangle diagram scaled to your sides.

Use Cases

  • • Find the hypotenuse from two legs with the full a² + b² = c² substitution — 3 and 4 give √25 = 5, ready for homework.
  • • Get a missing side as an exact simplified radical: legs of 5 and 5 return 5√2 ≈ 7.0711, never just a rounded decimal.
  • • Check whether sides like 5, 12, 13 form a right triangle with the squares compared exactly and the computation shown.