Hypotenuse Calculator

Enter leg lengths a and b to calculate c = √(a²+b²), area, perimeter, and acute angles.

Leg a

Leg b

5Hypotenuse c

6Area

12Perimeter

36.87° / 53.13°Acute angles

c=√(a²+b²)

Right-triangle solve with angles, area & visual check

Solve the hypotenuse from both legs, then verify the Pythagorean relation and inspect acute angles, area and perimeter.

Leg aLeg bUnit

—Hypotenuse

—Angles

—Area

—Perimeter

Ready.

Formula and interpretation

c = √(a² + b²) for a right triangle.

This formula applies only when the angle between the two legs is exactly 90°.

Worked check

With legs 3 and 4, c = √(3² + 4²) = 5. This check only applies when the two entered legs meet at exactly 90 degrees; for a general triangle use the triangle or law-of-cosines workflow instead.

Rule: c = √(a² + b²) for a right triangle. This formula applies only when the angle between the two legs is exactly 90°. For a final check, estimate the expected size of the answer before copying it, keep units consistent, and round only the displayed result rather than intermediate values. Re-enter one simple case by hand when possible; a result with the wrong sign or order of magnitude usually points to an input or reference-base mistake.

Practical guide and verification

Use the tool first, then use these checks to interpret, verify and hand off the result without displacing the primary workflow.

Confirm the triangle is actually right-angled

The Pythagorean relationship applies to a right triangle. If the included angle is not 90 degrees, the correct relationship is generally the law of cosines. Verify the geometry or drawing before treating two measured sides as perpendicular legs.

Keep both legs in the same length unit

Squaring hides unit mistakes because a mixed foot-and-inch or meter-and-centimeter input can still produce a tidy number. Convert both legs to one unit first, calculate the hypotenuse, then label the result with that same unit before converting it for reporting or purchasing.

Round only after the full calculation

Carry sufficient precision through a² + b² and the square root, then round the final result to the precision justified by the measurements. Early rounding can accumulate noticeably in layout, fabrication, surveying, or repeated geometric calculations.

Use a second relation as a quick verification

For a valid right triangle the hypotenuse must be longer than either leg, and squaring the reported result should approximately recover a² + b². This simple round-trip check catches swapped units, negative or mistyped inputs, and transcription errors before the value is reused.