Pythagorean Theorem Calculator
Solve a missing side of a right triangle and convert the result between length units.
Content updated August 1, 2026
Both entered sides must use the selected input unit. Lengths and area are converted to the selected output unit after the triangle is solved.
The Pythagorean theorem connects the three sides of a right triangle: the square of the hypotenuse equals the sum of the squares of the two legs. Knowing any two sides is enough to solve the third when one angle is exactly 90 degrees.
Choose whether the missing side is the hypotenuse or a leg, enter the two known lengths in a single unit, and optionally convert the result. The calculator also derives area, perimeter, and both acute angles as useful cross-checks.
The Pythagorean Theorem formula
c² = a² + b²; missing leg = √(c² − known leg²)a and b are perpendicular legs in the same unit, and c is the hypotenuse opposite the 90° angle.
Worked example
With legs 3 m and 4 m, c = √(9 + 16) = 5 m. The area is 6 m² and the perimeter is 12 m.
Assumptions, rounding, and limitations
Assumptions
- The triangle contains one angle of exactly 90 degrees.
- Both known sides use the selected input unit.
- All side lengths are positive, and a known leg is shorter than the hypotenuse.
Rounding: Calculations retain JavaScript floating-point precision; displayed lengths and areas use up to eight decimal places and angles use up to four.
Limitations
- Each entered length must be 1 trillion or less.
- This does not solve non-right triangles or account for measurement uncertainty and significant-figure rules.
Choosing the correct Pythagorean form
When the hypotenuse is unknown, add the squares of both legs and take the square root. When a leg is unknown, subtract the known leg's square from the hypotenuse's square before taking the root.
The hypotenuse must be longer than either leg. If a known leg equals or exceeds the entered hypotenuse, those lengths cannot form a non-degenerate right triangle.
Lengths, squared area units, and angles
All entered sides must use the same input unit. A length conversion applies one scale factor, while area uses that scale factor squared; for example, 1 m² equals 10,000 cm².
After solving the sides, the calculator uses inverse sine for one acute angle and subtracts it from 90 degrees for the other. Those angles do not change when the length unit changes.
Frequently asked questions
▶What is the hypotenuse of a 3-4 right triangle?
It is 5 because √(3² + 4²) = √25 = 5.
▶How do I find a missing leg?
Square the hypotenuse, subtract the square of the known leg, then take the square root of the difference.
▶Can the known leg equal the hypotenuse?
No. That would leave a missing leg of zero, creating a degenerate shape rather than a right triangle.
▶Why does area conversion square the unit factor?
Area has two length dimensions. Converting metres to centimetres multiplies each dimension by 100, so square metres convert by 100².
Related calculators
Solve the missing fourth term in an equivalent proportion written as a:b = c:x.
Open calculator →Round positive or negative numbers to decimal places, whole places, tens, hundreds, or beyond.
Open calculator →Find the greatest common factor and least common multiple of 2–20 integers.
Open calculator →Disclaimer: Pythagorean Theorem Calculator results are estimates for general information and education only, and are not financial, tax, legal or medical advice. Verify important decisions with a qualified professional.