Pythagorean Theorem Calculator
Choose the side to solve and enter the other two positive side lengths. The calculator validates that an entered hypotenuse exceeds the known leg before applying the Pythagorean theorem. This page covers “pythagoras equation solver”, “hypotenuse calculator”.
How to use the Pythagorean Theorem Calculator
Enter the side to solve and the other two positive side lengths in the same unit.
Review which side is the hypotenuse, consistent units, measurement precision, and whether the triangle is known to contain a 90° angle.
Read both legs, the hypotenuse, and triangle area.
Formula
For legs a and b, c = √(a² + b²). When c and one leg are known, the other leg is √(c² − known-leg²). Area = a × b ÷ 2.
Example
A right triangle with legs 3 and 4 has hypotenuse √(3² + 4²) = 5.
Assumptions and limitations
- The theorem applies only to a Euclidean right triangle; measured construction corners may require a tolerance rather than exact equality.
- Pythagorean Theorem Calculator treats the entered values as estimates and does not infer missing project, account, or personal details.
- Calculations retain working precision except where the cited method requires an intermediate rounding step; displayed values are then formatted separately. Source rules and dated rates must be rechecked when they change.
Sources
- OpenStax: College Algebra 2eAlgebraic, ratio, radical, equation, and function formulas. Reviewed 2026-08-14.
- OpenStax: Elementary Algebra 2eOfficial formula, rate, or program guidance used by this calculator. Reviewed 2026-08-14.
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Frequently asked questions
How does the Pythagorean Theorem Calculator work?
For legs a and b, c = √(a² + b²). When c and one leg are known, the other leg is √(c² − known-leg²). Area = a × b ÷ 2.
What information should I enter in the Pythagorean Theorem Calculator?
Enter the side to solve and the other two positive side lengths in the same unit, then verify which side is the hypotenuse, consistent units, measurement precision, and whether the triangle is known to contain a 90° angle.
What should I verify before using this Pythagorean Theorem Calculator result?
The theorem applies only to a Euclidean right triangle; measured construction corners may require a tolerance rather than exact equality.
Reviewed 2026-08-14 · any-two-sides-v2 · content-2026-08-14 · Trusty Calculator Editorial Team