Pythagorean theorem calculator
Leave one box empty to find the missing side, or fill all three to test whether the lengths satisfy the Pythagorean theorem.
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How to use it
- Enter leg a, leg b and hypotenuse c.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
a² + b² = c², so c = √(a² + b²) and a = √(c² - b²). With three lengths, the longest is taken as the hypotenuse and its square is compared with the sum of the other two squares.
Example
Inputs: Leg a = 3, Leg b = 4. Result: Hypotenuse c: 5; Equation: 3² + 4² = 5²; Pythagorean triple?: Yes, all sides are whole numbers.
Limits and caveats
- The theorem applies to right triangles only.
- With three rounded decimal lengths, the squares may not match exactly because of the rounding.
Questions about this tool
What does the Pythagorean theorem say?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
What is a Pythagorean triple?
Three whole numbers that satisfy the theorem, such as 3, 4, 5, then 5, 12, 13, and 8, 15, 17.
How do I check a right angle on site?
Measure 3 units along one side and 4 along the other. If the diagonal between the marks is 5 units, the corner is square.