About the Pythagorean theorem calculator
The Pythagorean theorem states that in a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides. This calculator finds whichever of the three sides is missing, and checks whether your triangle is a Pythagorean triple with whole-number sides.
It also reports the area and perimeter.
Who should use the Pythagorean theorem calculator
- Students learning the theorem.
- Builders checking that a corner is square (the 3-4-5 rule).
- Anyone finding a diagonal.
How to use the Pythagorean theorem calculator: what each input means
- Which side to find
- The hypotenuse c, or leg a or b.
- The other two sides
- Positive lengths in the same unit. The hypotenuse must be longer than either leg.
How the Pythagorean theorem calculator works: method and formula
From a² + b² = c², the hypotenuse is c = √(a² + b²) and a leg is √(c² − b²). The calculator also shows a check by squaring the sides back.
- Theorem
- a² + b² = c²
- Hypotenuse
- c = √(a² + b²)
- Leg
- a = √(c² − b²)
How to read your Pythagorean theorem calculator result
The hypotenuse is always the longest side, opposite the right angle. If all three sides are whole numbers, they form a Pythagorean triple, such as 3-4-5, 5-12-13 or 8-15-17.
Pythagorean Theorem Calculator worked example
Legs of 6 and 8.
- c = √(6² + 8²) = √(36 + 64) = √100.
- c = 10.
- Check: 6² + 8² = 100 = 10². This is a multiple of the 3-4-5 triple.
The hypotenuse is 10, and the area is 24.
Practical uses of the Pythagorean theorem calculator
- Finding the diagonal of a rectangle or screen.
- Checking a corner is square with 3-4-5 measurements.
- Calculating ladder reach and ramp lengths.
Assumptions and limitations of this calculator
- Valid only for right triangles.
- All lengths must be in the same unit.