Pythagorean Theorem Calculator
This Pythagorean theorem calculator finds the missing side of a right triangle from the other two sides, using a² + b² = c². Enter two sides and leave the unknown one at 0, and the Pythagorean theorem calculator returns the missing side plus the triangle's area and perimeter. It works as a hypotenuse calculator or to find a missing leg.
Results
The Pythagorean Theorem Calculator is part of our Geometry collection. Browse more geometry to size, convert, and check your work alongside this tool.
What the Pythagorean theorem calculator shows
In a right triangle, the square of the longest side, the hypotenuse, equals the sum of the squares of the other two sides. The Pythagorean theorem calculator uses that relationship to find whichever side is missing. It also gives the area and perimeter of the triangle once all three sides are known.
Pythagoras formula calculator equations
The theorem holds only for right triangles. The area is half the product of the two legs, and the perimeter is the sum of all three sides.
Pythagorean theorem calculator example
Legs of 3 and 4:
With a hypotenuse of 13 and one leg of 12, the missing leg is √(169 − 144) = 5, with an area of 30.
How to use the hypotenuse calculator
Enter the two sides you know and leave the unknown side at 0. To use it as a hypotenuse calculator, enter sides a and b. To find a leg, enter the hypotenuse c and the other leg. The tool checks that the hypotenuse is the longest side and returns an error if it is not.
Reading the Pythagorean theorem solver result
The hypotenuse is always the longest side, opposite the right angle. Whole-number answers such as 3-4-5 and 5-12-13 are Pythagorean triples; most inputs give decimals. If the triangle is not right-angled, use a general triangle method instead.
When to calculate Pythagoras
- Finding a ladder length or diagonal with the hypotenuse calculator
- Checking a corner is square on a building site
- Finding a screen or room diagonal
- Solving right triangle homework
Common Pythagorean theorem calculator mistakes
- Using it on a non-right triangle.
- Treating a leg as the hypotenuse. c must be the longest side.
- Forgetting the square root.
Tips for accurate results
- Label the hypotenuse before you start.
- Check your answer with a² + b² = c².
- Use the 3-4-5 rule to check corners.
Pythagorean theorem calculator find b
To find a leg rather than the hypotenuse, rearrange the theorem: b = √(c² − a²). A 13 m ladder whose foot is 5 m from a wall reaches √(169 − 25) = 12 m up the wall. Builders use the same idea to find rafter lengths from a roof's rise and run, which the roof pitch calculator works out along with the pitch.
Calculate Pythagoras on site: the 3-4-5 rule
To check a corner is square, measure 3 units along one side and 4 along the other; the diagonal between the marks should be exactly 5. Multiples such as 6-8-10 work too.
Pythagorean theorem calculator reference: common triples
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 6 | 8 | 10 |
Pythagorean Theorem Calculator FAQ
What is the Pythagorean theorem?
In a right triangle, a² + b² = c², where c is the hypotenuse.
How do I find the hypotenuse?
Square both legs, add them, and take the square root.
How do I find a missing leg?
Subtract the square of the known leg from the square of the hypotenuse, then take the square root.
Does it work for any triangle?
No, only for right triangles.