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Pythagorean theorem calculator and converse
Calculate a side of a right triangle with the Pythagorean theorem or test whether a triangle is right using its converse. The worked solution is generated automatically in your browser.
- 100% local
- Instant
- Free
- No account
- Works offline
- Clipboard
Result
—
Enter two valid lengths. The hypotenuse must be longer than a known leg.
Enter three valid lengths that form a triangle.
Worked solution
Calculate a side of a right triangle
Why use this tool?
Use the Pythagorean theorem to calculate a side of a right triangle, or its converse to determine whether a triangle is right. A full worked solution is generated automatically.
Smart processing
Generate, convert, or validate technical data with purpose-built controls.
Supported formats
Technical formats and syntaxes suited to each generator, converter, or validator.
Save time
Get a clean, ready-to-use result in seconds without installing software or configuring a complex workflow.
Understanding the Pythagorean theorem
The Pythagorean theorem applies to a right triangle. The hypotenuse is opposite the right angle and is the longest side.
Finding the hypotenuse
c² = a² + b² ⇒ c = √(a² + b²)
If a and b are the legs, add their squares and take the square root.
Finding a leg
a² = c² − b² ⇒ a = √(c² − b²)
When hypotenuse c is known, subtract the square of the other leg from the square of the hypotenuse.
Converse of the Pythagorean theorem
a² + b² = c² ⇒ right triangle
If c is the longest side and the equality holds, the triangle is right.
- a, b
- legs adjacent to the right angle
- c
- hypotenuse, opposite the right angle
Example: with a = 3 and b = 4, c = √(3² + 4²) = √25 = 5.
Fonctionnement
How does this tool work?
Use the Pythagorean theorem to calculate a side of a right triangle, or its converse to determine whether a triangle is right. A full worked solution is generated automatically. The calculator applies the geometric relationship that matches the dimensions you provide. Values are validated first, then the shared geometry engine evaluates the formula while keeping units consistent. The result updates whenever an input changes, making it easier to see how each dimension affects the calculation and to verify the method without repeating every operation by hand.
Use cases
Exercises and revision
Check a geometry exercise after writing down the formula and completing the calculation yourself, while keeping the solution method easy to review.
Practical measurements
Estimate a length, perimeter or area from measured dimensions for a plan, layout, drawing or small practical project.
Formula checking
Compare a result from a calculator or spreadsheet and identify an input, unit or formula mistake more easily before using the value.
Guide
How to use this tool
- 1
Choose Theorem or Converse
The Theorem mode calculates a missing length. The Converse mode compares the squares of all three sides.
- 2
Enter the known lengths
Calculations update automatically as soon as the values are valid.
- 3
Use the worked solution
The solution keeps the exact value and adds a decimal approximation when the square root is not an integer.
Tips and best practices
- In a right triangle, the hypotenuse is opposite the right angle and is always the longest side.
- For the converse, the tool automatically identifies the longest side before comparing squares.
- Keep all dimensions in consistent units and check the displayed formula before using the result in an exercise, plan or practical project.
Frequently asked questions
What is the difference between the theorem and its converse?
The theorem finds a length in a triangle already known to be right. The converse tests whether a triangle is right from its three side lengths.
Why show both a square root and an approximate value?
The square root preserves the exact value. When it is not an integer, the tool also displays a decimal approximation.
Is the calculation local?
Yes. Calculations and the worked solution are generated directly in your browser.
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