Interactive Pythagorean Theorem Calculator
Calculated result
Enter the known values and select Calculate.
How to use this calculator
- Identify the hypotenuse opposite the right angle and label it c.
- Enter exactly two positive side lengths.
- Leave the side you want to find blank.
- Use one consistent length unit for all entries.
Formula and method
a² + b² = c². To find c, use √(a² + b²). To find a, use √(c² − b²); to find b, use √(c² − a²).
Worked example
If a = 5 and b = 12, then c = √(25 + 144) = √169 = 13. If c = 13 and b = 12, then a = √(169 − 144) = 5.
Assumptions and result interpretation
- The triangle is a right triangle.
- The hypotenuse c must be longer than either leg.
- The output uses the same generic length unit as the inputs.
- Rounding is applied only to the displayed result.
Understanding the result
This page owns the direct missing-side job. Use the broader right-triangle calculator when angles, area, or perimeter are also needed.
Common mistakes
- Labeling a leg as c
- Entering three conflicting values
- Subtracting in the wrong order when solving a leg
- Mixing feet and inches without converting first
Pythagorean theorem formula
a² + b² = c², where a and b are the legs and c is the hypotenuse, the side opposite the right angle.
Find the hypotenuse
When both legs are known, use c = √(a² + b²). For legs 3 and 4, c = √(9 + 16) = 5.
Find a missing leg
When the hypotenuse and one leg are known, subtract the known leg squared from c², then take the square root.
When the theorem applies
The Pythagorean theorem applies only to right triangles. It does not solve an arbitrary triangle without a known 90-degree angle.
Methodology sources
Use this result as a calculation aid. Confirm input definitions, required precision, and any governing policy or professional standard separately.