1. Select the missing side
Choose whether you need to calculate side a, side b or the hypotenuse c.
Free Right Triangle Solver
Pythagorean Theorem Calculator
Find the missing side of a right triangle using two known side lengths. Get an accurate answer, the applied formula and step-by-step calculations.
Triangle Calculator
Enter the known sides
Choose the side you need to calculate, then enter positive values for the other two sides.
Which side do you want to find?
Right Triangle
Visualize your values
a
b
c
Missing side
0
Calculation steps
How It Works
Calculate a triangle side in three steps
The calculator rearranges the Pythagorean theorem according to the side you need to find.
2. Enter two known values
Add the lengths of the two sides you already know. You can use whole numbers or decimals.
3. Review the result
The missing length appears with its formula, substituted values and calculation steps.
Pythagorean theorem formula
a² + b² = c²
In a right triangle, a and b are the two shorter sides, while c is the hypotenuse opposite the 90-degree angle.
Formula Explained
What is the Pythagorean theorem?
The Pythagorean theorem describes the relationship between the three sides of a right-angled triangle. It states that the square of the hypotenuse equals the sum of the squares of the other two sides.
The theorem can only be used when one angle of the triangle is exactly 90 degrees. The hypotenuse is always the longest side and is located directly opposite the right angle.
Find the hypotenuse with
c = √(a² + b²).
Find side a with
a = √(c² − b²).
Find side b with
b = √(c² − a²).
Common Examples
Pythagorean triangle examples
These common right-triangle combinations show how the formula works with different side lengths.
| Side a | Side b | Hypotenuse c | Calculation |
|---|---|---|---|
| 3 | 4 | 5 | √(3² + 4²) = 5 |
| 5 | 12 | 13 | √(5² + 12²) = 13 |
| 8 | 15 | 17 | √(8² + 15²) = 17 |
| 7 | 24 | 25 | √(7² + 24²) = 25 |
| 9 | 40 | 41 | √(9² + 40²) = 41 |
Important:
All side lengths must use the same unit. For example, do not
enter one side in centimeters and another in meters unless you
convert them first.
FAQs
Frequently asked questions
Helpful answers about right triangles, hypotenuse calculations and using the calculator.
It calculates a missing side of a right triangle when the other two side lengths are known.
Square both shorter sides, add the squared values and take the square root of the total. The formula is c = √(a² + b²).
Square the hypotenuse, subtract the square of the known shorter side and take the square root of the remaining value.
Yes. The calculator accepts whole numbers and positive decimal values, such as 4.5, 7.25 or 12.8.
No. The Pythagorean theorem applies only to right triangles containing one 90-degree angle.
The hypotenuse is opposite the largest angle, which is the 90-degree angle. Therefore, its length must be greater than either of the two shorter sides.
You can use centimeters, meters, inches, feet or another length unit. Both entered values must use the same unit, and the answer will use that unit too.