Right Triangle Side Calculator
Enter exactly two sides. Leave the missing side blank, then click calculate.
How this right triangle calculator works
This right triangle calculator for sides uses the Pythagorean theorem to find the missing side of a right triangle. In every right triangle, the two shorter sides are called legs (a and b), and the longest side opposite the 90° angle is the hypotenuse (c).
a² + b² = c²
If you know any two sides, the third side can be calculated immediately:
- Find hypotenuse: c = √(a² + b²)
- Find leg a: a = √(c² - b²)
- Find leg b: b = √(c² - a²)
Step-by-step usage
1) Enter two known sides
Type values into any two boxes. Leave the side you want to solve empty. You can use decimals, such as 7.25 or 12.8.
2) Click “Calculate Missing Side”
The tool computes the missing side and also provides the triangle’s area and perimeter.
3) Check the output
If your entries are not valid for a right triangle, the calculator will show a helpful error. For example, the hypotenuse must be larger than either leg.
Example calculations
Example 1: Classic 3-4-5 triangle
Given a = 3 and b = 4:
c = √(3² + 4²) = √(9 + 16) = √25 = 5
Example 2: Find a missing leg
Given c = 13 and b = 5:
a = √(13² - 5²) = √(169 - 25) = √144 = 12
Example 3: Decimal values
Given a = 6.5 and b = 2.1:
c = √(6.5² + 2.1²) = √(42.25 + 4.41) = √46.66 ≈ 6.8308
Common mistakes to avoid
- Entering all three sides when only one is supposed to be unknown.
- Using a hypotenuse value smaller than a leg value.
- Entering negative numbers or zero for side lengths.
- Rounding too early in multi-step manual calculations.
Why right triangle side calculations matter
Right triangle formulas appear everywhere: construction, surveying, navigation, engineering, computer graphics, and even fitness tracking apps. Anytime you need distance, slope, diagonal length, or height from partial data, this method is useful.
Quick reference
- Legs: the two sides that form the right angle (a and b)
- Hypotenuse: side opposite the right angle (c), always the longest side
- Area: (a × b) / 2
- Perimeter: a + b + c
Use the calculator above whenever you need fast, accurate right triangle side results.