Pythagorean Theorem Calculator
Pythagorean theorem: a² + b² = c² for right triangles, where c is the hypotenuse (longest side opposite the right angle). To find c: c = √(a² + b²). For example, sides 3 and 4: c = √(9+16) = √25 = 5. To find a leg: a = √(c² - b²). Common Pythagorean triples: (3,4,5), (5,12,13), (8,15,17). Use in construction (squaring corners), navigation (distance calculation), and surveying. Works only for right triangles (90° angle).
Calculate the missing side of a right triangle using the Pythagorean theorem (a² + b² = c²). Find hypotenuse or leg, plus area and angles.
What do you want to find?
Side a (leg)
Side b (leg)
Common Pythagorean Triples
Hypotenuse (c)
5
Triangle Properties
Side a
3
Side b
4
Side c (hypotenuse)
5
Area
6 sq units
½ × base × height
Perimeter
12 units
a + b + c
Angles
Angle A
36.8699°
Angle B
53.1301°
Angle C
90°
Pythagorean Theorem
a² + b² = c²
- The hypotenuse (c) is always the longest side
- Only works for right triangles (one 90° angle)
- Pythagorean triples are integer solutions (e.g., 3-4-5)
- Named after Greek mathematician Pythagoras (c. 570-495 BC)
How to Use
- Enter your value in the input field
- Click the Calculate/Convert button
- Copy the result to your clipboard
Frequently Asked Questions
- What is the Pythagorean theorem?
- The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle) and a, b are the legs. Named after Greek mathematician Pythagoras (~570-495 BCE).
- What are Pythagorean triples?
- Pythagorean triples are sets of three positive integers that satisfy a² + b² = c². Common examples: (3,4,5), (5,12,13), (8,15,17), (7,24,25). Any multiple of a triple is also a triple: (6,8,10), (9,12,15). Infinite triples exist.
- How do I find the hypotenuse?
- Square both legs, add them, take the square root: c = √(a² + b²). For a=3, b=4: c = √(9+16) = √25 = 5. The hypotenuse is always the longest side and opposite the 90° angle.
- How do I find a missing leg?
- Rearrange to a = √(c² - b²). If hypotenuse c=13 and one leg b=5: a = √(169-25) = √144 = 12. The missing leg must be shorter than the hypotenuse.
- Where is the Pythagorean theorem used?
- Used in: construction (checking right angles), navigation (shortest distance), computer graphics (distance between points), physics (vector magnitude), surveying, architecture. Any time you need to find distance or verify a right angle.