Pythagorean Theorem Calculator

Find the missing side of a right triangle, verify if three sides form a right triangle, and calculate area and perimeter.

Find Hypotenuse (c)

Unit:
The two legs of the right triangle
c must be greater than b
c must be greater than a
Enter all three sides to check if they form a right triangle
a b c
Invalid input: Please check your values.

Sides

Side a --
Side b --
Side c (hypotenuse) --

Measurements

Perimeter --
Area --

Verification

a² + b² --
c² --
Calculated Value --

Common Pythagorean Triples

Click a triple to load it into the calculator

3, 4, 5
Most common
5, 12, 13
Classic
8, 15, 17
Primitive
7, 24, 25
Primitive
6, 8, 10
2x (3,4,5)
9, 12, 15
3x (3,4,5)
20, 21, 29
Nearly equal legs
9, 40, 41
Large ratio

Pythagorean Theorem Formulas

Pythagorean Theorem

a² + b² = c²
The sum of squares of the legs equals the square of the hypotenuse

Find Hypotenuse (c)

c = sqrt(a² + b²)
Given both legs a and b

Find Leg (a or b)

a = sqrt(c² - b²)
Given hypotenuse and one leg

Area of Right Triangle

Area = (1/2) × a × b
Half the product of the two legs

Perimeter

P = a + b + c
Sum of all three sides

Verify Right Triangle

a² + b² = c² ?
If equal, it's a right triangle (c is the longest side)

Frequently Asked Questions

What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. Written as: a² + b² = c², where c is the hypotenuse.

How do I find the hypotenuse of a right triangle?

To find the hypotenuse (c), use the formula c = √(a² + b²). Enter the lengths of the two shorter sides (a and b), and this calculator will compute the hypotenuse for you.

What are Pythagorean triples?

Pythagorean triples are sets of three positive integers (a, b, c) that satisfy the Pythagorean theorem. Common examples include 3-4-5, 5-12-13, 8-15-17, and 7-24-25. Any multiple of these also works (e.g., 6-8-10).

How can I verify if a triangle is a right triangle?

Enter all three side lengths and use the 'Verify Right Triangle' mode. The calculator will check if a² + b² = c². If the equation holds true, it's a right triangle.