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 and 'a' and 'b' are the legs.

How do I find the hypotenuse if I know both legs?

Use the formula c = √(a² + b²). For example, if a = 3 and b = 4, then c = √(9 + 16) = √25 = 5. This is the famous 3-4-5 right triangle.

How do I find a leg if I know the hypotenuse and one leg?

Rearrange the Pythagorean theorem: a = √(c² - b²). For example, if c = 13 and b = 5, then a = √(169 - 25) = √144 = 12.

What are Pythagorean triples?

Pythagorean triples are sets of three positive integers that satisfy a² + b² = c². Common examples include (3,4,5), (5,12,13), (8,15,17), and (7,24,25). Any multiple of these also works, like (6,8,10).

How is the area of a right triangle calculated?

The area of a right triangle is (1/2) × base × height. Since the two legs are perpendicular, you can use them directly: Area = (1/2) × a × b. For a 3-4-5 triangle, the area is (1/2) × 3 × 4 = 6 square units.

What is the perimeter of a right triangle?

The perimeter is simply the sum of all three sides: P = a + b + c. For a 3-4-5 triangle, the perimeter is 3 + 4 + 5 = 12 units.

Right Triangle Calculator

Calculate hypotenuse, legs, area, and perimeter using the Pythagorean theorem (a² + b² = c²).

Unit of Measurement

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Side A (Leg)

One leg of the right triangle

Side B (Leg)

The other leg of the right triangle

Pythagorean Theorem

a² + b² = c²

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Hypotenuse

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c = √(a² + b²) = √(0 + 0) = 0

Area

½ × a × b

0 cm²

Perimeter

a + b + c

0 cm

Angles

α, β, 90°

0° / 0°

Side A

0 cm

Side B

0 cm

Hypotenuse

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Documentation

Understanding Right Triangles

A right triangle has one angle that is exactly 90 degrees. The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs.

Pythagorean Theorem

3, 4, 5 • 5, 12, 13 • 8, 15, 17

Tip: Common Pythagorean triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25).

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About the Right Triangle Calculator

What it calculates

This right triangle calculator solves mathematical and statistical problems using standard formulas. Calculate sides, area, and perimeter using Pythagorean theorem.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

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Right Triangle Calculator

Pythagorean Theorem

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Understanding Right Triangles

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