Math

Pythagorean Theorem Calculator

Solve for any side of a right triangle using a² + b² = c².

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

Missing side
Missing side
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Area of the triangle
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Pythagorean Theorem Calculator by TheCalcTools

How the Pythagorean Theorem Calculator works

Choose whether you want the hypotenuse or a leg.

To find the hypotenuse, enter legs a and b. To find leg a, enter leg b and the hypotenuse c.

The calculator applies a² + b² = c².

The formula

a² + b² = c²c = √(a² + b²)

Worked example

Using the default values shown in the calculator:

FindHypotenuse (c)
Leg a / known leg3
Leg b4
Hypotenuse (c), if known5
  1. With legs 3 and 4: a² + b² = 9 + 16 = 25.
  2. c = √25 = 5.00.
  3. The triangle’s area is ½ × 3 × 4 = 6.00.

Result:

Missing side5.0000
Area of the triangle6.0000

Frequently asked questions

What is a Pythagorean triple?

A set of whole numbers that satisfies the theorem, such as 3-4-5, 5-12-13 and 8-15-17.

Does it work for any triangle?

No. It applies only to right triangles. For other triangles use the law of cosines.

Sources and further reading

Triangle Area Calculator (Heron's Formula)Enter three side lengths to find the triangle's area, perimeter and angles Law of Cosines CalculatorEnter two sides and the included angle (SAS) to solve the rest of the triangle Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA)Choose what you know and enter the values Circle CalculatorEnter the radius to get the diameter, circumference and area of a circle Rectangle CalculatorEnter the length and width to find the area, perimeter and diagonal Trapezoid Area CalculatorEnter the two parallel sides and the height to find the area of a trapezoid

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