What is the Pythagorean theorem?

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs, written a² + b² = c².

Which side is the hypotenuse?

The hypotenuse, side c, is the longest side and lies opposite the right angle.

How is the area calculated?

For a right triangle the area is half the product of the two legs, a times b divided by 2.

Can I use it for any triangle?

No, the theorem holds only for right triangles. Other triangles need the law of cosines or sines.

Online Pythagorean Theorem Calculator

What Is This Tool?

The Pythagorean Theorem Calculator finds an unknown side of a right triangle from the other two sides, using the rule a² + b² = c². Choose which side to solve for, enter the two known lengths, and it returns the missing side along with the triangle's area. For example, with legs of 3 and 4, the hypotenuse is 5.

How to Use This Tool?

Select the side you want to find: a, b, or c.
Enter the two known side lengths.
Make sure each leg is smaller than the hypotenuse.
Click Calculate to see the result and area.

Key Features

Solves for either leg or the hypotenuse.
Uses the Pythagorean theorem a² + b² = c².
Returns the triangle's area as well.
Checks that each leg is shorter than the hypotenuse.
Gives instant results from two known sides.

Examples

Legs of 3 and 4 give a hypotenuse of 5.
Legs of 6 and 8 give a hypotenuse of 10.
A hypotenuse of 13 with a leg of 5 gives the other leg as 12.
Legs of 4 and 5 give a hypotenuse of about 6.40.

Common Use Cases

Finding a missing side in geometry problems.
Checking that a corner is a true right angle.
Measuring diagonal distances in construction.
Calculating cable, ramp, or rafter lengths.
Verifying right-triangle homework.

Tips & Best Practices

Identify the hypotenuse c as the side opposite the right angle.
Enter both known sides in the same unit.
Remember that c is always the longest side.
Use this only for right triangles.
Each leg must be smaller than the hypotenuse.

Limitations

It works only for right triangles.
All side lengths must be positive numbers.
Each leg must be shorter than the hypotenuse.
Results are rounded for display.

Frequently Asked Questions

What is the Pythagorean theorem?: In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs, written a² + b² = c².
Which side is the hypotenuse?: The hypotenuse, side c, is the longest side and lies opposite the right angle.
How is the area calculated?: For a right triangle the area is half the product of the two legs, a times b divided by 2.
Can I use it for any triangle?: No, the theorem holds only for right triangles. Other triangles need the law of cosines or sines.

Key Terminology

Hypotenuse: The longest side of a right triangle, opposite the right angle.
Leg: Either of the two shorter sides that form the right angle.
Right triangle: A triangle with one angle of exactly 90 degrees.
Pythagorean theorem: The rule that a² + b² = c² for the sides of a right triangle.
Area: The space inside the triangle, equal to half the product of its two legs.

Quick Knowledge Check

In a² + b² = c², the side c is the:

Hypotenuse

Shortest leg

Right angle

The Pythagorean theorem applies to:

Right triangles only

All triangles

Only equilateral triangles

If the legs are 3 and 4, the hypotenuse is: