Important Note : Use this calculator only for right triangles. The hypotenuse $c$c is always the longest side and must be opposite the right angle.

Use this Pythagorean Theorem Calculator to solve the missing side of a right triangle quickly. Enter any two sides, leave one blank, and the calculator will find the missing value along with the triangle’s area and perimeter.

Reviewed by: AjaxCalculators Editorial Team
Last updated: April 24, 2026
Method source: Standard Pythagorean theorem relationships for right triangles
Editorial standards: AjaxCalculators Editorial Policy

What This Pythagorean Theorem Calculator Calculates

This calculator helps you solve a right triangle when you know any two of these three sides:

• Leg a
• Leg b
• Hypotenuse c

It also shows:

• Solved side
• Area
• Perimeter
• Summary

How the Pythagorean Theorem Calculator Works

The Pythagorean Theorem applies to right triangles only.

The formula is:

a² + b² = c²

Where:

• a and b are the two legs
• c is the hypotenuse, the longest side opposite the right angle

1) Solve for the Hypotenuse

If both legs are known:

c = √(a² + b²)

2) Solve for a Missing Leg

If one leg and the hypotenuse are known:

a = √(c² − b²)

or

b = √(c² − a²)

This is why the hypotenuse must be the longest side. If c is not larger than the known leg, the triangle is not valid.

Area and Perimeter

Once all three sides are known, the calculator can also find:

Area = (a × b) ÷ 2

Perimeter = a + b + c

Because the two legs meet at the right angle, they work directly as the base and height for area.

Assumptions and Important Notes

• This calculator is for right triangles only.
• c must be the hypotenuse and therefore the longest side.
• If you enter values that do not make a valid right triangle, the result will not make geometric sense.
• All side measurements should use consistent units.
• Area uses square units, while perimeter uses linear units.

Worked Examples

Example 1: Find the Hypotenuse

Suppose:

• a = 6
• b = 8

Step 1: Write the formula
a² + b² = c²

Step 2: Substitute the values
6² + 8² = c²

Step 3: Simplify
36 + 64 = 100

Step 4: Take the square root
c = 10

So the hypotenuse is 10.

Example 2: Find a Missing Leg

Suppose:

• c = 13
• a = 5

Step 1: Use the leg formula
b = √(c² − a²)

Step 2: Substitute the values
b = √(13² − 5²)

Step 3: Simplify
b = √(169 − 25) = √144

Step 4: Solve
b = 12

So the missing leg is 12.

How to Use This Pythagorean Theorem Calculator

1. Enter any two known side lengths.
2. Leave the unknown side blank.
3. Make sure c is used for the hypotenuse.
4. Select the preferred unit.
5. Click Calculate to see the solved side, area, perimeter, and summary.

How to Interpret the Result

Solved side is the missing triangle side based on the Pythagorean theorem.

Area is the amount of space inside the right triangle.

Perimeter is the total distance around the triangle.

If the values fail to produce a valid right triangle, check that the hypotenuse was entered as c and that it is longer than either leg.

Practical Uses of a Pythagorean Theorem Calculator

• find the hypotenuse of a right triangle
• solve for a missing leg
• check geometry homework
• estimate diagonal distances in construction and layout work
• find right-triangle area and perimeter from side lengths

References

1. OpenStax Prealgebra 2e – The Pythagorean Theorem
2. OpenStax Contemporary Mathematics – right triangle formula reference
3. Khan Academy – introduction to the Pythagorean theorem

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Disclaimer: This calculator is for educational and general geometry use. It applies only to right triangles, where the hypotenuse is the longest side and lies opposite the right angle.