What Is a FREE Pythagorean Theorem Calculator?
A FREE Pythagorean Theorem Calculator is an online tool that calculates the missing side length of a right triangle when the other two side lengths are known.
It is based on the Pythagorean theorem, one of the most important formulas in geometry.
a2+b2=c2a^2 + b^2 = c^2
c=15.02+15.02=21.21c=\sqrt{\text{15.0}^2+\text{15.0}^2}=\text{21.21}c=15.02+15.02=21.21
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Pythagorean Theorem Formula
The formula is:
a² + b² = c²
Where:
- a = first leg of the right triangle
- b = second leg
- c = hypotenuse
- c is always the side opposite the 90° angle and is the longest side.
How Does the Calculator Work?
A FREE Pythagorean Theorem Calculator can solve for any one missing side when the other two sides are known.
Finding the Hypotenuse
If a = 3 and b = 4:
c = √(3² + 4²)
c = √25
c = 5
So, a right triangle with legs of 3 and 4 has a 5-unit hypotenuse.
Finding a Missing Leg
If the hypotenuse is 10 and one leg is 6:
b = √(10² − 6²)
b = √64
b = 8
Therefore, the missing side is 8 units.
What Can a FREE Pythagorean Theorem Calculator Calculate?
It can calculate:
- Missing hypotenuse
- Missing first leg
- Missing second leg
- Right-triangle side lengths
- Results in different measurement units
Common units include:
- Inches
- Feet
- Yards
- Centimeters
- Meters
- Millimeters
Common Uses
A Pythagorean Theorem Calculator is useful for:
- Geometry and mathematics
- School assignments
- Construction
- Carpentry
- Architecture
- Engineering
- Surveying
- Landscaping
- Distance calculations
- Technical design
Construction Example
Suppose you need to determine the diagonal distance across a rectangular area that is 12 feet wide and 16 feet long.
Using the theorem:
c = √(12² + 16²)
c = √400
c = 20 feet
The diagonal is therefore 20 feet.
When Can You Use the Pythagorean Theorem?
The theorem only applies directly to right triangles, meaning one angle must be exactly 90°.
It is not intended for arbitrary triangles without additional information.
Key Benefit
A FREE Pythagorean Theorem Calculator provides a quick and accurate way to find a missing side of a right triangle. It eliminates repetitive calculations and is especially helpful for geometry, construction, engineering, carpentry, surveying, and everyday distance measurements.
