What Is FREE TOOLS Pythagorean Theorem Calculator?
A Pythagorean Theorem Calculator is a free online tool used to find the missing side of a right triangle when the lengths of the other two sides are known.
The calculator is based on the Pythagorean Theorem, one of the most important formulas in geometry.
Pythagorean Theorem Formula
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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The formula is: a2+b2=c2\boxed{a^2+b^2=c^2}
Where:
- a = first leg of the right triangle
- b = second leg
- c = hypotenuse, the longest side opposite the 90° angle
Finding the Hypotenuse
If both legs are known: c=a2+b2c=\sqrt{a^2+b^2}
For example, if:
- a=3a=3
- b=4b=4
Then: c=32+42c=\sqrt{3^2+4^2} c=9+16c=\sqrt{9+16} c=5c=5
So, the hypotenuse is 5 units.
Finding a Missing Leg
If the hypotenuse and one leg are known, you can calculate the other leg: a=c2−b2a=\sqrt{c^2-b^2}
For example, if c=13c=13 and b=5b=5: a=132−52a=\sqrt{13^2-5^2} a=169−25a=\sqrt{169-25} a=144=12a=\sqrt{144}=12
Therefore, the missing side is 12 units.
How Does a Pythagorean Theorem Calculator Work?
A FREE TOOLS Pythagorean Theorem Calculator typically allows you to enter any two known sides of a right triangle. It then calculates the third side automatically.
It can calculate:
- Hypotenuse
- First leg
- Second leg
- Missing side length
When Should You Use It?
A Pythagorean Theorem Calculator is useful for:
- Geometry homework
- Mathematics problems
- Construction measurements
- Architecture
- Engineering
- Surveying
- Distance calculations
- Determining diagonal lengths
- Checking right-angle measurements
Important Note
The Pythagorean Theorem applies only to right triangles, meaning triangles containing a 90° angle.
It should not be directly used for arbitrary triangles. For non-right triangles, formulas such as the Law of Sines or Law of Cosines may be more appropriate.
In Simple Terms
A FREE TOOLS Pythagorean Theorem Calculator makes it easy to find a missing side of a right triangle.
The key formula is: a2+b2=c2\boxed{a^2+b^2=c^2}
Simply enter two known side lengths, and the calculator determines the missing side quickly and accurately.
