# Pythagorean Theorem Calculator toFind Missing Length of Right Triangle

The Pythagorean Theorem Solver on this page will find the length of a side given the lengths of the other two.

This free online geometry calculator will use the Pythagorean Theorem to solve for the missing length of a right triangle given the lengths of the other two sides.

Plus, unlike other online calculators, this calculator will show its work and draw the shape of the right triangle based on the results.

Finally, this page also includes a mini calculator that checks to see if the given lengths of three sides of a triangle form a right triangle (Converse of Pythagorean Theorem).

If you are unfamiliar with the Pythagorean Theorem, you may want to read the following brief explanation before using the calculator.

### What is the Pythagorean Theorem?

The Pythagorean Theorem is the relationship between the lengths of the two legs of a right triangle and its hypotenuse. The relationship is expressed as follows:

 a2 + b2 = c2 where ... a = the length of the vertical side. b = the length of the base. c = the length of the side opposite of the 90° angle.

Based on this relationship, we can isolate each unknown length to solve for it.

 Hypotenuse c = √ a2 + b2
 Leg a = √ c2 - b2
 Leg b = √ c2 - a2
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### Converse of Pythagorean Theorem

If you already know the lengths of all three sides of a triangle, the Converse of the Pythagorean Theorem can be used to determine whether or not the triangle is a right triangle.

 If a2 + b2 = c2 is true, then the triangle is a right triangle. If a2 + b2 = c2 is false, then the triangle is not a right triangle.

You can conduct your own test here:

a   b   c
2 + 2 = 2
+ =
=
Enter values for a, b, and c

With that, let's use the Pythagorean Theorem Calculator to find the missing side of a right triangle.

Pythagorean Theorem Calculator

Instructions: Select your rounding preference.

Next, select the side you want to solve for (Hypotenuse c, Leg a, or Leg b).

Enter the two known lengths of the right triangle and tap the "Calculate Unknown Length" button. This will solve for the missing length and, if you have an HTML5 compatible web browser, redraw the triangle.

Mouse over the blue question marks for a further explanation of each entry field or button. More in-depth explanations can be found in the glossary of terms located beneath the Pythagorean Theorem Calculator.

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Number of decimal places to round result to:
Solve for: Hypotenuse c Leg a Leg b
Length of Leg a:
Length of Leg b:
Length of Hypotenuse:
Area of triangle:
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### Pythagorean Theorem Calculator Glossary of Terms

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Number of decimal places to round result to: Select how many decimal places you would like the result rounded to. Note that you can change the number of places before or after calculating the missing length. Also note that the Pythagorean Theorem Calculator will always display the raw results (out to 14 places) in the steps that will appear beneath the calculator.

Solve for: Select the right triangle side you wish to solve for.

Length of first side: Enter the first known length on this line.

Length of second side: Enter the second known length on this line.

Calculate Unknown Length button: Clicking this button will calculate the missing length, display the steps and formula used, and attempt to draw a scaled version of the right triangle below.

Length of missing side: This is the missing length of the right triangle.

Area of triangle: This is the area of the right triangle formed by Leg a, Leg b, and Leg c (hypotenuse). The formula used is, Area (K) = 1/2 x b x a.

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