Pythagorean Theorem Calculator
Pythagorean Theorem Calculator helps to find the unknown side length of rightangled triangle when two side lengths are known.
What is the Pythagorean Theorem Calculator?
Pythagorean Theorem Calculator is an online tool to find any of the sides of a rightangled triangle.
Cuemath's online Pythagorean Theorem Calculator helps to find one side of a right angled triangle faster, by entering the other two sides of a rightangled triangle.
What is Pythagorean Theorem?
In a rightangled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The hypotenuse is the side of the triangle opposite to the right angle.
In the given \(\Delta ABC \),
\[\begin{align}
\text{BC}^2 &= \text{AB}^2 +\text{AC}^2
\end{align}\]
where,
 \( \text{AB}\) is the base,
 \( \text{AC}\) is the altitude or the height, and
 \( \text{BC}\) is the hypotenuse.
If 'c' is the hypotenuse of a right triangle and 'a' and 'b' are the other two sides, then,
\(\begin{equation} a^{2}+b^{2}=c^{2} \end{equation}\) 
Pythagorean theorem equation helps us to solve Pythagorean theorem problems.
How to Use the Pythagorean Theorem Calculator?
Follow these steps which will help you to use the calculator.
 Step 1: Select the side of the rightangled triangle to be calculated, from the dropdown list.
 Step 2: Enter the value for the other two sides in the corresponding input boxes.
 Step 3: Click on "Calculate" to find the unknown side of the triangle.
 Step 4: Click on "Reset" to clear the fields and enter the new values.

Solved Example 1:
A rightangled triangle ABC, has base BC = 12 units, height AB = 5 units. What is the length of AC?
Solution:
By Pythagoras theorem we know that,
AB^{2} + BC^{2} = AC^{2}
AC^{2} = 5^{2 }+ 12^{2}
AC = (5^{2} + 12^{2})^{½} = √(5^{2} + 12^{2})
AC = 13 units.Answer: The length of AC is 13 units.

Solved Example 2:
A rightangled triangle PQR, has angle Q = 90°. PQ = 8 units. PR = 10 units. Find QR.
Solution:
By Pythagoras Theorem we know that,
PR^{2}= PQ^{2} + QR^{2}^{ }
10^{2} = 8^{2 } + QR^{2}
QR^{2} = 10^{2}  8^{2 }
QR = (10^{2}  8^{2})^{½} = √(10^{2}  8^{2})
QR = 6 units.Answer: The length of QR is 6 units.
Now use the calculator to find the hypotenuse of rightangled triangles with:
 Side a = 6 units and side b = 8 units.
 Side a = 12 units and side b = 5 units.