Pythagorean theorem calculator
Know two sides of a right-angled triangle? Find the third, along with the area, perimeter and both acute angles.
How the pythagorean theorem calculator works
In any triangle with a right angle, the square on the longest side (the hypotenuse) equals the sum of the squares on the other two. That lets you find a missing length from the other two, no protractor required.
Once all three sides are known the calculator also gives the area (half the two short sides multiplied), the perimeter and the two other angles using the inverse tangent.
The formula behind it
a² + b² = c²
Hypotenuse: c = √(a² + b²). Short side: b = √(c² - a²).
A worked example
A ladder leans against a wall with its foot 3 m from the base and reaching 4 m up. c = √(9 + 16) = √25 = 5 m. Another well-known set is 5, 12, 13: given c = 13 and a = 5, b = √(169 - 25) = √144 = 12.
Questions people ask
Does it only work for right angles?
Yes. For other triangles you need the cosine rule, which is a generalisation of this theorem.
Which side is the hypotenuse?
Always the one opposite the right angle, and always the longest.
What is a Pythagorean triple?
Three whole numbers that fit exactly, such as 3-4-5, 5-12-13 and 8-15-17.
Where is this used in real life?
Carpentry, navigation, screen sizes (the diagonal of a TV) and checking that a corner is square.