Pythagorean Theorem Calculator
Find the missing side of a right-angled triangle. Builders use it to check a corner is square (the 3-4-5 rule) and to find the diagonal of a room or plot.
Updated
Formula
a² + b² = c²
c = √(a² + b²)
b = √(c² − a²)
c is the hypotenuse — the longest side, opposite the right angle.
Examples
Sides 3 and 4
Hypotenuse c = 5
Plot 30 × 60 ft — diagonal
Hypotenuse c = 67.082039325
Hypotenuse 13, side 5
Side b = 12
Important information
- To check a wall corner is square, mark 3 ft along one wall and 4 ft along the other: the diagonal should be exactly 5 ft. Scale up to 6-8-10 for bigger rooms.
Frequently asked questions
Does it work for any triangle?
No, only right-angled triangles (one angle exactly 90°).
What is a Pythagorean triple?
Three whole numbers that fit a² + b² = c², such as 3-4-5, 5-12-13 and 8-15-17.
How do I find the diagonal of a rectangle?
Use the length and width as a and b; the hypotenuse is the diagonal.
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