The Pythagorean theorem calculator finds any side of a right triangle using a² + b² = c². Enter two sides to find the third, with unit support for meters, feet, inches, and centimeters.
Pythagorean Theorem Calculator (a² + b² = c²)
How to Use the Pythagorean Theorem Calculator
The Pythagorean theorem applies only to right triangles (one 90° angle). The hypotenuse (c) is always the side opposite the right angle and is the longest side.
Finding the Hypotenuse
Given legs a=3 and b=4: c = √(3²+4²) = √(9+16) = √25 = 5. The 3-4-5 right triangle is the most common Pythagorean triple. Construction workers use this to check right angles: if a corner with sides 3 ft and 4 ft has a diagonal of exactly 5 ft, the corner is square.
Finding a Leg
If c=13 and b=12: a = √(13²−12²) = √(169−144) = √25 = 5. The 5-12-13 triple is another common Pythagorean triple. Use this when you know the hypotenuse and one leg.
3D Extension
In 3D space, distance d = √(Δx² + Δy² + Δz²). The space diagonal of a 3×4×5 box = √(9+16+25) = √50 ≈ 7.07. Apply the theorem twice: first in a horizontal plane, then vertically.
Frequently Asked Questions
What is the Pythagorean theorem?
In a right triangle with legs a and b and hypotenuse c (opposite the right angle): a² + b² = c². To find c: c = √(a² + b²). To find leg a: a = √(c² − b²). The theorem only applies to right triangles (with one 90° angle).
What are Pythagorean triples?
Pythagorean triples are integer solutions: {3,4,5}, {5,12,13}, {8,15,17}, {7,24,25}, {20,21,29}. Check: 3²+4²=9+16=25=5². Multiples work too: {6,8,10}, {9,12,15}. The 3-4-5 triangle is commonly used in construction to check right angles.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
Can the Pythagorean theorem be used in 3D?
Yes. The 3D distance formula is d = √(a² + b² + c²). The space diagonal of a rectangular box with sides l, w, h is d = √(l² + w² + h²). This extends directly from the 2D Pythagorean theorem applied twice.