Pythagorean Theorem Calculator
Calculate the missing side of a right triangle using a²+b²=c². Find hypotenuse, legs, area, and perimeter. Includes 2D distance formula, right triangle checker, and Pythagorean triples.
Quick Calculator Get a fast estimate
units
units
units
Hypotenuse c
5.000000 units
Area
6.0000 sq units
Perimeter
12.0000 units
Formula
√(3²+4²) = √25
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How to Use the Pythagorean Theorem Calculator
Select which side you want to find, enter the known two sides, and the result appears instantly. The calculator also gives you the triangle area and perimeter.
The Extended Calculator includes a triangle SVG diagram, a right triangle checker, and a 2D distance calculator. The Professional Calculator handles 3D space diagonals and generates Pythagorean triples.
Need more detail?
Extended Calculator More options, charts, and scenario comparison
Hypotenuse c
5 units
Area
6 sq units
Perimeter
12 units
Angle A
36.87°
Angle B
53.13°
Pythagorean Theorem Formula
a² + b² = c²
Find hypotenuse: c = √(a² + b²)
Find leg a: a = √(c² − b²)
Find leg b: b = √(c² − a²)
Area of right triangle: A = ½ × a × b
2D distance: d = √((x₂−x₁)² + (y₂−y₁)²)
3D diagonal: d = √(a² + b² + c²)
Common Pythagorean Triples
| a | b | c | Verification |
|---|---|---|---|
| 3 | 4 | 5 | 9+16=25 ✓ |
| 5 | 12 | 13 | 25+144=169 ✓ |
| 8 | 15 | 17 | 64+225=289 ✓ |
| 7 | 24 | 25 | 49+576=625 ✓ |
| 20 | 21 | 29 | 400+441=841 ✓ |
Need full precision?
Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown
Cuboid dimensions (length × width × height)
3D Space Diagonal
3 units
Formula
√(a²+b²+c²)
Floor diagonal √(a²+b²)
2.2361 units
Volume
4 cubic units
Surface area
16 sq units
3D Pythagorean theorem: d = √(a²+b²+c²). This gives the length of the space diagonal — the longest straight line inside a cuboid. Used in 3D geometry and room acoustics.
Frequently Asked Questions
In any right triangle (one 90° angle), the square of the hypotenuse equals the sum of the squares of the two legs: a²+b²=c². Named after ancient Greek mathematician Pythagoras.
c = √(a²+b²). Square both legs, add the results, then take the square root. Example: a=6, b=8 → c = √(36+64) = √100 = 10.
Three positive whole numbers satisfying a²+b²=c². The most famous is (3,4,5). Any multiple is also a triple: (6,8,10), (9,12,15). Primitive triples have no common factor other than 1.
a = √(c²−b²). Subtract the square of the known leg from the square of the hypotenuse, then take the square root. The hypotenuse must always be larger than either leg.
Yes. The space diagonal of a box with dimensions a×b×c is d = √(a²+b²+c²). Apply the 2D theorem twice: first find the floor diagonal √(a²+b²), then use that as the base for the height.