Pythagorean Theorem Calculator
Find any side of a right triangle. Enter two sides to solve for the third.
a² + b² = c² where c is the hypotenuse (longest side). To find c: c = √(a² + b²). To find a: a = √(c² − b²). The famous 3-4-5 triple: 3² + 4² = 9 + 16 = 25 = 5².
Find hypotenuse c — a² + b² = c²
Common Pythagorean Triples
Historical Context by Country
| Culture / Country | Discovery / Usage | Approximate date |
|---|---|---|
| 🇮🇶 Babylon (Iraq) | Plimpton 322 tablet lists Pythagorean triples | ~1800 BCE |
| 🇮🇳 India | Baudhayana Sulba Sutras describe the theorem | ~800 BCE |
| 🇨🇳 China | Zhoubi Suanjing (周髀算經) contains the theorem | ~1000 BCE |
| 🇬🇷 Greece | Pythagorean proof and name attribution to Pythagoras | ~570–495 BCE |
| 🌍 Universal | Now taught in every country worldwide | Present day |
Frequently Asked Questions
What is the Pythagorean theorem?
In any right triangle: a² + b² = c², where c is the hypotenuse (the side opposite the right angle). It works for any consistent unit — mm, cm, m, ft, in.
What are the most common Pythagorean triples?
(3,4,5), (5,12,13), (8,15,17), (7,24,25), (20,21,29). Any multiple works: (6,8,10), (9,12,15). These are used in construction to verify right angles.
Is the Pythagorean theorem taught under different names?
Yes! In China: 勾股定理 (Gou-Gu theorem). In Germany: Satz des Pythagoras. In France: Théorème de Pythagore. In Japan: ピタゴラスの定理. The same theorem, many names.
How is it used in construction?
The '3-4-5 rule' is used worldwide to check right angles on construction sites. Mark 3 units on one wall, 4 units on the adjacent wall — if the diagonal is exactly 5 units, the angle is 90°.