📐 Pythagorean Theorem Calculator
a² + b² = c²Enter any two sides. The missing side, area, and perimeter update in real time. Change units anytime—values are converted automatically.
🅰️ Leg a
i
Leg adjacent to the right angle. Use a length unit below; the calculator converts internally.
Choose a length unit. Conversions use exact SI definitions (e.g., 1 in = 2.54 cm).
🅱️ Leg b
i
The other leg adjacent to the right angle. Any length unit works; we handle the math.
Pick your preferred length unit for b. You can mix units between a and b.
🧭 Hypotenuse c
i
The longest side of a right triangle, opposite the right angle. Enter to solve for a or b, or leave blank to compute from a and b.
Length unit for c. We’ll keep values consistent as you switch units.
🧮 Area
i
Area of a right triangle: (a × b) / 2. Units are squared (e.g., cm²).
Select an area unit. We convert from m² using exact factors (e.g., 1 ft² = 0.09290304 m²).
📏 Perimeter
i
Perimeter is the sum a + b + c. Same unit as lengths.
Choose a length unit for perimeter (e.g., meters, feet, miles).
🧩 Step-by-step derivation
Provide any two sides to see the algebra here.
📚 Quick Reference
🧠 Essentials
| Formula | Pythagorean a² + b² = c² |
|---|---|
| Hypotenuse | c = √(a² + b²) |
| Find a | a = √(c² − b²) |
| Find b | b = √(c² − a²) |
| Area | A = (a × b)/2 |
| Perimeter | P = a + b + c |
🔎 Sources
Units follow SI definitions (inch = 2.54 cm exactly, foot = 0.3048 m exactly, mile = 1609.344 m, etc.).