Pythagorean Theorem Calculator
Calculate the hypotenuse or missing leg of any right triangle using the fundamental formula a² + b² = c².
c (hypotenuse)
5
Area = 6 | Perimeter = 12
How to Use the Pythagorean Theorem Calculator
- Select what you want to solve for: Hypotenuse (c), Leg a, or Leg b.
- Enter the lengths of the two known triangle sides.
- The calculator computes the missing side length, triangle area, and perimeter.
Formulas & Principles
Hypotenuse: c = √(a² + b²)
Leg a: a = √(c² - b²)
Leg b: b = √(c² - a²)
Area: A = 0.5 × a × b | Perimeter: P = a + b + c
Frequently Asked Questions
What is the Pythagorean Theorem formula?
In any right triangle with legs a and b and hypotenuse c: a² + b² = c². Therefore, c = √(a² + b²).
Can the Pythagorean Theorem be used for non-right triangles?
No, the theorem only applies to right triangles (90-degree angle). For non-right triangles, use the Law of Cosines (c² = a² + b² - 2ab cos(C)).
What are common Pythagorean triples?
Common integer triples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).
Why this calculator matters
This calculator helps solve mathematical problems faster and with fewer manual arithmetic mistakes. It is useful for studying, research verification, technical engineering checks, and everyday problem-solving.
When to use it
Use it when you need a fast answer, a cross-check for manual calculations, or a clear step-by-step verification of your result.
Quick tips
Double-check your inputs, keep units consistent across all fields, and verify boundary conditions.
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