Pythagorean Theorem Calculator
Calculate right triangle hypotenuse (a² + b² = c²).
Quadratic Equation Solver (ax² + bx + c = 0)
About Pythagorean Theorem Calculator
The Pythagorean Theorem ($a^2 + b^2 = c^2$) & Right Triangle Solver computes unknown hypotenuse ($c = \sqrt{a^2 + b^2}$) or leg lengths ($a = \sqrt{c^2 - b^2}$), internal angles ($\alpha, \beta$), perimeter, area ($A = \frac{1}{2}ab$), and inradius with exact radical simplification.
How to Use Pythagorean Theorem Calculator
Step 1
Select what you want to solve for (Hypotenuse $c$ or Leg $a/b$).
Step 2
Enter the lengths of the two known sides.
Step 3
Review computed side length, exact radical form, angles, and area.
Step 4
Click "Copy Solution".
Practical Use Cases for Pythagorean Theorem Calculator
Carpentry, Construction & Squaring Corners (3-4-5 Rule)
Verify perfectly square 90-degree framing corners for building walls, decks, and foundations using Pythagorean triples.
Roof Rafter Length & Diagonal Screen Sizing Calculations
Calculate diagonal roof rafter lengths and TV monitor diagonal dimensions from horizontal width and vertical height.
Input & Output Examples
Solving for Hypotenuse with Legs 6 and 8
Leg a: `6`, Leg b: `8`
Hypotenuse (c): `10.0` | Perimeter: `24.0` | Area: `24.0` | Angles: `36.87°`, `53.13°`, `90.0°` | Pythagorean Triple: `Yes (3-4-5 family)`
Key Features & Performance
- ✓Solves for Hypotenuse ($c$) or either Leg ($a$ or $b$) with automated formula selection.
- ✓Exact Simplified Radicals: outputs exact forms (e.g. $c = 3\sqrt{5}$) alongside decimal values.
- ✓Computes: All 3 Sides, All 3 Angles, Area, Perimeter, Altitude to Hypotenuse, Inradius, Circumradius.
- ✓Pythagorean Triple Identifier (e.g. 3-4-5, 5-12-13, 8-15-17, 7-24-25).
- ✓100% Client-Side geometry engine.
- ✓1-Click Copy full triangle solution.
Key Terminology & Definitions
Pythagorean Theorem
A fundamental geometric principle stating that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides ($a^2 + b^2 = c^2$).
Pythagorean Triple
A set of three positive integers $(a, b, c)$ that perfectly satisfy the equation $a^2 + b^2 = c^2$ (e.g. 3, 4, 5).