Endpoints of a Diameter of a Circle Calculator

Endpoints Calculation:

\[ \text{Endpoint}_1 = (x_c - \frac{d}{2}\cosθ, y_c - \frac{d}{2}\sinθ) \] \[ \text{Endpoint}_2 = (x_c + \frac{d}{2}\cosθ, y_c + \frac{d}{2}\sinθ) \]

Endpoint 1:

Endpoint 2:

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1. What is the Endpoints of a Diameter Calculator?

This calculator determines the coordinates of both endpoints of a diameter when given the circle's center, diameter length, and angle of orientation. It's useful in geometry, engineering, and computer graphics applications.

2. How Does the Calculator Work?

The calculator uses these formulas:

\[ \text{Endpoint}_1 = (x_c - \frac{d}{2}\cosθ, y_c - \frac{d}{2}\sinθ) \] \[ \text{Endpoint}_2 = (x_c + \frac{d}{2}\cosθ, y_c + \frac{d}{2}\sinθ) \]

Where:

\( (x_c, y_c) \) — Center coordinates
\( d \) — Diameter length
\( θ \) — Angle of diameter orientation (degrees)

Explanation: The endpoints are calculated by moving half the diameter length in opposite directions from the center along the specified angle.

3. Importance of Diameter Endpoints

Details: Knowing diameter endpoints is essential for circle-related constructions, collision detection in games, CAD designs, and various geometric calculations.

4. Using the Calculator

Tips: Enter center coordinates, positive diameter length, and angle (0° = horizontal right, 90° = vertical up). The calculator handles all angle values (including negative and >360°).

5. Frequently Asked Questions (FAQ)

Q1: What if I only know the radius?
A: Simply multiply your radius by 2 to get the diameter before using the calculator.

Q2: How does angle affect the result?
A: The angle determines the orientation of the diameter line. 0° gives horizontal endpoints, 90° gives vertical.

Q3: Can I use negative coordinates?
A: Yes, the calculator works with all real numbers for coordinates.

Q4: What units should I use?
A: Use consistent units for all measurements (pixels, meters, inches, etc.).

Q5: How precise are the results?
A: Results are calculated with double precision and displayed with 2 decimal places.