Diameter of Circumcircle of Rectangle given Area and Angle between Diagonal and Breadth Calculator

Formula Used:

\[ D_c = \frac{\sqrt{A \cdot \cot\left(\frac{\pi}{2} - \angle_{db}\right)}}{\cos\left(\frac{\pi}{2} - \angle_{db}\right)} \]

Diameter of Circumcircle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Diameter of Circumcircle of Rectangle?

The diameter of the circumcircle of a rectangle is the diameter of the circle that passes through all four vertices of the rectangle. This circle is also known as the circumscribed circle of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D_c = \frac{\sqrt{A \cdot \cot\left(\frac{\pi}{2} - \angle_{db}\right)}}{\cos\left(\frac{\pi}{2} - \angle_{db}\right)} \]

Where:

\( D_c \) — Diameter of circumcircle (m)
\( A \) — Area of rectangle (m²)
\( \angle_{db} \) — Angle between diagonal and breadth (degrees)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula calculates the diameter of the circle that circumscribes a rectangle based on its area and the angle between its diagonal and breadth.

3. Importance of Circumcircle Diameter Calculation

Details: Calculating the circumcircle diameter is important in geometry, engineering design, and various applications where circular boundaries containing rectangular objects need to be determined.

4. Using the Calculator

Tips: Enter the area of the rectangle in square meters and the angle between the diagonal and breadth in degrees. The angle must be between 0 and 90 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between rectangle dimensions and circumcircle?
A: The diameter of the circumcircle equals the length of the diagonal of the rectangle.

Q2: Can this formula be used for squares?
A: Yes, for squares the angle between diagonal and breadth is 45 degrees, and the formula simplifies accordingly.

Q3: What are the units for the inputs and outputs?
A: Area should be in square meters, angle in degrees, and the result will be in meters.

Q4: Why use trigonometric functions in this calculation?
A: Trigonometric functions help relate the geometric properties of the rectangle (area and angle) to the diameter of its circumcircle.

Q5: Are there alternative methods to calculate circumcircle diameter?
A: Yes, if you know the length and width of the rectangle, you can calculate the diagonal directly using the Pythagorean theorem.