Circumradius of Rectangle given Area and Acute Angle between Diagonals Calculator

Circumradius of Rectangle Formula:

\[ r_c = \frac{1}{2} \times \frac{\sqrt{A \times \cot(\frac{\angle_{d(acute)}}{2})}}{\cos(\frac{\angle_{d(acute)}}{2})} \]

Circumradius of Rectangle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Circumradius of Rectangle?

The circumradius of a rectangle is the radius of the circle that passes through all four vertices of the rectangle. For any rectangle, the circumradius is equal to half the length of the diagonal.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{1}{2} \times \frac{\sqrt{A \times \cot(\frac{\angle_{d(acute)}}{2})}}{\cos(\frac{\angle_{d(acute)}}{2})} \]

Where:

\( r_c \) — Circumradius of Rectangle (m)
\( A \) — Area of Rectangle (m²)
\( \angle_{d(acute)} \) — Acute Angle between Diagonals of Rectangle (degrees)
\( \cot \) — Cotangent trigonometric function
\( \cos \) — Cosine trigonometric function

Explanation: The formula calculates the circumradius based on the area of the rectangle and the acute angle between its diagonals using trigonometric relationships.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry problems, architectural design, and engineering applications where circular patterns or circumscribed circles around rectangular shapes are involved.

4. Using the Calculator

Tips: Enter the area of the rectangle in square meters and the acute angle between diagonals in degrees (must be between 0 and 90 degrees). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between circumradius and diagonal?
A: The circumradius of a rectangle is exactly half the length of its diagonal.

Q2: Can a rectangle always be circumscribed by a circle?
A: Yes, all rectangles can be circumscribed by a circle, and the center of this circle is the intersection point of the diagonals.

Q3: What is the range of acute angles between diagonals?
A: The acute angle between diagonals of a rectangle ranges from 0° to 90°, with 90° occurring only in a square.

Q4: How does the circumradius change with different angles?
A: For a fixed area, the circumradius increases as the acute angle between diagonals decreases from 90° toward 0°.

Q5: What are practical applications of this calculation?
A: This calculation is used in various fields including architecture, mechanical engineering, computer graphics, and geometric design problems.