Circumradius of Nonagon given Inradius Calculator

Circumradius of Nonagon Formula:

\[ r_c = \frac{2 \times r_i \times \tan(\pi/9)}{2 \times \sin(\pi/9)} \]

Circumradius of Nonagon (r_c):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Circumradius of Nonagon?

The Circumradius of a Nonagon is the radius of a circumcircle that touches each of the vertices of the Nonagon. It is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{2 \times r_i \times \tan(\pi/9)}{2 \times \sin(\pi/9)} \]

Where:

\( r_c \) — Circumradius of Nonagon (m)
\( r_i \) — Inradius of Nonagon (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \tan \) — Tangent trigonometric function
\( \sin \) — Sine trigonometric function

Explanation: This formula calculates the circumradius of a regular nonagon based on its inradius, using trigonometric relationships specific to the 9-sided polygon.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry, architecture, and engineering for designing and analyzing nonagonal structures, patterns, and components.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between circumradius and inradius?
A: In a regular nonagon, the circumradius is always larger than the inradius, and their ratio is constant for all regular nonagons.

Q2: Can this formula be used for irregular nonagons?
A: No, this formula applies only to regular nonagons where all sides and angles are equal.

Q3: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, and geometric pattern creation involving nonagonal shapes.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for regular nonagons, with accuracy limited only by the precision of the input value and computational floating-point arithmetic.

Q5: What units should be used for the input?
A: The calculator uses meters as the default unit, but any consistent unit of length can be used as long as the input and output use the same unit.