1. What is the Width of Octagon given Circumradius Formula?

The formula calculates the width of a regular octagon when its circumradius is known. The circumradius is the radius of the circle that passes through all vertices of the octagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
• \( Circumradius \) — Radius of the circumscribed circle (m)

Explanation: The formula derives from the geometric properties of a regular octagon and trigonometric relationships between its sides and circumradius.

3. Importance of Octagon Width Calculation

Details: Calculating the width of an octagon is essential in architecture, engineering, and design applications where regular octagonal shapes are used, such as in building design, mechanical parts, and decorative elements.

4. Using the Calculator

Tips: Enter the circumradius of the octagon in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular octagon?
A: A regular octagon is an eight-sided polygon where all sides are equal in length and all angles are equal in measure.

Q2: How is circumradius different from inradius?
A: Circumradius is the radius of the circle that passes through all vertices, while inradius is the radius of the circle inscribed within the octagon that touches all sides.

Q3: Can this formula be used for irregular octagons?
A: No, this formula applies only to regular octagons where all sides and angles are equal.

Q4: What are practical applications of octagon width calculation?
A: Applications include architectural design (octagonal buildings, rooms), mechanical engineering (octagonal bolts, nuts), and urban planning (octagonal traffic signs, plazas).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular octagons, though practical measurements may have slight variations due to manufacturing tolerances.