1. What is Inradius of Hexadecagon?

The inradius of a hexadecagon (16-sided polygon) is the radius of the circle that fits perfectly inside the hexadecagon, touching all its sides. It represents the distance from the center to any side of the polygon.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

This formula establishes the precise mathematical relationship between the circumradius (radius of the circumscribed circle) and the inradius of a regular hexadecagon.

3. Formula Explanation

The formula incorporates:

• Square root functions to handle geometric relationships
• Nested radical expressions specific to 16-sided polygons
• Precise mathematical constants derived from polygon geometry
• The relationship between circumradius and inradius for regular polygons

4. Using the Calculator

Instructions: Enter the circumradius value in meters. The circumradius must be a positive number greater than zero. Click "Calculate" to get the corresponding inradius value.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between inradius and circumradius?
A: Inradius is the radius of the inscribed circle (touching all sides), while circumradius is the radius of the circumscribed circle (passing through all vertices).

Q2: Does this formula work for irregular hexadecagons?
A: No, this formula is specifically for regular hexadecagons where all sides and angles are equal.

Q3: What are typical values for hexadecagon dimensions?
A: For a regular hexadecagon, the inradius is always smaller than the circumradius, typically about 0.98 times the circumradius.

Q4: Can this calculator handle very large values?
A: Yes, the calculator can process any positive numerical value within computational limits.

Q5: What practical applications does this calculation have?
A: This calculation is useful in geometry, architecture, engineering design, and any field dealing with regular polygonal shapes.