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Circumradius of Octagon Formula:
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The circumradius of a regular octagon is the radius of the circumscribed circle that passes through all eight vertices of the octagon. It represents the distance from the center of the octagon to any of its vertices.
The calculator uses the circumradius formula:
Where:
Explanation: The formula calculates the circumradius based on the perimeter of a regular octagon, using the mathematical constant relationship specific to octagonal geometry.
Details: Calculating the circumradius is essential in geometry, architecture, and engineering for designing octagonal structures, determining spatial relationships, and solving geometric problems involving regular octagons.
Tips: Enter the perimeter of the octagon in meters. The value must be a positive number greater than zero. The calculator will compute the circumradius based on the standard geometric formula.
Q1: What is a regular octagon?
A: A regular octagon is an eight-sided polygon where all sides are equal in length and all interior angles are equal (135 degrees each).
Q2: How is circumradius different from inradius?
A: Circumradius is the radius of the circumscribed circle passing through all vertices, while inradius is the radius of the inscribed circle tangent to all sides.
Q3: Can this calculator be used for irregular octagons?
A: No, this calculator is specifically designed for regular octagons where all sides and angles are equal.
Q4: What are practical applications of octagon circumradius calculation?
A: This calculation is used in architectural design, mechanical engineering, tile patterns, and various construction projects involving octagonal shapes.
Q5: How accurate is the calculated result?
A: The result is mathematically precise based on the input perimeter value, with rounding to six decimal places for practical use.