Inner Radius of Circular Ring given Outer Radius and Perimeter Calculator

Formula Used:

\[ r_{Inner} = \frac{P}{2\pi} - r_{Outer} \]

Inner Radius of Circular Ring (r_Inner):

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1. What is the Inner Radius of Circular Ring?

The Inner Radius of Circular Ring is the radius of its cavity and the smaller radius among two concentric circles that form the ring's boundary.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Inner} = \frac{P}{2\pi} - r_{Outer} \]

Where:

\( r_{Inner} \) — Inner Radius of Circular Ring (m)
\( P \) — Perimeter of Circular Ring (m)
\( r_{Outer} \) — Outer Radius of Circular Ring (m)
\( \pi \) — Archimedes' constant (≈ 3.14159)

Explanation: This formula calculates the inner radius of a circular ring by subtracting the outer radius from the radius calculated from the perimeter using the circumference formula.

3. Importance of Inner Radius Calculation

Details: Calculating the inner radius is important in engineering, architecture, and manufacturing for designing rings, washers, pipes, and other circular components with specific dimensions and clearances.

4. Using the Calculator

Tips: Enter the perimeter in meters and the outer radius in meters. Both values must be positive numbers. The calculator will compute the inner radius based on the provided inputs.

5. Frequently Asked Questions (FAQ)

Q1: What is a circular ring?
A: A circular ring is the region between two concentric circles, forming a ring-shaped object with inner and outer boundaries.

Q2: Can this formula be used for elliptical rings?
A: No, this formula is specifically for circular rings. Elliptical rings require different calculations based on ellipse geometry.

Q3: What if the calculated inner radius is negative?
A: A negative inner radius indicates invalid input values where the outer radius is larger than the radius calculated from the perimeter, which is not physically possible for a circular ring.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect circular rings. The accuracy depends on the precision of the input values.

Q5: Can this be used for three-dimensional rings?
A: This formula is for two-dimensional circular rings. For three-dimensional toroidal shapes, different formulas involving cross-sectional radii are required.