1. What is Cap Radius of Spherical Cap?

The Cap Radius of a Spherical Cap is the radius of the base circle of a Spherical Cap. It represents the distance from the center of the base to its edge in a spherical segment.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_{Cap} \) — Cap Radius of Spherical Cap (m)
• \( h \) — Height of Spherical Cap (m)
• \( r_{Sphere} \) — Sphere Radius of Spherical Cap (m)

Explanation: This formula calculates the radius of the circular base of a spherical cap given the height of the cap and the radius of the sphere from which it's cut.

3. Importance of Cap Radius Calculation

Details: Calculating the cap radius is essential in geometry, architecture, and engineering for determining the dimensions of spherical segments and designing curved surfaces.

4. Using the Calculator

Tips: Enter the height of the spherical cap and the sphere radius in meters. Both values must be positive, and the height cannot exceed twice the sphere radius.

5. Frequently Asked Questions (FAQ)

Q1: What is a spherical cap?
A: A spherical cap is a portion of a sphere cut off by a plane. It consists of a circular base and a curved surface.

Q2: What are the limitations of this formula?
A: The formula assumes a perfect sphere and requires that the height does not exceed the sphere's diameter (2 × sphere radius).

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurements to meters first or adjust the result accordingly.

Q4: What if the height equals the sphere diameter?
A: When height equals 2 × sphere radius, the cap becomes a hemisphere, and the cap radius equals the sphere radius.

Q5: How is this calculation used in real-world applications?
A: This calculation is used in architecture (domes), engineering (tank design), and physics (lens calculations) where spherical segments are involved.