Spherical Radius of Spherical Sector Calculator

Formula Used:

\[ \text{Spherical Radius of Spherical Sector} = \frac{1}{2} \times \left( \frac{\text{Spherical Cap Radius of Spherical Sector}^2}{\text{Spherical Cap Height of Spherical Sector}} + \text{Spherical Cap Height of Spherical Sector} \right) \]

Spherical Radius of Spherical Sector:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Spherical Radius of Spherical Sector?

The Spherical Radius of Spherical Sector is the distance from the center to any point on the surface of the sphere from which the Spherical Sector is cut. It represents the radius of the original sphere before the sector was extracted.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Sphere} = \frac{1}{2} \times \left( \frac{r_{Cap}^2}{h_{Cap}} + h_{Cap} \right) \]

Where:

\( r_{Sphere} \) — Spherical Radius of Spherical Sector (m)
\( r_{Cap} \) — Spherical Cap Radius of Spherical Sector (m)
\( h_{Cap} \) — Spherical Cap Height of Spherical Sector (m)

Explanation: This formula calculates the radius of the original sphere based on the cap dimensions of the spherical sector.

3. Importance of Spherical Radius Calculation

Details: Calculating the spherical radius is essential for determining the complete geometry of spherical sectors, which is crucial in various engineering, architectural, and mathematical applications involving spherical shapes.

4. Using the Calculator

Tips: Enter the spherical cap radius and spherical cap height in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between spherical radius and cap dimensions?
A: The spherical radius can be derived from the cap radius and cap height using the geometric relationship between these parameters in a sphere.

Q2: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can use any consistent unit system as long as both inputs use the same units.

Q3: What are typical applications of spherical sector calculations?
A: Spherical sectors are used in architecture, tank design, astronomy, and various engineering applications involving spherical geometries.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of spheres, provided accurate input values are given.

Q5: What if I have the total sphere radius but need cap dimensions?
A: The formula can be rearranged to solve for cap radius or cap height if the spherical radius and one other dimension are known.