Insphere Radius of Octahedron given Total Surface Area Calculator

Calculate Insphere Radius



Formula

The formula to calculate the Insphere Radius of an Octahedron given its total surface area is:

\[ \text{Insphere Radius} = \sqrt{\frac{\text{Total Surface Area}}{2\sqrt{3}}} \div \sqrt{6} \]

Definition

The Insphere Radius of an Octahedron is the radius of the sphere that is contained by the octahedron in such a way that all the faces are just touching the sphere. The Total Surface Area of an Octahedron is the total quantity of plane enclosed by the entire surface of the octahedron.

Example Calculation

Let's assume the following value:

Using the formula:

\[ \text{Insphere Radius} = \sqrt{\frac{350}{2\sqrt{3}}} \div \sqrt{6} \approx 4.1036 \, \text{meters} \]

The Insphere Radius is approximately 4.1036 meters.

Conversion Chart

Total Surface Area (square meters) Insphere Radius (meters)
340 4.044534290501121
345 4.074164974470443
350 4.103581710087432
355 4.132789065936760
360 4.161791450287818