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Insphere Radius of Tetrahedron given Face Area Calculator

Formula

The formula to calculate the Insphere Radius of a Tetrahedron given its face area is:

$\text{Insphere Radius} = \frac{\sqrt{\left(\frac{4 \cdot \text{Face Area}}{\sqrt{3}}\right)}}{2 \cdot \sqrt{6}}$

Definition

The Insphere Radius of a Tetrahedron is the radius of the sphere that is contained by the tetrahedron in such a way that all the faces just touch the sphere. The face area of a tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the tetrahedron.

Example Calculation

Let's assume the following value:

Face Area = 45 square meters

Using the formula:

$\text{Insphere Radius} = \frac{\sqrt{\left(\frac{4 \cdot 45}{\sqrt{3}}\right)}}{2 \cdot \sqrt{6}} \approx 2.0809 \, \text{meters}$

The Insphere Radius is approximately 2.0809 meters.

Conversion Chart

Face Area (square meters)	Insphere Radius (meters)
40	1.961887304255141
42	2.010336261506363
44	2.057644763815479
46	2.103889746110079
48	2.149139863647084
50	2.193456688254154