Tetrahedron Volume Calculator

Height

Height (cm): Height (in): Height (ft): Height (m):

Volume

Volume (cm³): Volume (in³): Volume (ft³): Volume (m³): Volume (L):

Surface Area

Surface Area (cm²): Surface Area (in²): Surface Area (ft²): Surface Area (m²):

Surface Area to Volume Ratio

Surface Area to Volume Ratio (cm⁻¹): Surface Area to Volume Ratio (in⁻¹): Surface Area to Volume Ratio (m⁻¹):

Sphere Radii

Insphere Radius (cm): Insphere Radius (in): Insphere Radius (ft): Insphere Radius (m): Midsphere Radius (cm): Midsphere Radius (in): Midsphere Radius (ft): Midsphere Radius (m): Circumsphere Radius (cm): Circumsphere Radius (in): Circumsphere Radius (ft): Circumsphere Radius (m):

1. What is a Tetrahedron Volume Calculator?

Definition: This calculator computes the volume, surface area, height, surface area to volume ratio, and the radii of insphere, midsphere, and circumsphere of a tetrahedron based on its edge length \( L \).

Purpose: Useful in geometry, engineering, and chemistry for analyzing tetrahedral shapes and their properties.

2. How Does the Calculator Work?

The calculations are based on the following formulas:

\[ H = \frac{\sqrt{6}}{3} L \] \[ V = \frac{L^3}{6 \sqrt{2}} \] \[ A = \sqrt{3} L^2 \] \[ \text{SVR} = \frac{A}{V} \] \[ r_i = \frac{L}{\sqrt{24}} \] \[ r_k = \frac{L}{\sqrt{8}} \] \[ r_u = \frac{L \sqrt{6}}{4} \]

Unit Conversions:

Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48) to cm
Length: cm (direct), in (×0.393701), ft (×0.0328084), m (×0.01)
Area: cm² (direct), in² (×0.155), ft² (×0.00107639), m² (×0.0001)
Volume: cm³ (direct), in³ (×0.0610237), ft³ (×0.0000353147), m³ (×0.000001), L (×0.001)
SVR: cm⁻¹ (direct), in⁻¹ (×0.393701), ft⁻¹ (×0.0328084), m⁻¹ (×0.01)

Explanation: The edge length is converted to cm, properties are calculated, and then converted to other units.

3. Importance of Tetrahedron Calculations

Details: Tetrahedrons are used in simulations, molecular modeling, and even historical board games. Accurate calculations help in understanding spatial properties and optimizing designs.

4. Using the Calculator

Tips: Enter the edge length \( L \) in mm, cm, m, in, or ft (must be >0). Results show the height, volume, surface area, surface area to volume ratio, and sphere radii in multiple units.

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