Torus Surface Area Calculator

Inner Radius (a):

Outer Radius (b):

Tube Radius (r, cm): Tube Radius (r, m): Tube Radius (r, in): Tube Radius (r, ft):

Revolution Radius (R, cm): Revolution Radius (R, m): Revolution Radius (R, in): Revolution Radius (R, ft):

Surface Area (cm²): Surface Area (m²): Surface Area (mm²): Surface Area (in²): Surface Area (ft²):

1. What is a Torus Surface Area Calculator?

Definition: This calculator computes the surface area of a torus (ring or horn type) using the inner radius (a) and outer radius (b), calculating the cross-section radius (r) and revolution radius (R).

Purpose: Useful for geometry, engineering, and design applications involving toroidal shapes like doughnuts, tires, and tubes.

2. How Does the Calculator Work?

Formulas:

Cross-Section Radius: \( r = \frac{b - a}{2} \)
Revolution Radius: \( R = \frac{a + b}{2} \)
Surface Area: \( A = \pi^2 \times (b - a) \times (b + a) \)

Explanation: Inputs are converted to meters, and r, R, a, b, and the surface area are calculated and converted to cm, m, in, ft, cm², m², mm², in², and ft².

3. Importance of Torus Surface Area Calculation

Details: Essential for determining material requirements, structural analysis, and surface coating for toroidal objects.

4. Using the Calculator

Tips: Enter inner radius (a) and outer radius (b) in units (mm, cm, m, in, ft; a ≥ 0, b ≥ a). Results include r, R, a, b in cm, m, in, ft, and surface area in multiple units. Only ring or horn type tori are supported (R ≥ r).