Ring torusVEXQOMIRA / GEOMETRY 24
Ring torus / Calculators
3D GEOMETRY / FREE CALCULATOR

Surface area and major radius

Your measurements

Use one common unit for every length. Selecting another unit relabels the numbers; it does not convert them. Angles are in degrees.

How to use this calculator

  1. Identify the measurements labelled Surface area S, Major radius R. Check whether the figure satisfies the assumptions described below.
  2. Enter positive measurements in a common unit. Use the degree symbol convention for angles. Ratios such as eccentricity have no unit.
  3. Select Calculate. Inspect the result labels: lengths, areas and volumes have different dimensions. Copy the output or print the page if you need a record.

The formula

r = S/(4π²R)

Surface area S = 473.741011252; Major radius R = 6

Worked example

For Surface area S = 473.741011252 cm², Major radius R = 6 cm, applying the displayed relationship gives major radius r ≈ 6 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.

Model and limitations

Its outer radius is R+r and its hole radius is R−r. Its volume is the tube’s circular area multiplied by the distance travelled by its centre. The analogous product of circumferences gives surface area.

Major radius is not outer radius. All tools reject R ≤ r so that the result remains a ring torus. Inputs are limited to 10⁹ for lengths, 10¹⁸ for areas and 10²⁷ for volumes. Extremely thin or nearly degenerate figures may lose numerical accuracy; avoid treating displayed rounding as a measurement tolerance.

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