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Torus radii from volume: Tube radius Calculator

Torus radii from volume: Calculate tube radius from Volume, Centre-circle radius. Check the formula, input units and worked result on this page.

Enter your values

cm³
Formula symbol: V. Required unit: cm³. Must be greater than zero.
cm
Formula symbol: R. Required unit: cm. Distance from the centre to the edge; half the diameter. Must be greater than zero.

Use a decimal point, without thousands separators.

Lengths use cm, areas cm² and volumes cm³ on one consistent scale. The positive real branch is selected; the supplied quantities must describe the stated shape.
Example result
Tube radius
2 cm

The initial result uses the example values. Enter your own values and calculate again.

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How it works

Use a ring torus with circular cross-section. Tube radius is smaller than centre-circle radius; spindle and horn tori are excluded. This form solves for tube radius; enter the known quantities in Volume, Centre-circle radius.

Inputs and units
Torus radii from volume: Tube radius Calculator · Inputs and units
InputExample valueWhat to enter
Volume394.7841760435743 cm³Formula symbol: V. Required unit: cm³. Must be greater than zero.
Centre-circle radius5 cmFormula symbol: R. Required unit: cm. Distance from the centre to the edge; half the diameter. Must be greater than zero.
r = √(V/(2π²R))

Worked example

Show example inputs and results

This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.

Volume
394.7841760435743 cm³
Centre-circle radius
5 cm

Complete example results

Tube radius
2 cm

Reading the result

The result solves for tube radius from the entered quantities. Check the result unit and the formula conditions before using it.

Questions and answers

Can I use the example values for my own calculation?

The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.

When can I use the tube radius result?

Lengths use cm, areas cm² and volumes cm³ on one consistent scale. The positive real branch is selected; the supplied quantities must describe the stated shape.

Why are some results rounded?

Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.

Are my inputs sent to a server?

The calculator processes inputs in your browser. Its code does not send your values to a server.

Method sources: pryor.mathcs.wilkes.edu

Methods & accuracy

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