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Torus measures from surface: Volume Calculator

Torus measures from surface: Calculate volume from Surface area, Tube radius. Check the formula, input units and worked result on this page.

Enter your values

cm²
Formula symbol: S. Required unit: cm². 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
Volume
394.78417604 cm³

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

Edit inputs

How it works

Area covers the entire closed curved surface. The centre circle is traced by the centre of the tube cross-section during rotation. This form solves for volume; enter the known quantities in Surface area, Tube radius.

Inputs and units
Torus measures from surface: Volume Calculator · Inputs and units
InputExample valueWhat to enter
Surface area394.7841760435743 cm²Formula symbol: S. Required unit: cm². Must be greater than zero.
Tube radius2 cmFormula symbol: r. Required unit: cm. Distance from the centre to the edge; half the diameter. Must be greater than zero.
V = Sr/2

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.

Surface area
394.7841760435743 cm²
Tube radius
2 cm

Complete example results

Volume
394.78417604 cm³

Reading the result

The result solves for volume 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 volume 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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