Torus volume and surface area calculator
A torus is a ring shape like an inner tube or a doughnut. Enter the distance from the center to the middle of the tube and the tube radius.
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How to use it
- Enter major radius (center to tube center), tube radius and length unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Volume = 2π²Rr², surface area = 4π²Rr, where R is the major radius and r the tube radius.
Example
Inputs: Major radius (center to tube center) = 5, Tube radius = 2, Length unit = Centimeter (cm). Result: Volume: 394.7842 cm³; Surface area: 394.7842 cm²; Outer diameter: 14 cm.
Limits and caveats
- Covers ring tori with a circular cross section whose tube does not self-intersect (r not above R).
- Results are in the cube or square of the unit you chose, so enter every dimension in that same unit.
Questions about this tool
What is the major radius?
It is the distance from the ring center to the middle of the tube. From the outer and inner diameters it is a quarter of their sum.
How do I get the tube radius from the diameters?
Tube radius = (outer diameter − inner diameter) / 4.
Why does π² appear?
The volume is the tube cross section πr² times the length of the circle it sweeps, 2πR.