Torus Calculator

Calculate the surface area and volume of a torus (donut shape).

Torus Dimensions

Major Radius (R)

Minor Radius (r)

R is the distance from the center of the ring to the center of the tube. r is the thickness (radius) of the tube.

Output Parameters

1776.53u³

Volume

Calculated based on its dual-radius geometry.

Surface Area1184.35u²

Ring Circumference62.83

Ring Torus

What is a Torus?

A torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. In simpler terms, it's the shape of a donut or an inner tube. It is defined by two radii: the major radius (R), which is the distance from the center of the tube to the center of the torus, and the minor radius (r), which is the radius of the tube itself.

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Pro Tips

The major radius (R) must always be greater than or equal to the minor radius (r) for a standard ring torus.
If R = r, you get a 'horn torus' with no hole in the middle.
If R < r, you get a 'spindle torus'.

Fun Facts

"In topology, a torus is a surface of genus 1, meaning it has one 'hole'."
"The magnetic field in a tokamak (a nuclear fusion device) is shaped like a torus."
"The game 'Pac-Man' takes place on a flat torus, as moving off one side brings you scale to the other."

Formula: Volume = 2π²Rr² | Surface Area = 4π²Rr

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