Torus Area and Volume Calculator


Online Torus Area and Volume Calculator: Calculate the volume and area of a Torus based on its small radius and large radius. Enter two unknowns in the form and press the CALCULATE button.

Table of contents:

What is a Torus?

The torus is a cylinder curved on itself whose ends meet, thus forming a ring.

The characteristics of the Torus

The shape of the torus is determined by the two real parameters R (large radius) and r (small radius):

For R = 0, the corresponding torus is a ball; in this case, we also speak of a full torus.

If R < r, the situation results in a cross torus that looks like a pumpkin.

If R = r, the two poles merge and we speak of a null collared torus.

If R> r, we get the torus in its most accepted form, an open torus in the shape of a donut, as in the illustration above.

Calculate the area of the Torus

The area A of a torus of radius R generated by a disk of radius r is given by:

A = 4π2 . R . r

in which :

R: large radius

r: small radius

Calculate the volume of the Torus

The volume V of a torus of radius R generated by a disk of radius r is given by:

V = 2π2 . r2 . R

in which :

R: large radius

r: small radius