Torus Surface Area Calculator

Calculate the surface area of a torus by entering the major radius (R) and minor radius (r). A torus is a doughnut-shaped object.

🍩 Torus Surface Area

Metric (cm, m) Imperial (in, ft)

Major Radius (R) (cm) Distance from center of torus to center of tube

Minor Radius (r) (cm) Radius of the tube cross-section

Show calculation steps Show π in results Show volume calculation

Formula

Surface Area: SA = 4π²Rr

Where R is the major radius and r is the minor radius

Torus Surface Area Formulas

Surface Area

SA = 4π²Rr

Complete surface area of the torus

Volume

V = 2π²Rr²

Volume enclosed by the torus

Major Circumference

C_major = 2πR

Circumference of the major circle

Minor Circumference

C_minor = 2πr

Circumference of the tube cross-section

Torus Surface Area Examples

Example 1: Small Torus

Given: Major radius R = 5 cm, Minor radius r = 2 cm

Formula: SA = 4π²Rr

Solution: SA = 4π² × 5 × 2 = 40π² ≈ 394.78 cm²

Example 2: Medium Torus

Given: Major radius R = 8 cm, Minor radius r = 3 cm

Formula: SA = 4π²Rr

Solution: SA = 4π² × 8 × 3 = 96π² ≈ 947.48 cm²

Example 3: Large Torus

Given: Major radius R = 12 cm, Minor radius r = 4 cm

Formula: SA = 4π²Rr

Solution: SA = 4π² × 12 × 4 = 192π² ≈ 1894.95 cm²

Torus Surface Area FAQ

What is a torus?

A torus is a 3D shape that looks like a doughnut or inner tube. It's formed by rotating a circle around an axis that doesn't intersect the circle.

What are major and minor radii?

The major radius (R) is the distance from the center of the torus to the center of the tube. The minor radius (r) is the radius of the tube's circular cross-section.

How do you calculate torus surface area?

Use the formula SA = 4π²Rr, where R is the major radius and r is the minor radius. This accounts for the entire curved surface.

Why does the formula contain π²?

The torus involves two circular dimensions: the major circle (contributing π) and the minor circle (contributing another π), resulting in π² in the formula.