Annulus Area Calculator
An annulus is the region between two concentric circles, creating a ring or donut shape. This calculator computes the area of an annulus from the outer radius (the distance from the center to the outer edge) and the inner radius (the distance from the center to the inner edge). The calculator also displays the width of the ring (the difference between the outer and inner radii) and the circumferences of both the outer and inner circles. The area formula is simply pi times the difference of the squared radii. Annulus calculations are commonly used in engineering, manufacturing, and architectural design for rings, pipes, and similar structures.
Annulus formulas
Area = pi * (R^2 - r^2)
Width = R - r
Outer circumference = 2 * pi * R
Inner circumference = 2 * pi * r
Example calculation
For an annulus with outer radius 10 and inner radius 6:
- Area = pi * (10^2 - 6^2) = pi * (100 - 36) = pi * 64 = 201.06 square units
- Width = 10 - 6 = 4 units
- Outer circumference = 2 * pi * 10 = 62.83 units
- Inner circumference = 2 * pi * 6 = 37.70 units
Annulus area calculator: frequently asked questions
What is an annulus?
An annulus is a ring-shaped geometric shape formed by two concentric circles (circles with the same center). It is the region between the outer circle and the inner circle. Common examples include the area of a pipe cross-section or a donut.
What is the formula for the area of an annulus?
The area of an annulus is the difference between the areas of the outer and inner circles: Area = pi * (R^2 - r^2), where R is the outer radius and r is the inner radius.
What is the width of an annulus?
The width (or thickness) of an annulus is the difference between the outer radius and the inner radius: Width = R - r. This represents the radial distance from the inner circle to the outer circle.
How do I find the circumferences of an annulus?
An annulus has two circumferences. The outer circumference is 2 * pi * R, and the inner circumference is 2 * pi * r, where R and r are the outer and inner radii respectively.
What are practical applications of annulus calculations?
Annulus calculations are used in engineering for pipe design, ring dimensions, circular cross-sections, and material calculations. They are also used in architecture and manufacturing where ring-shaped objects need to be precisely measured.
Official sources
- Wolfram MathWorld: Annulus.
- ISO 80000-2: Mathematical signs and symbols.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.