How to calculate the area of an annulus using outer diameter and thickness?

Annulus area = π/4 × [outer diameter² - (outer diameter - 2×thickness)²] = π × thickness × (outer diameter - thickness)

How to calculate the area of an annulus using inner diameter and thickness?

Annulus area = π/4 × [(inner diameter + 2×thickness)² - inner diameter²] = π × thickness × (inner diameter + thickness)

How to calculate the area of an annulus using outer and inner diameter?

Annulus area = π/4 × (outer diameter² - inner diameter²)

How to calculate the area of an annulus using pitch diameter and thickness?

Annulus area = π × pitch diameter × thickness

Annulus Area Calculation

Enter the required parameters to calculate the area of a hollow ring (annulus) instantly, with unit conversion.

Input

Outer diameter & Thickness

Inner diameter & Thickness

Outer diameter & Inner diameter

Pitch diameter & Thickness

Outside Diameter O.D.

Thickness t

Area

Annulus Area Formulas

Area = π/4 × [OD² - (OD - 2t)²] = π × t × (OD - t)
Area = π/4 × [(ID + 2t)² - ID²] = π × t × (ID + t)
Area = π/4 × (OD² - ID²)
Area = π × pitch diameter × thickness

FAQ

What is an annulus and what are its common applications?
An annulus is a ring-shaped area between two concentric circles. It's commonly used in engineering for calculating cross-sectional areas of pipes, tubes, washers, flanges, and hollow shafts. Applications include material quantity estimation, flow area calculations, and structural analysis.
When should I use pitch diameter instead of outer/inner dimensions?
Pitch diameter is the average of outer and inner diameters, useful when the centerline dimension is known or when dealing with threaded components, gears, or bearings. It simplifies calculations when thickness is uniform and the middle dimension is the design reference.
How do I measure thickness for hollow circular sections?
For pipes and tubes, thickness is the wall thickness measured radially. For machined parts, use calipers or micrometers. Remember that thickness relates to radius (t = (OD-ID)/2), not diameter. Always verify measurements are consistent between outer, inner, and thickness values.
What's the difference between using diameter vs radius in calculations?
This calculator uses diameter inputs for consistency with standard engineering drawings and specifications. Internally, it converts to radius for calculations. Using diameter is more practical as most engineering drawings specify diameters rather than radii.
How accurate are annulus area calculations for flow and stress analysis?
The calculations are mathematically precise and suitable for engineering applications. For fluid flow calculations, the area represents the flow cross-section. For stress analysis, it represents the material cross-section. Consider manufacturing tolerances in critical applications.
Can I use this calculator for non-circular hollow sections?
This calculator is specifically for circular annular areas. For rectangular hollow sections, elliptical shapes, or other non-circular geometries, different formulas are required. The circular annulus formula only applies to concentric circular boundaries.

Annulus Area Equations (LaTeX)

\[Torus\, area = {\pi \over 4} (OD^2 - ID^2)\]

\[Torus\, area = {\pi \over 4} [OD^2 - (OD - 2t)^2] = \pi t (OD - t)\]

\[Torus\, area = {\pi \over 4} [(ID + 2t)^2 - ID^2] = \pi t (ID + t)\]

\[Torus\, area = \pi t PD\]