Annulus Area Calculation

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Outer diameter
Thickness Inner diameter
Thickness Outer diameter
Inner diameter Medium diameter
Thickness

Outside Diameter O.D.

Thickness t

Area

Use outer diameter and thickness to calculate the ring area

\[Torus\, area \\[12pt] = Large\, circle\, area - Small\, circle\, area \\[12pt] = {Pi \over 4} \, (Outer\, diameter^2 - Inner\, diameter^2) \\[12pt] = {Pi \over 4} \, [Outer\, diameter^2 - (Outer\, diameter - 2 \cdot thickness)^2] \\[12pt] = pi \, (outer\, diameter \cdot thickness - thickness^2) \\[12pt] = \pi \, t \, (OD - t) \]

Use inner diameter and thickness to calculate the ring area

\[Torus\, area \\[12pt] = Large\, circle\, area - Small\, circle\, area \\[12pt] = {Pi \over 4} \, (Outer\, diameter^2 - Inner\, diameter^2) \\[12pt] = {Pi \over 4} \, [(Inner\, diameter + 2 \cdot thickness)^2 - Inner\, diameter^2] \\[12pt] = pi \, (inner\, diameter \cdot thickness + thickness^2) \\[12pt] = \pi \, t \, (ID + t) \]

Use outer diameter and inner diameter to calculate the ring area

\[Torus\, area \\[12pt] = Large\, circle\, area - Small\, circle\, area \\[12pt] = {Pi \over 4} \, (Outer\, diameter^2 - Inner\, diameter^2) \\[12pt] = {\pi \over 4} \, (OD^2 - ID^2) \]

Use median diameter and thickness to calculate the ring area

\[Torus\, area \\[12pt] = Large\, circle\, area - Small\, circle\, area \\[12pt] = {Pi \over 4} (outer\, diameter^2 - inner\, diameter^2) \\[12pt] = {pi \over 4} [(pitch\, diameter + thickness)^2 - (pitch\, diameter - thickness)^2] \\[12pt] = pi \cdot pitch\, diameter \cdot thickness \\[12pt] = \pi t \, PD \]