Enter outer and inner radii to calculate the geometry of an annulus.
Keep linear inputs in a consistent unit, verify that side lengths or coordinate points can form the stated shape, and treat sketches as explanatory unless explicitly marked to scale. Coordinate formulas can become unstable for nearly degenerate shapes, so invalid or nearly collinear inputs are rejected rather than silently returning misleading values.
An annulus requires an outer radius greater than or equal to the inner radius. Swapping them can produce a negative intermediate difference even though the intended geometry is obvious. Label the measurements before entering them and keep units consistent across both radii.
Ring area estimates surface coverage, while outer and inner circumferences describe boundary lengths. Paint, sheet material, edging, seals, and machining allowances may depend on different quantities. Choose the output that matches the physical job instead of using one geometric number for every estimate.
Many real objects are measured across the full circle. If the source gives diameters, divide by two before using radius fields. Mixing one diameter with one radius can create a plausible-looking but incorrect result. Keep the original measurements in notes when the calculation must be checked later.
The formula assumes perfect concentric circles. Real washers, gaskets, pipes, and machined rings can have tolerance, eccentricity, bevels, and surface loss. Use the calculator for nominal geometry, then apply the material or manufacturing tolerance required by the actual specification.
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