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Quickly calculate the area of an annulus by entering the inner and outer radii. Ideal for math education and engineering drafting.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
An annulus is the flat ring-shaped region between circles that share a center. Enter outer radius R and inner radius r; the calculator subtracts the inner disk area from the outer disk area.
For example, outer radius 10 and inner radius 5 give 75π, or about 235.6194 square units. The result uses the squared input length unit: inches produce square inches, centimeters square centimeters. Use the same unit for both radii.
Ring is a familiar everyday name; annulus is the mathematical term. Some calculus problems call the same shape a washer. The geometry remains the region between the two circular boundaries.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Enter distance from the shared center to the outside edge as outer radius, then distance to the inner boundary as inner radius. Do not enter a diameter.
Use one length unit for both values. The calculator does not convert units or attach a written unit to the numerical answer.
The result updates from the two radii and displays four decimal places. As a hand check, calculate πR² and πr², then subtract.
With R=10 and r=5, the outer disk is about 314.1593, inner disk 78.5398, and ring area 235.6194 square units.
Use cases
See how the tool fits into real work and everyday tasks.
Calculate a shaded region between circles and explain the subtraction method.
Estimate the flat area of a washer-shaped sketch when inner and outer radii are known. Keep the unit beside the answer.
Represent a hollow circular section for a basic area calculation. Area alone does not give volume, mass, strength, or a manufacturing specification.
Q&A
Find concise answers to common questions and confusing cases.
No. Divide each diameter by two before entering the radii.
Both values must be positive and outer radius must exceed inner radius. Equal or reversed radii do not describe a positive ring area.
No. It uses the same unit for both inputs and returns the corresponding squared unit. Convert both first if needed.
Notes
Review scope, result limitations, and important precautions before use.
The formula assumes ideal concentric circles and computes two-dimensional area. It does not account for material thickness, imperfect alignment, or measurement uncertainty. The display rounds to four decimal places; retain adequate precision for downstream work. For engineering or fabrication decisions, confirm dimensions and tolerances against applicable specifications.
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