Crescent Area
Calculate the area of a crescent or annular ring shape using outer and inner radii. Free online geometry tool using the formula A = pi(R^2 - r^2) for the region between two concentric circles.
About This Calculator
The crescent area calculator computes the area between two concentric circles -- also known as an annulus or ring -- using the formula A = pi(R^2 - r^2), where R is the outer radius and r is the inner radius. This shape appears frequently in engineering (pipe walls, washers, gaskets), architecture (circular ring structures), and everyday objects like rings and donuts.
The formula is straightforward: compute the area of the outer circle (piR^2), subtract the area of the inner circle (pir^2), and the remainder is the annular region. The calculator also visualizes the breakdown using a pie chart showing the crescent area versus the inner circle area.
Enter both radii in consistent units. The inner radius must be smaller than the outer radius, and both must be positive numbers. The result includes the crescent area, outer radius, and inner radius for a complete reference.
Frequently Asked Questions
What is the formula for crescent area?
The area of a crescent (annular) shape between two concentric circles is A = pi(R^2 - r^2), where R is the outer radius and r is the inner radius. For example, with outer radius 10 units and inner radius 6 units, the crescent area is pi(100 - 36) ≈ 201.06 square units.
What is the difference between a crescent and a lune?
A crescent (annulus) is the region between two concentric circles that share the same center. A lune is the region between two intersecting circles with different centers. This calculator computes the concentric crescent (annulus) area.
Can the inner radius be larger than the outer radius?
No. The inner radius must be smaller than the outer radius. If the inner radius equals the outer radius, the crescent area is zero. The calculator validates that inner radius is less than outer radius before computing.
What units should I use?
Use any consistent unit of length (inches, feet, cm, m) for both radii. The area will be in the corresponding square unit (sq in, sq ft, cm^2, m^2).
Where is crescent (annular) area calculation used?
Annular area calculations are used in engineering (pipe cross-sections, washers, gaskets), architecture (circular ring structures, domes), design (rings, circular patterns), and physics (moment of inertia computations for annular objects).
Can this calculator be used for washer or gasket area?
Yes. Washers, gaskets, and ring-shaped objects are exactly annular shapes -- the area between an outer and inner circle. Enter the outer and inner radii to get the cross-sectional area.