Calculate the area and perimeter of a crescent (lune) shape formed by two semicircles. Perfect for architectural design, logos, and geometric art.
Last updated: April 2026 | By Patchworkr Team
A crescent, also called a lune in geometry, is a shape formed by the area between two circular arcs. The most common form is created when a smaller semicircle is subtracted from a larger semicircle, producing the familiar crescent moon shape.
Key characteristics of a crescent:
Crescents appear in Islamic art and architecture, national flags, logos, and are of course most famously seen as the phases of the moon. The shape has cultural significance across many civilizations and is widely used in design.
Determine the radius of the large semicircle (R) and the radius of the small semicircle (r). The large radius must be greater than the small radius. Why: The two radii define the size of both semicircles. The difference between them (R - r) determines the crescent's width. Without accurate radius measurements, all downstream calculations will be incorrect.
Confirm that R > r and that both radii are positive numbers. Check that the configuration makes geometric sense (the smaller semicircle fits inside the larger one). Why: Invalid configurations (R ≤ r, negative radii, or zero values) produce meaningless results. Validation prevents silent calculation errors and ensures the shape actually forms a crescent.
Why: Breaking the problem into steps ensures clarity and allows verification at each stage. Each semicircle contributes a known amount to the final area. Computing them separately is more verifiable than a single combined formula.
Why: The crescent IS the region occupied by the large semicircle but NOT by the small semicircle. Subtraction captures this geometric relationship precisely. This formula works universally for any two concentric or aligned semicircles with R > r.
Why: Perimeter measures the boundary of the crescent (both curved edges). Width provides a geometric "thickness" property useful for design and material calculations. Together, area + perimeter + width give complete geometric specification for manufacturing, construction, or artistic applications.
Islamic Mosque Window Design
Crescent area = (π/2) × (R² - r²), where R is the large radius and r is the small radius. It's the difference between two semicircle areas.
No. The small radius must be less than the large radius, otherwise you don't have a crescent shape.
A lune is the geometric name for a crescent shape formed by the area between two circular arcs. The word comes from Latin luna (moon).
Add the arc lengths of both semicircles: Perimeter = πR + πr. This gives you the total curved boundary length.
A crescent is formed by two circular arcs (often semicircles). A circular segment is formed by a chord cutting off part of a circle.
This calculator is for geometric crescents. Moon phases involve spherical geometry and lighting angles, which are more complex.
Crescents appear in Islamic architecture, national flags (Turkey, Pakistan), religious symbols, logos, and decorative design elements.
If concentric (same center), you get an annular segment (ring segment), not a crescent. Crescents typically have offset centers.