Easily calculate the area of a crescent or lune with our online tool. Learn the formula for finding the area between two intersecting circles. Perfect for students, engineers, or anyone needing precise geometric calculations to determine the area of this unique shape based on radii and the distance between their centers.
Formula:
The area of a crescent (lune), defined as the overlapping region of two circles, is calculated using their radii and the distance between their centers. The formula for the area of intersection is:
A = 0.5 × R₁² × (θ₁ - sin(θ₁)) + 0.5 × R₂² × (θ₂ - sin(θ₂))
Where:
R₁: Radius of the first circle
R₂: Radius of the second circle
d: Distance between the centers of the two circles
θ₁: The central angle of the first circle subtended by the common chord
θ₂: The central angle of the second circle subtended by the common chord
Derived from: θ₁ = 2 × arccos( (d² + R₁² - R₂²) / (2 × d × R₁) )
θ₂ = 2 × arccos( (d² + R₂² - R₁²) / (2 × d × R₂) )