Area of Crescent (Lune) Calculator

Your details

Radius of the larger (outer) circle. Must be greater than 0.
cm
Radius of the second (inner) circle. The two circles must overlap.
cm
Centre-to-centre distance. Must be between |r1 - r2| and r1 + r2 for the circles to overlap without one containing the other.
cm
Lune 1 area
142.2597

Area of circle 1 outside circle 2 (the main crescent)

Lune 2 area54.2951
Lens (overlap) area58.8022
Circle 1 total area201.0619
Circle 2 total area113.0973
Crescent perimeter (arc)53.0788
_unitLabelcm
Lune 1142.2597
Lens (overlap)58.8022
Lune 254.2951

Lune 1 area: 142.2597 cm². Lune 2 area: 54.2951 cm².

  • Lune 1 covers 70.8% of circle 1's total area of 201.0619 cm².
  • The shared lens region is 58.8022 cm², representing the overlap of both circles.
  • Lune 1 is larger than lune 2, meaning circle 1 extends further beyond the overlap than circle 2 does.
  • A crescent is a lune whose inner arc does not pass through the centre of the outer circle.

Next stepTo confirm the result, add the two lune areas and the lens area together: the sum should equal the sum of both full circle areas.

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