Area of Crescent Calculator – Guide & Formulas

The Area of Crescent Calculator computes the area of a crescent (lune) shape formed by the intersection of two circles. A crescent is created when one circle partially overlaps another, and the remaining crescent-shaped region is what you want to measure. This free online crescent area calculator is perfect for geometry students and enthusiasts.

How to Use the Area of Crescent Calculator

1. Enter the radius of the larger circle (R).
2. Enter the radius of the smaller circle (r).
3. Enter the distance (d) between the centers of the two circles.
4. Review the calculated crescent area and the step-by-step derivation.

The Formula

Variable Definitions

• R: Radius of the larger circle
• r: Radius of the smaller circle
• d: Distance between the centers of the two circles
• A_overlap: The overlapping (intersection) area of the two circles

Example: Crescent Formed by R=5 and r=3, d=4

Calculate the crescent area when the larger circle has radius 5, the smaller has radius 3, and their centers are 4 units apart.

1. Step 1: Calculate the area of the larger circle: π × 5² = 78.54.
2. Step 2: Calculate the area of the smaller circle: π × 3² = 28.27.
3. Step 3: Using the lens overlap formula, compute the intersection area of the two circles.
4. Step 4: The overlap area is approximately 12.19 square units.
5. Step 5: The crescent area = πR² — overlap = 78.54 — 12.19 = 66.35 square units.

Frequently Asked Questions