Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Area of Intersecting Circles

Calculate area of intersecting circles

The area of intersecting circles can be calculated as

Area of intersecting circles

Thanks to Eric Eberly for providing this information.

If radii r₁, r₂ and distance d between the centers are given - then the angles α₁ and α₂ can be calculated as

α₁ = acos((d² + r₁² - r₂²) / (2 d r₁))

α₂ = acos((d² + r₂² - r₁²) / (2 d r₂))

Circle - the Chord Lengths when Divided in to Equal Segments
Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.
Circle Equation
The equation for a circle
Circles on the Outside of a Circle
Calculate the numbers of circles on the outside of an inner circle - like the geometry of rollers on a shaft.
Circles within a Rectangle - Calculator
Calculate the maximum number of circles within a rectangle - can be used to calculate the numbers of pipes or wires in a conduit or similar.
Elementary Curves
Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines.
Elementary Surfaces
Ellipsoid, sphere, hyperboloid, cone and more.
Equal Areas - Circles vs. Squares
Radius and side lengths of equal areas, circles and squares.
Geometric Shapes - Areas
Areas, diagonals and more - of geometric figures like rectangles, triangles, trapezoids ..
Length of a Spiral
Calculate the length of a spiral or the length of material contained in a roll.
Maximizing Space: Fit Small Rectangles Inside a Larger Rectangle
The maximum number of smaller rectangles - or squares - within a larger rectangle (or square).