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# Equal Areas - Circles vs. Squares

The area of a circle can be expressed as

Ac = π r2                             (1)

where

Ac = circle area (m2, ft2)

r = circle radius (m, ft)

The area of a square can be expressed as

As = s2                                 (2)

where

As = square area (m2, ft2)

s = side of square (m,ft)

If the area of the circle is equal to the area of the square - then Ac = As and (1) and (2) can be combined to

π r2 = s2                             (3)

### Radius of Circle - Side of Square is known

r = (s2/ π)1/2                              (4)

### Side of Square - Radius of a Circle if known

s = (π r2)1/2                               (5)

### Example - Circle and Square with equal Area

The side length of a square with the same area as a circle with radius 2 m can be calculated as

s = (π (2 m)2)1/2

= 3.54 m

## Related Topics

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US American (ASTM) vs. British (BSi) piping standards - specifications, grades and material descriptions.

### Area of Intersecting Circles

Calculate area of intersecting circles

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Online app that can be used to make an exact plot of a surveyed area - like a room, a property or any 2D shape.

### Area Units Converter

Convert between units of area.

### Centroids of Plane Areas

The controid of square, rectangle, circle, semi-circle and right-angled triangle.

### Circle - Equation

The equation for a circle

### Circles - Circumferences and Areas

Circumferences and areas of circles with diameters in inches.

### Circles Outside 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.

### Geometric Shapes - Areas

Areas, diagonals and more - of geometric figures like rectangles, triangles, trapezoids ..

### Hexagons and Squares - Diagonal Lengths

Distances between corners for hexagons and squares.

### Pythagorean Theorem

Verifying square corners.

### Smaller Circles within a Large Circle - Calculator

Calculate the number of small circles that fits into an outer larger circle - ex. how many pipes or wires fits into a larger pipe or conduit.

### Smaller Rectangles within a Larger Rectangle

The maximum number of smaller rectangles - or squares - within a larger rectangle (or square).

### Solids - Volumes and Surfaces

The volume and surface of solids like rectangular prism, cylinders, pyramids, cones and spheres - online calculator.

### Squaring with Diagonal Measurements

A rectangle is square if the lengths of both diagonals are equal.

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