Circumradius of Rectangle given Perimeter and Length Calculator

Formula

The formula to calculate the Circumradius of Rectangle (rc) is:

\[ rc = \frac{\sqrt{P^2 - (4 \cdot P \cdot l) + (8 \cdot l^2)}}{4} \]

Where:

\(rc\) is the Circumradius of Rectangle (measured in meters).
\(P\) is the Perimeter of Rectangle (measured in meters).
\(l\) is the Length of Rectangle (measured in meters).

Definition

Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle lying on the circle.

Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.

Length of Rectangle is any one of the pair of parallel sides which are longer than the remaining pair of parallel sides.

How to calculate Circumradius of Rectangle

Let's assume the following values:

Perimeter of Rectangle (P) = 28 meters
Length of Rectangle (l) = 8 meters

Using the formula:

\[ rc = \frac{\sqrt{28^2 - (4 \cdot 28 \cdot 8) + (8 \cdot 8^2)}}{4} \]

Evaluating:

\[ rc \approx 5 \, \text{meters} \]

The Circumradius of Rectangle is approximately 5 meters.

Conversion Chart

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Perimeter (P) (meters)	Length (l) (meters)	Circumradius (rc) (meters)