Jump to
Jump to
Share this
See also
Properties of a Circular area
Properties of a Semi-Circular area
Properties of a Circular Sector
Properties of a Circular Segment
Properties of an Elliptical Area
All Geometric Shapes tools

Properties of a Quarter-Circular Area

This tool calculates the basic geometric properties of a quarter-circular area. Enter the shape dimensions R or D below. The calculated results will have the same units as your input. Please use consistent units for any input.

R =
...or
D =
Geometric properties:
Area =
Perimeter =
Arc length =
xc =
yc =
shape details
Jump to
Share this

Definitions

Geometry

The area A, the perimeter P and the arc length L of a quarter-circular area, with radius R, can be found with these formulas:

\[ \begin{split} A & = \frac{\pi R^2}{4} \\ P & = \left(\frac{\pi}{2}+2\right) R \\ L & = \frac{\pi R}{2} \end{split} \]

The centroid (center of gravity) of the quarter-circular area is located at equal distances from the radial edges that define its border, given by the formula:

\[ x_c = y_c = \frac{4 r}{3 \pi} \]

See also
Properties of a Circular area
Properties of a Semi-Circular area
Properties of a Circular Sector
Properties of a Circular Segment
Properties of an Elliptical Area
All Geometric Shapes tools