Round Corner Calculator

Name: Round Corner - Geometry Calculator
Author: Jürgen Kummer

Calculations at a round corner, or rather in a quarter circle, the most simple form of a round corner. This is the intersecting set of a square with edge length a and a circle with radius a, where one corner of the square is at the center of the circle. The missing piece, the part of the square outside the quarter circle, is also called spandrel.
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:

l = \frac{1}{2} π a

p = l + 2 \cdot a

A_{1} = \frac{1}{4} π a^{2}

A_{2} = a^{2} - A_{1}

pi:

π = 3.141592653589793...

Lengths and perimeter have the same unit (e.g. meter), the areas have this unit squared (e.g. square meter).

A quarter circle is the more precise geometric term for this shape, in which a right angle originating at the center of a circle forms a circular sector. In a rounded corner, however, the curve can also be formed by an elliptic curve or another curved shape, which is often very difficult to calculate. Rounded corners are used in real objects for safety reasons, to make collisions less dangerous. In smaller objects, they can improve the haptic quality, making them easier or more pleasant to touch. They are also a frequently used design element; rounded corners appear softer and gentler than right angles.
A quarter circle is axially symmetrical to the bisector of the right angle. The two lines that complete the quarter circle to form a square are tangents to the circle, and the other two lines are right-angled secants of the circle. The perimeter of this rounded corner is equal to the perimeter of the missing piece, since both have equally long edges. However, the area of the rounded corner is considerably larger than that of the missing piece.

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