Circumference of objects

Here is the section of the perimeter functions. Find the circumference of an object.

The first of those, is rather easy: Perimeter of circle:

perimeterCircle(x ) - Calculate the perimeter of an circle

Where

• x = diameter

Using the following formula:

$$\begin{aligned} x &\colon\quad \text{diameter} \\[0.6em] \mathrm{result} &= \pi\cdot x \end{aligned}$$

Example:

Perimeter of a circle of 15 cm diameter:

perimeterCircle(15)=47.12388981

The next one, is the perimeter of an ellipse. Unfortunately, there is no easy formula to calculate this. There is some formulas that do it approximately. The only exact way is to use a infinite series calculation.

The famous Indian mathematician Srinivasa Ramanujan developed a close approximation. FormulaCalculator uses its native ellipse-perimeter implementation for this function.

perimeterEllipse(x; y ) - Calculate the perimeter of an ellipse

Where

• x = height of ellipse
• y = width of ellipse

The function is implemented natively. The following formula block documents the approximation stored with the current function reference:

$$\begin{aligned} x &\colon\quad \text{height of ellipse} \\ y &\colon\quad \text{width of ellipse} \\[0.6em] a &= \frac{x}{2} \\ b &= \frac{y}{2} \\ \mathrm{result} &= \pi\cdot \left(3\cdot \left(a + b\right) - \sqrt{\left(3\cdot a + b\right)\cdot \left(a + 3\cdot b\right)}\right) \end{aligned}$$

Example:

An ellipse, 15 cm high, and 20 cm wide. What is the perimeter.

perimeterEllipse(15;20)=55.258729

The next perimeter function, is calculation of the perimeter of an regular polygon:

perimeterRegPolygon(x; y ) - Calculate the perimeter of an regular polygon

Where

• x = number of sides
• y = distance from center to one of its corners

Using the following formula:

$$\begin{aligned} x &\colon\quad \text{number of sides} \\ y &\colon\quad \text{distance from center to one of its corners} \\[0.6em] \mathrm{result} &= 2\cdot x\cdot y\cdot \cos\left(\frac{90\cdot \left(x - 2\right)}{x}\right) \end{aligned}$$

Example:

Calculate the perimeter of a hexagon, where the circumcircle is 10 cm.

perimeterRegPolygon(6;10)=60 cm

The last function in this series, is the perimeter of a rectangle.

perimeterRectangle(x; y ) - Calculate the perimeter of an rectangle

Where

• x = width
• y = height

Using the following formula:

$$\begin{aligned} x &\colon\quad \text{width} \\ y &\colon\quad \text{height} \\[0.6em] \mathrm{result} &= 2\cdot \left(x + y\right) \end{aligned}$$

Example:

perimeterRectangle(10;20)=60

This completes the geometric functions. See also the conversion functions.