Free Perimeter of a Polygon Calculator

Regular Polygon Perimeter Calculator

This free regular polygon perimeter calculator is built to quickly determine the perimeter of any regular polygon. Just choose the shape type, enter the side length, and the tool outputs the result. It eliminates repetitive multiplication and reduces errors, making it ideal for geometry students, engineers, and anyone needing fast, accurate perimeter values.

Polygon Perimeter Formula

For a regular polygon, the perimeter ( $P$ ) is the product of the number of sides ( $n$ ) and the side length ( $a$ ):

$$P = n \times a$$

Whether the polygon is a triangle, square, pentagon, or dodecagon, this simple relationship applies as long as all sides are equal.

General Perimeter Calculation

If the polygon is not regular, you can still find its perimeter by summing the lengths of all sides:

$$P = \sum_{i=1}^{n} a_i$$

where $a_1, a_2, \dots, a_n$ are the individual side lengths.

When only vertex coordinates are known, compute each edge with the distance formula and sum:

$$P = \sum_{i=1}^{n} \sqrt{(x_{i+1} - x_i)^2 + (y_{i+1} - y_i)^2}$$

using the convention $(x_{n+1}, y_{n+1}) = (x_1, y_1)$ to close the shape.

Step‑by‑Step Example: Octagon Perimeter

To see how the polygon perimeter formula works in practice, here’s a quick example for a regular octagon:

1. Select the polygon type – choose “Octagon” (or “Other” and set 8 sides).
2. Enter the side length – for example, $17$ inches.
3. Read the result – the calculator shows:

$$P = 8 \times 17 = 136\ \text{in}$$

So a regular octagon with side length 17 inches has a perimeter of 136 inches.

Additional Tips

Once you have the perimeter, you may also want the polygon’s area. Many online tools complement this perimeter of a regular polygon calculator with area computations, or you can apply the standard area formulas for your shape. The perimeter itself is frequently used in fencing, framing, and material estimation tasks.