Decagon Perimeter Calculator

This regular decagon perimeter calculator allows you to calculate the perimeter of a regular decagon, which is the total length of all ten equal sides. But it can do more than that: given any one value, you can calculate the remaining four, namely side length, perimeter, inradius (the distance from the center of the polygon to the middle of its side), circumradius (the distance from the center of the polygon to one of the vertices) and area.

Enter a value into any field and the other values will be calculated automatically as well as the perimeter which is shown as the main result. If you open the option for the circumscribed rectangle, then you can also find out the height and width of your decagon.

What is the perimeter of a decagon?

A decagon is a polygon with ten sides and ten vertices. A regular decagon has all ten sides the same length and all ten interior angles are equal. This tool calculates the perimeter of this shape. The perimeter is the total distance around the edge, or the length that you would measure if you went around the outside. Since in a regular decagon each side is the same length, the perimeter is simply the sum of all ten sides. It can be measured using common units of length such as centimeters, meters, or inches.

Here's how to use this tool.

Enter a known measurement into the input field and select a unit (e.g. centimeters or inches). As you enter a value, the tool will automatically fill in the remaining four fields and display the circumference as the main result. You do not need to specify which type of measurement you entered first. If you want to start over with a different known value, simply delete the previously entered values and enter new ones. To also determine the height between two opposite sides and the width across the longest diagonal, open the enclosing rectangle option.

Formula for the perimeter of a decagon:

For a regular decagon the perimeter is determined by the length of its sides alone. Since all ten sides are equal in length, multiply the side length by ten.

In this formula, P is the perimeter and a is the length of one side.

If each side has a length of 6 cm, then multiplying by ten gives you the perimeter.

Conversely, if the perimeter is known, then the side length can be found by dividing it by ten.

This is a general rule for all regular polygons, where the number ten is replaced by the number of sides. As a regular decagon has exactly ten sides, its perimeter at equal side length is larger than that of any other regular polygon with fewer sides.

Calculation based on center distance, circumferential radius and area:

It doesn't always have to start with the side length. The apothem is the distance from the center to the middle of a side, the circumradius is the distance from the center to a vertex, and the area describes the extent of the interior of the figure.

A decagon consists of ten triangles, and these quantities are all geometrically related to the side length. So if any one of them is known, then the side length can be calculated backwards, and the perimeter determined.

In these formulas, r is the distance from the center of a side, R is the circumradius and A is the area. Since the calculations for trigonometric functions are performed by a calculator tool, you only need to enter the values that are available. There's also an interesting fact: The circumradius of a regular decagon is exactly equal to the product of the length of its side times the golden ratio, which is about 1.618 times the length of the side.

Check all measurements for the decagon

All measurements of a regular decagon are related to each other through the side length. The following table summarizes the relationships used by the calculator so that all other values can be calculated when only one value is entered.

Examples of calculations

The following table shows the perimeter for some common side lengths. Note that as the side length increases, so does the perimeter, and it is directly proportional to it since there is no calculation involved in squaring the side length.

Converting from perimeter is just as easy. A regular decagon with a perimeter of 80 centimeters has sides that are the result of dividing 80 by 10, or 8 centimeters long. If you type in 80 for the perimeter field, the side length will be immediately shown along with the distance from center to a vertex, the circumradius and area.

The interior angles of a decagon sum to a particular value and the diagonals have certain properties.

The angles of a regular decagon do not change regardless of whether the figure is drawn large or small. Each of its ten interior angles measures 144 degrees, and their sum is 1440 degrees. The central angle is the angle between two line segments that extend from the center to adjacent vertices, and it measures 36 degrees. The exterior angle also measures 36 degrees. A decagon has 35 diagonals, with the longest diagonal passing through the center and connecting opposite vertices; its length is twice the radius of the circumscribed circle.

Regular vs Irregular Decagons

This calculator assumes a regular decagon, where all ten sides are the same length. If a decagon is irregular and has different side lengths, then you cannot simply multiply the side length by 10 to find the perimeter. In this case, add up the lengths of all ten sides to find the perimeter. The formulas for apothem, circumradius, and area only work for regular decagons.

Applications of a decagon in size

Decagons are found in coins, pavilions, decorative tiles, flower beds and mechanical parts such as nuts and molds. When the perimeter is known, a manufacturer can use it to calculate how much material (e.g., skirting boards, trim pieces, fences, frames) will be needed to cover that perimeter of the decagon. Designers and draftsmen use the same relationship to fit a decagon into a given circle or determine the size of a circle that can just contain a decagon.

Tips for accurate results:

Measure each side carefully and do not try to measure the entire perimeter at once. Let the calculator do the multiplication for you. Make sure that your units are consistent. If you input the length of a side in centimeters, then the result for the perimeter will also be in centimeters. Note that the formula for a regular decagon assumes that all ten sides are exactly the same length. Therefore, make sure that the figure is actually a regular decagon before using methods based on the distance from the center to any vertex (radius of the circumscribed circle) or area.