Heptagon Perimeter Calculator

This regular heptagon perimeter calculator calculates the perimeter of a regular heptagon given its side length, which is the sum of lengths of all seven sides. It also supports other calculations such as calculating the area or radius of circumscribed circle.

Just enter one existing measurement - side length, perimeter, distance from center to side, circumradius or area - and the tool will calculate all others automatically. After entering a value and selecting its unit, the rest values are filled in automatically with the perimeter being shown as the main result. A heptagon is also called "septagon", so both terms refer to the same geometric object.

What is the circumference of a regular heptagon?

A heptagon is a polygon with seven sides and seven corners. If all seven of the sides are equal in length and all seven interior angles are equal in size then it is called a regular heptagon. This is the shape that this tool deals with. The perimeter is the total length of the boundary, i.e. the path that goes once around the outside edge.

Since a regular heptagon has all sides the same length, its perimeter is seven times the length of one side. It is usually expressed in linear units such as centimeters or inches.

How to use this calculator:

Enter any one of the existing measurements into its respective field and select the unit (e.g., centimeters or inches). Once you have entered a value, the tool will automatically fill in the remaining four fields and display the circumference as the main result. It is not necessary to specify which measurement was entered.

To start over with another known value, erase the fields you entered and enter new values. By opening the compare option, you can compare a heptagon with its circumscribed circle and inscribed circle. When you open the diagram, you can see how the perimeter changes as the length of the sides increases.

Formula for calculating the perimeter of a heptagon:

For a regular heptagon, the perimeter is determined only by the length of one side. Since all seven sides are the same length, simply multiply the side length by seven.

where P is the perimeter and a is the length of one side. Let's say that each side has a length of 10 centimeters.

If we multiply this by seven, we get the following perimeter:

Conversely, if you know the perimeter and want to find the length of a side, divide it by seven.

This is the same rule that applies to all regular polygons, except that the number of sides is replaced by seven. This simple method only works if all the sides are the same length.

Calculation based on center-to-side distance, circumferential radius or area.

It does not always start with the length of the sides. The side midpoint distance is the distance from the center to a side midpoint, the circumradius is the distance from the center to a vertex, and the area describes the space inside the figure. All these quantities are connected by geometric relationships between the seven triangles that make up the heptagon and the length of the sides. So if one of those values is known, then you can find the side length and calculate the perimeter from it.

In these formulas 'r' is the inradius, 'R' is the circumradius and 'A' is the area. The angle created by dividing 180 by 7 is approximately 25.71 degrees. Calculations of trigonometric functions are done by a tool so you only need to input the values that are given. Unlike pentagons or decagons, these constants for heptagons do not have simple whole numbers or the golden ratio. This is because a heptagon cannot be constructed with just a compass and straightedge.

All measurements of a heptagon.

Every measurement of a regular heptagon is related to the side length by other measurements. This table shows the relationships used by the calculator so that entering one value will determine all the others.

Examples of calculations.

The following table shows the perimeter for various typical side lengths. It is important to note that the perimeter increases with the length of a side and is directly proportional, as the length of a side is not squared.

It is just as easy to calculate the side length from the perimeter. A regular heptagon with a perimeter of 84 centimeters has sides that are each 12 centimeters long, which is the result of dividing 84 by 7. If you enter the value for the perimeter in field 84, then the side length and the distance from center to side, circumradius and area will immediately be shown.

Two types of diagonals in a heptagon

A diagonal is a line that connects two non-adjacent vertices. A heptagon has 14 diagonals. This can be checked using the formula for polygons: multiply the number of sides by a number that is three less than the number of sides, and then divide the result by two.

There are only two different lengths for these diagonals, because the distance between any two vertices is either two or three sides. The calculator shows both the short diagonal and the long diagonal. They are related to the side length by a simple relationship: the reciprocal of the side length equals the sum of the reciprocals of the short and long diagonals. This is a property unique to regular heptagons.

Angles of a regular heptagon

A regular heptagon will have the same angles regardless of how large or small it is drawn. The seven interior angles each measure approximately 128.57 degrees and add up to 900 degrees. The central angle, formed by a center point and two adjacent vertices, also measures about 51.43 degrees, as do the exterior angles.

Regular and irregular heptagons

This calculator assumes a regular heptagon, where all seven sides are an equal length. If the heptagon is irregular and has different side lengths, you cannot simply multiply the side length by seven. In this case, however, the perimeter is still the sum of the side lengths, so it can be found by adding up each individual side. The formulas for the apothem, circumradius, and area only apply to regular heptagons.

Use of a heptagon's circumference

The shape of a heptagon is closer than you think. Both the British 20p and 50p coins are seven-sided with a slight curve to their edge that allows them to roll smoothly through vending machines while also being easily distinguishable by feel. Heptagons are also used in architecture, flower beds, decorative tiles, screw heads and logos.

The circumference tells manufacturers how many packages of materials they need to lay along the perimeter of a heptagon for trim, fencing or framing. Designers and draftsmen use the same relationship to fit a heptagon into a given circle or determine the size of a circle that will just fit around a heptagon.

Tips for accurate results:

Carefully measure each side and input the values into a calculation tool rather than measuring the entire perimeter. Make sure all units are equal. If you enter the length of one side in centimeters, then the perimeter will be calculated in centimeters. Note that the formula for a regular heptagon requires that all sides are the same length. So make sure it is actually a regular heptagon before using methods based on distance from center to side, circumradius or area.