Hexagon Perimeter Calculator

This hexagon perimeter calculator allows you to find the perimeter of a regular hexagon, which is essentially the total length of all six sides. In addition, given any one value, you can calculate the remaining four by inputting it into our calculator.

Enter a value and select its unit - whether that be side length, perimeter, distance from center to side, circumradius or area - then watch as the other values update automatically with the main result being the perimeter. By opening up additional options, you'll also be able to display both diagonals of your hexagon as well as areas for each of its six triangles.

What is the perimeter of a hexagon?

A hexagon is a polygon with six sides and six vertices. A regular hexagon has all six sides the same length and all six interior angles are equal. This tool calculates the perimeter of such shapes.

The perimeter is the total length of the outer edge, or the distance around the shape once. In a regular hexagon each side is the same length, so the perimeter is six times the length of one side. It can be measured in common units of length like centimeters, meters, or inches.

How to use this calculator:

Enter a known measurement into the appropriate input field and select its unit (e.g. centimeters or inches). After entering one value, the tool will automatically fill in the other four fields and display the perimeter as the main result. It is not necessary to specify which of the entered values corresponds to which dimension. If you want to start over with a different known value, simply delete the previously entered values and enter new ones. If you also want to find out the length of the long diagonal, short diagonal or area of one of the six equilateral triangles, please open the additional options.

Formula for calculating the perimeter of a regular hexagon:

The perimeter of a regular hexagon is simply six times the length of one of its sides, since it has 6 sides of equal length.

In this formula, P is the perimeter and a is the length of one side. If each side has a length of 8 centimeters,

then the perimeter is:

Conversely, if you know the perimeter and want to find the length of a side, just divide by 6.

This is the same rule that applies to any regular polygon, except using the number of sides instead of six sides. Bees and tile makers often choose hexagons because six of them can fit around a point with no gaps.

The radius of the circumcircle is equal to the side length and consists of six triangles.

A regular hexagon has a special property that other regular polygons do not have: the radius of its circumcircle (the distance from the center to any vertex) is exactly equal to the length of its sides. So you can determine the radius of the circumcircle if you know the side length, and vice versa.

This is because a regular hexagon consists of six congruent equilateral triangles, which meet at the center point. Each side of these triangles corresponds to one side length of the hexagon, and the radius of the circumscribed circle is exactly one of those side lengths. The apothem length, or distance from the center point to the midpoint of a side, can also be calculated using these triangles. It is equal to the square root of three times the side length divided by two, which is approximately 0.866 times the side length.

The area is the sum of the areas of these six triangles, leading to the simple formula: it is approximately 2.598 times the square of the side length.

You can use the apothem length, circumradius or area to calculate other values.

Calculations don't always start with the side length. The apothem is the distance from the center to the midpoint of a side, the circumradius is the distance from the center to any vertex, and the area describes the space inside the hexagon. All of these are geometrically related to each other and depend on the side length. So if you know one of them, you can figure out the side length, and therefore also the perimeter.

In these formulas, "r" stands for the length of the apothem, "R" is the radius of the circumcircle, and "A" represents the area. The calculations are done by a tool so all you need to do is enter the available values.

Check all measured values of the hexagon.

The individual measurements of a regular hexagon are related to each other through the side length. The following table summarizes the relationships used, explaining why knowing one measurement allows you to calculate the remaining ones.

Example calculation:

The following table shows the perimeter for some common side lengths. The perimeter increases in direct proportion to the length of a side, and they are both directly proportional to each other. This is because the length of a side is not squared.

It is just as easy to calculate the side length from the perimeter. A regular hexagon with a perimeter of 60 centimeters has sides that are each 10 centimeters long, which is the result of dividing 60 by 6. If you enter 60 in the field for the perimeter, the side length and the distance from the center to the side, the radius of the circumscribed circle, and the area will be shown immediately.

The two diagonals of a hexagon:

A regular hexagon has two different lengths of diagonals. The short diagonal connects two opposite vertices and is about 1.732 times the length of a side. This corresponds to the width between parallel sides, or the distance between two opposite sides that is twice the distance from the center to a side. The long diagonal passes through the center and connects two opposite vertices, being exactly twice as long as a side. A hexagon has nine diagonals in total, three of which are long and six are short.

Angle of a regular hexagon

The angles of a regular hexagon are constant regardless of whether it is drawn large or small. Each of the six interior angles measures 120 degrees and their sum is 720 degrees. The central angle formed by two adjacent vertices at the center is 60 degrees. Also, the exterior angles measure 60 degrees each. A hexagon has six lines of symmetry and opposite sides are always parallel.

Regular and irregular hexagons

This tool assumes that a hexagon is regular, meaning it has six equal sides. If the hexagon is irregular and each side is a different length, then the simple formula of multiplying the side length by six cannot be used to find the perimeter. In this case, you would have to add together the lengths of all six sides in order to find the perimeter. The formulas for the apothem, circumradius, and area only apply to regular hexagons.

Use of the perimeter of a hexagon

Hexagons are found everywhere. They are used in beehives, floor and bathroom tiles, bolt heads, pavilions, pencils, snowflakes, and the basalt pillars of Giant's Causeway. When the perimeter is known, a manufacturer can determine how much material will be required to place a border, decoration or frame along the perimeter of a hexagon. Because a hexagon can fill a plane completely, it is the most efficient method for dividing an area into equal units, which is why bees use them.

Tips for accurate results:

Carefully measure each side and let the tool do the multiplication for you rather than measuring around the entire perimeter. Be sure to keep all units consistent. If you are using centimeters to measure a side length, then your perimeter will be in centimeters as well. Note that the formula for a regular hexagon assumes that all six sides are equal lengths. Check to see if the figure is actually a regular hexagon before using methods based on distance from center to side, circumscribing circle radius, or area.