Updated on April 21st, 2026

Hexagon Calculator

Created By Jehan Wadia

Please enter a positive number greater than 0.
Side Length (a)
5
cm
Long Diagonal (d)
10
cm
Short Diagonal (s)
8.6603
cm
Apothem (r)
4.3301
cm
Circumradius (R)
5
cm
Perimeter (P)
30
cm
Area (A)
64.9519
sq cm
a = 5 d = 10 r = 4.33 R = 5 s = 8.66
Formulas Used
Property Formula (from side a) Calculated Value
Side length (a)a5 cm
Long diagonal (d)d = 2a10 cm
Short diagonal (s)s = a × √38.6603 cm
Apothem / Inradius (r)r = (a × √3) / 24.3301 cm
Circumradius (R)R = a5 cm
Perimeter (P)P = 6a30 cm
Area (A)A = (3√3 / 2) × a²64.9519 sq cm
Property Proportions (relative to side length)

Introduction

A hexagon is a shape with six sides and six angles. You see hexagons everywhere — from honeycombs to nuts and bolts. This hexagon calculator helps you find important measurements like area, perimeter, and side length quickly and easily. Just enter one known value, and the calculator does the rest of the math for you.

A regular hexagon has six equal sides and six equal angles, each measuring 120 degrees. Because of this, if you know just one measurement — like the side length or the area — you can figure out everything else. This tool uses simple geometry formulas so you don't have to work them out by hand.

How to use our Hexagon Calculator

Enter one known measurement of a regular hexagon, and this calculator will find all other properties, including side length, diagonals, apothem, circumradius, perimeter, and area.

Solve by: Pick which hexagon property you already know. You can choose from side length, long diagonal, short diagonal, apothem (incircle radius), circumradius, perimeter, or area. The calculator will use this single value to figure out every other measurement.

Value and unit: Type in the number for your chosen property. Then select the unit of measurement from the dropdown next to it, such as centimeters, inches, meters, feet, or other common length units. The value must be a positive number greater than zero.

Calculate and Reset: Click the "Calculate" button to see your results, or simply type your number and watch the results update right away. The "Reset" button sets everything back to the default values so you can start over quickly.

Results: All seven hexagon properties appear as cards at the top, showing each value with its correct unit. The property you entered is highlighted so you can easily tell it apart from the calculated outputs. Below the cards, a labeled diagram of the hexagon shows the side length, long diagonal, short diagonal, apothem, and circumradius drawn directly on the shape. A formulas table lists the exact equation used for each property, along with the calculated value. Finally, a bar chart displays how each linear property compares to the side length as a simple ratio.

What Is a Regular Hexagon?

A regular hexagon is a flat shape with six straight sides that are all the same length and six angles that are all equal. Each interior angle in a regular hexagon measures exactly 120 degrees, and the total of all interior angles adds up to 720 degrees. You can find hexagons everywhere in nature and daily life — from honeycombs and snowflakes to nuts and bolts, floor tiles, and even the giant storm on Saturn's north pole.

Key Parts of a Regular Hexagon

To fully describe a regular hexagon, you only need to know one measurement. Every other property can be calculated from it. Here are the main parts:

  • Side length (a) — The length of one of the six equal edges.
  • Long diagonal (d) — The distance from one vertex straight across to the opposite vertex, passing through the center. It equals exactly twice the side length: d = 2a.
  • Short diagonal (s) — The distance between two vertices that are separated by one vertex in between. It equals the side length times the square root of 3: s = a × √3.
  • Apothem (r) — The distance from the center to the midpoint of any side. This is also the radius of the inscribed circle (incircle). It equals r = (a × √3) / 2.
  • Circumradius (R) — The distance from the center to any vertex. In a regular hexagon, this is equal to the side length: R = a.
  • Perimeter (P) — The total distance around the hexagon: P = 6a.
  • Area (A) — The space enclosed inside the hexagon: A = (3√3 / 2) × a², which is roughly 2.598 × a².

Why Does R Equal the Side Length?

A regular hexagon has a unique property that sets it apart from other polygons. You can divide it into exactly six equilateral triangles by drawing lines from the center to each vertex. Because these triangles are equilateral, the distance from the center to any corner (the circumradius) is the same as the side length. This is why R = a — a fact that makes hexagon calculations simpler than those for most other shapes. You can explore related triangle geometry with our Triangle Area Calculator or the Right Triangle Calculator.

How to Use the Hexagon Calculator

This calculator lets you find every property of a regular hexagon from just one known value. Pick the property you already know — such as side length, diagonal, apothem, perimeter, or area — enter its value, choose your unit, and the calculator does the rest instantly. It shows all results in a clear set of cards, updates a labeled diagram of the hexagon, displays the exact formulas used, and plots a bar chart comparing each property as a ratio to the side length.

Practical Uses of Hexagon Geometry

Hexagons are popular in engineering and design because they tile a flat surface with no gaps and no overlaps, using the least total perimeter for a given area. This is why bees build honeycomb cells as hexagons — it saves wax while maximizing storage space. Engineers use hexagonal patterns in structures, game boards, satellite mirrors, and even city planning. Knowing how to quickly calculate a hexagon's dimensions is useful for carpentry, metalwork, 3D printing, tiling projects, and math homework alike.

If you're working on a construction or flooring project involving hexagonal tiles, our Square Footage Calculator, Tile Calculator, and Flooring Calculator can help you determine material quantities. For circular shapes and comparisons, try the Circle Area Calculator. And if your project involves three-dimensional hexagonal forms like prisms, tools like the Cylinder Volume Calculator or Sphere Volume Calculator may come in handy. For general math tasks such as working with square roots in hexagon formulas, the Percentage Calculator and Slope Calculator are also useful companions, and for finding the center point between two vertices, check out the Midpoint Calculator or the Distance Calculator.


Frequently Asked Questions

What is the difference between the long diagonal and the short diagonal of a hexagon?

The long diagonal goes from one corner straight across to the opposite corner, passing through the center. It equals 2 × side length. The short diagonal connects two corners that have one corner between them. It equals side length × √3. The long diagonal is always longer than the short diagonal.

What is an apothem?

The apothem is the distance from the center of a regular hexagon to the middle of any side. It is also the radius of the largest circle that fits perfectly inside the hexagon. The formula is apothem = (side length × √3) / 2.

Can I use this calculator for irregular hexagons?

No. This calculator only works for regular hexagons, where all six sides are equal and all six angles are equal (each 120°). If your hexagon has sides or angles of different sizes, these formulas will not give correct results.

How do I find the side length if I only know the area?

Select "Area (A)" from the "Solve by" dropdown, type in your area value, and choose your unit. The calculator will use the formula a = √(2A / (3√3)) to find the side length and all other properties for you.

Why is the circumradius equal to the side length in a regular hexagon?

A regular hexagon can be split into six equilateral triangles. In each of these triangles, every side is the same length. Since the circumradius is one side of these triangles, it equals the hexagon's side length. So R = a always.

What units can I use with this calculator?

You can use millimeters, centimeters, decimeters, meters, kilometers, inches, feet, yards, or miles. For area inputs, the calculator automatically shows squared units (like sq cm or sq ft). All results use the same unit you select.

Does this calculator convert between different units?

No. The calculator does not convert between units. All results are displayed in the same unit you choose for your input. If you enter a value in centimeters, all outputs will be in centimeters (or square centimeters for area).

How many degrees are in each angle of a regular hexagon?

Each interior angle of a regular hexagon is exactly 120 degrees. The sum of all six interior angles is 720 degrees.

What does the proportions chart show?

The bar chart shows how each linear property (long diagonal, short diagonal, apothem, circumradius, and perimeter) compares to the side length as a ratio. For example, the long diagonal is always the side length, and the perimeter is always the side length.

How accurate are the results from this hexagon calculator?

Results are shown with up to four decimal places. The calculator uses precise mathematical formulas and the full value of √3 (not a rounded version), so the answers are very accurate for everyday and school use.

How do I find the perimeter if I know the apothem?

Select "Apothem / Incircle radius (r)" from the dropdown and enter your value. The calculator first finds the side length using a = (2 × apothem) / √3, then multiplies by 6 to get the perimeter.

What is the maximum value I can enter?

You can enter any positive number up to 99,999,999. If you enter a number larger than that, or a zero or negative number, the calculator will show an error message.

How is the area of a regular hexagon calculated?

The area formula is A = (3√3 / 2) × a², where a is the side length. This is roughly 2.598 × a². The formula comes from adding up the areas of the six equilateral triangles that make up the hexagon.


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