The formula for the area of a regular hexagon is A = (3√3/2)·s², where s is the length of one side and the constant 3√3/2 equals approximately 2.598076. That single expression packs in everything you need: square the side length and multiply by about 2.598 to get the hexagon's area in square units. It works for any regular hexagon — every shape with six equal sides and six equal interior angles — whether the side is a centimeter, an inch, a meter, or a foot. The same side length also gives you the perimeter (6·s), the apothem (√3/2·s, the radius of the inscribed circle), and the circumradius (s, the distance from the center to any vertex), so you can describe the whole shape from a single measurement. This guide walks through what the formula means, why it works, and how to apply it — including a free Hexagon Area Calculator that does the arithmetic for you and runs the calculation locally in your browser.
The Hexagon Area Formula in One Line
For a regular hexagon with side length s, the area is A = (3√3/2)·s². The constant 3√3/2 is irrational and has the decimal value 2.598076211..., which means the area sits just under 2.6 times the side squared. The formula assumes all six sides are equal and all six interior angles are equal at 120°. As soon as a hexagon has unequal sides or unequal angles, the (3√3/2)·s² shortcut no longer applies and you have to fall back on triangle-by-triangle or coordinate methods.
The unit you use for s becomes the unit of the area after squaring, with no conversion along the way. A side of 5 cm gives an area of (3√3/2)·25 ≈ 64.95 cm², while a side of 5 inches gives the same numerical value in square inches. The hexagon area formula is therefore unit-agnostic — keep the side in one consistent unit and the math stays exact.
Where the Formula Comes From: Six Equilateral Triangles
Draw lines from the center of a regular hexagon to each of its six corners. The hexagon is now cut into six triangles, and because of the symmetry of the shape every one of those triangles is equilateral with side length s — the same length as the hexagon's edge. An equilateral triangle with side s has area (√3/4)·s², so six of them stacked around the center give:
Area = 6 × (√3/4)·s² = (6√3/4)·s² = (3√3/2)·s²
That is the entire derivation. The hexagon is the friendliest of the regular polygons precisely because it tiles into equilateral triangles with no leftover pieces — no slivers, no overlap, no approximation. The same trick works because the central angle of each slice is exactly 60° (360° ÷ 6), and a triangle with all three interior angles at 60° is equilateral by definition. Other regular polygons need extra trigonometry to reach their area formulas; the regular hexagon just splits and adds.
Perimeter, Apothem, and Circumradius From One Side
The hexagon area formula is the headline, but the same side length s feeds three companion measurements. Together, these four values describe the entire shape without any further input:
| Measurement | Formula | Meaning | For s = 2 |
|---|---|---|---|
| Area | A = (3√3/2)·s² | Space inside the hexagon | ≈ 10.3923 sq units |
| Perimeter | P = 6·s | Total edge length | 12 units |
| Apothem (inradius) | a = (√3/2)·s | Center to midpoint of a side | ≈ 1.7320508 units |
| Circumradius | R = s | Center to any vertex | 2 units |
The circumradius is the most striking identity in the list: for a regular hexagon, R equals s exactly. The distance from the center of the hexagon to any corner is the same as the length of one side. That is why a regular hexagon fits snugly around a circle of radius s, and why hex nuts have a clean geometric relationship with their wrenches — the distance across the flats (twice the apothem) and the distance across the corners (twice the circumradius, or 2s) are both easy to derive from the side alone.
How to Find Hexagon Area Using the Calculator
If you have a single side length in hand, the calculator does every step for you in real time. The interface is deliberately minimal so the focus stays on the formula and the result, not on configuration.
- Enter the side length (s) — the length of one edge of the regular hexagon — in any unit. Centimeters, inches, meters, feet, and millimeters all work the same way.
- Watch the calculator apply A = (3√3/2)·s² and display the worked formula with your value substituted in. The full expression is shown so the substitution can be verified at a glance.
- Read the hexagon area below, displayed in the same unit you used for s, squared. A side of 4 m gives an area in m²; a side of 4 in gives an area in in².
- Pick up the companion values at the same time: the perimeter (6·s), the apothem (√3/2·s), and the circumradius (s). All four numbers share the same input and the same unit family.
- Adjust the side length to compare shapes, scale a design, or sanity-check a homework answer. Every change re-runs the formula and refreshes all four results.
Because everything runs locally in your browser, the calculation is instant and nothing is uploaded. That makes the tool practical for homework checks, design sketches, and field measurements on a phone.
A Worked Example With s = 2
To see the formula in action, take a regular hexagon with side length s = 2 (in any unit). Substituting into A = (3√3/2)·s² gives:
A = (3√3/2)·(2)² = (3√3/2)·4 = 6√3 ≈ 10.3923 square units.
The same side length produces the rest of the shape's measurements in one pass. The perimeter is 6 × 2 = 12 units. The apothem is (√3/2)·2 = √3 ≈ 1.7320508 units. The circumradius is s itself, so R = 2 units — and indeed, the distance from the center to any vertex is exactly 2. Doubling the apothem gives the width across the flats (≈ 3.4641016), and doubling the circumradius gives the width across the corners (4), both of which are values quoted on hex nut specification sheets.
Where Hexagon Area Formulas Show Up in Real Life
Hexagon area shows up in surprisingly ordinary places. The most familiar are the hexagonal cross-sections of standard nuts and bolts: a hex nut's size is the width across the flats, which equals twice the apothem. From that single measurement the side length s falls out and the enclosed area follows directly from A = (3√3/2)·s². Machinists and mechanical engineers rely on the relationship constantly when checking tolerances or estimating material removed during machining.
Honeycomb, hexagonal floor tiles, board-game maps, chicken wire, and the lattice pattern visible in pencil cross-sections all rely on the fact that hexagons cover a plane with less perimeter per unit area than squares or triangles. That geometric efficiency is part of why bees build hexagonal cells and why hexagonal grids show up in cartography, materials science, computer graphics, and even graphene research — the same (3√3/2)·s² relationship between side and area drives the choice everywhere the six-triangle structure appears.
Beyond geometry class, the formula is handy for quilters cutting hexagonal patches, tilers estimating material, 3D modelers building regular hex prisms, and surveyors working with hex-based coordinate systems. Anywhere a six-sided regular shape needs a quick area, A = (3√3/2)·s² is the answer.
Units, Limits, and What the Calculator Does Not Convert
The Hexagon Area Calculator is intentionally unit-agnostic: enter the side in any unit and the area comes back in that unit squared. Centimeters produce square centimeters, meters produce square meters, inches produce square inches, and so on. The tool does not convert between units, so keep the input consistent — mixing inches and centimeters in the same calculation will silently produce a meaningless hybrid result.
Internally, the calculator uses the exact value of √3 (not the rough 1.732 approximation), which keeps the result accurate to many decimal places. The worked formula is displayed on screen so the substitution can be verified at a glance, and the only input is a single positive side length. There are no menus to navigate, no unit pickers, and no server round-trip — the page does the arithmetic in your browser and never sends the value anywhere.
Two related limits are worth noting. First, the formula applies only to regular hexagons with all six sides equal and all six angles at 120°; irregular hexagons need a different approach, such as splitting into triangles or working in coordinates. Second, the side length must be a positive number to describe a real hexagon — entering zero or a negative value does not represent a meaningful shape. Within those bounds, the calculator is the fastest path from one side length to a fully described hexagon.
If you're weighing options, How to Calculate Ideal Weight for Height with 4 Formulas covers this in detail.