Square Foot Calculator Hexagon
Calculate regular hexagon area in square feet from side length, apothem, or long diagonal. Formula, full reference table from 1–20 ft sides, gazebo and tile examples, perimeter and diagonal guide.
Regular Hexagon Calculator
Enter the side length or apothem of a regular (equal-sided) hexagon. If both are entered, side length is used.
All 6 sides equal length s.
Apothem a = s × 0.866 | Long diagonal = 2s
Hexagon Area Calculator — Square Footage from Side, Apothem or Diagonal
A regular hexagon has six equal sides and six 120° interior angles. It is the most efficient shape for tiling a plane — hexagons cover a surface with no gaps and minimal perimeter, which is why honeycomb, gazebo floors, hex tiles, and paving designs use them. Use this calculator to find the square footage from any known measurement: side length, apothem, or long diagonal.
Three Ways to Calculate Hexagon Area
All Regular Hexagon Formulas
| Measurement | Formula | Use when |
|---|---|---|
| Side length (s) | Area = 2.59808 × s² | You measured one outer edge |
| Apothem (a) | Area = 3.4641 × a² | You measured center to side midpoint |
| Long diagonal (d) | Area = 0.6495 × d² | You measured corner to opposite corner |
| Perimeter (P) | s = P / 6, then Area = 2.598 × s² | You know total edge length |
| Apothem → side | s = a ÷ 0.866 | Convert apothem to find side |
| Side → apothem | a = s × 0.866 | Find apothem from side |
| Side → long diagonal | d = 2 × s | Corner-to-corner distance |
| Side → short diagonal | d_short = s × √3 ≈ s × 1.732 | Flat-to-flat distance = 2 × apothem |
| Perimeter | P = 6 × s | Border trim, edging, fencing |
How to Measure a Hexagonal Space
- Side length: measure from one corner to the immediately adjacent corner along the edge.
- Long diagonal: measure from one corner straight across to the opposite corner — this equals 2× the side length.
- Apothem (width across the flats): measure from one flat side across to the opposite flat side — this equals 2× the apothem. Then apothem = that measurement ÷ 2.
- Enter whichever measurement you have in the calculator above.
Worked Example 1: Hexagonal Gazebo (8 ft sides)
Area = 2.59808 × 8² = 2.59808 × 64 = 166.28 sq ft (15.45 m²)
Perimeter = 6 × 8 = 48 ft (for decking border trim)
Apothem = 8 × 0.866 = 6.928 ft
Long diagonal = 2 × 8 = 16 ft
For composite decking: 166.28 × 1.15 = 191 sq ft to order (15% waste for angled cuts)
Worked Example 2: Hexagonal Tile Section (4 ft sides)
Area = 2.59808 × 4² = 2.59808 × 16 = 41.57 sq ft (3.86 m²)
For 12×12 in tiles (1 sq ft each): 41.57 + 15% waste = 48 tiles
Worked Example 3: From Apothem (hot tub surround, a = 6 ft)
Area = 3.4641 × 6² = 3.4641 × 36 = 124.71 sq ft (11.59 m²)
Side length = 6 ÷ 0.866 = 6.928 ft | Long diagonal = 2 × 6.928 = 13.856 ft
Complete Size Reference Table
| Side (ft) | Apothem (ft) | Long Diagonal (ft) | Perimeter (ft) | Area (sq ft) | Area (m²) |
|---|---|---|---|---|---|
| 1 ft | 0.866 ft | 2 ft | 6 ft | 2.60 sq ft | 0.24 m² |
| 2 ft | 1.732 ft | 4 ft | 12 ft | 10.39 sq ft | 0.97 m² |
| 3 ft | 2.598 ft | 6 ft | 18 ft | 23.38 sq ft | 2.17 m² |
| 4 ft | 3.464 ft | 8 ft | 24 ft | 41.57 sq ft | 3.86 m² |
| 5 ft | 4.330 ft | 10 ft | 30 ft | 64.95 sq ft | 6.03 m² |
| 6 ft | 5.196 ft | 12 ft | 36 ft | 93.53 sq ft | 8.69 m² |
| 7 ft | 6.062 ft | 14 ft | 42 ft | 127.31 sq ft | 11.83 m² |
| 8 ft | 6.928 ft | 16 ft | 48 ft | 166.28 sq ft | 15.45 m² |
| 9 ft | 7.794 ft | 18 ft | 54 ft | 210.44 sq ft | 19.55 m² |
| 10 ft | 8.660 ft | 20 ft | 60 ft | 259.81 sq ft | 24.14 m² |
| 12 ft | 10.392 ft | 24 ft | 72 ft | 374.12 sq ft | 34.76 m² |
| 15 ft | 12.990 ft | 30 ft | 90 ft | 584.57 sq ft | 54.31 m² |
| 20 ft | 17.321 ft | 40 ft | 120 ft | 1,039.23 sq ft | 96.56 m² |
Common Applications and Material Waste Guide
| Application | Typical Size | Area | Waste Factor | Material to Order |
|---|---|---|---|---|
| Small hexagonal gazebo | 6 ft sides | 93.53 sq ft | 15% | 108 sq ft decking |
| Medium hexagonal gazebo | 8 ft sides | 166.28 sq ft | 15% | 191 sq ft decking |
| Large hexagonal gazebo | 10 ft sides | 259.81 sq ft | 15% | 299 sq ft decking |
| Hex tile accent floor | 4 ft sides | 41.57 sq ft | 15% | 48 sq ft tile |
| Hexagonal hot tub deck | 7 ft sides | 127.31 sq ft | 12% | 143 sq ft |
| Honeycomb garden bed | 3 ft sides | 23.38 sq ft | 10% | 25.7 sq ft sod/soil |
| Hex patio section | 5 ft sides | 64.95 sq ft | 15% | 75 sq ft pavers |
Hexagonal Tile Counting Guide
For individual small hexagonal tiles (like 4-inch or 6-inch hex bathroom tiles):
- Calculate the room area in sq ft using a standard room calculator.
- Calculate one tile's area: 2.59808 × (tile_side_in_ft)²
- Divide room area by one tile's area = tile count.
- Add 15% for edge cuts (hexagonal tiles have more edge waste than square tiles).
One tile side = 4 in = 0.333 ft
One tile area = 2.59808 × 0.333² = 2.59808 × 0.111 = 0.2884 sq ft
100 ÷ 0.2884 = 347 tiles + 15% = 399 tiles to order
Regular vs. Irregular Hexagon
This calculator is for regular hexagons only — all 6 sides equal, all angles 120°. Properties of a regular hexagon:
- Can be divided into exactly 6 equilateral triangles from the center.
- The circumradius (center to corner) equals the side length.
- The inradius (apothem) = side × √3/2 ≈ side × 0.866.
- Long diagonal = 2 × side length (corner to opposite corner).
- Covers 82.7% of its circumscribed circle's area.
For irregular hexagons, split into triangles and rectangles and sum the areas, or use the irregular shape calculator.
Related Calculators
For a circular gazebo or pool, use the circle square footage calculator. For a pentagonal shape, try the pentagon calculator. For rectangular areas around a hexagonal feature, use the rectangle square footage calculator. For full project material planning, use the multiple areas calculator.
Frequently Asked Questions
How do I calculate the area of a hexagon in square feet? +
Use the formula: Area = (3√3/2) × s² ≈ 2.59808 × s², where s is the side length in feet. Example: a hexagon with 6 ft sides = 2.59808 × 36 = 93.53 sq ft. Or enter the side length above for an instant result.
Can I calculate hexagon area from the apothem? +
Yes. For a regular hexagon, Area = 2√3 × a² ≈ 3.4641 × a², where a is the apothem (center to midpoint of a side). Example: apothem = 5.196 ft → area = 3.4641 × 26.999 = 93.53 sq ft (same as a 6 ft side hexagon, since apothem = s × √3/2).
What is the area of a hexagon with 6 ft sides? +
Area = 2.59808 × 6² = 2.59808 × 36 = 93.53 square feet (8.69 m²). Perimeter = 6 × 6 = 36 ft. Apothem = 6 × 0.866 = 5.196 ft. Long diagonal = 12 ft. Short diagonal = 10.39 ft.
What is the area of a hexagon with 10 ft sides? +
Area = 2.59808 × 10² = 259.81 square feet (24.14 m²). Perimeter = 60 ft. Apothem = 8.66 ft. Long diagonal = 20 ft. This is a large hexagonal gazebo floor — roughly equivalent to a 16×16 ft square room.
What is the difference between a regular and irregular hexagon? +
A regular hexagon has all 6 sides equal and all interior angles exactly 120°. An irregular hexagon has sides or angles of different sizes. This calculator works only for regular hexagons. For irregular shapes, split into triangles and rectangles and use the irregular shape calculator.
How do I find the apothem if I only know the side length? +
Apothem = side × (√3/2) ≈ side × 0.866. Example: 8 ft sides → apothem = 8 × 0.866 = 6.928 ft. The apothem is the distance from the center of the hexagon perpendicular to a side — it's the inradius.
How many tiles do I need for a hexagonal area? +
Step 1: Calculate the hexagon area (2.59808 × s²). Step 2: Find tile area in sq ft (e.g., a 12×12 in tile = 1 sq ft). Step 3: Divide total area by tile area. Step 4: Add 15% for cuts at the angled edges of the hexagon. Example: 93.53 sq ft hexagon, 12×12 tiles → 94 tiles + 15% = 109 tiles.
What is the perimeter of a regular hexagon? +
Perimeter = 6 × side length. Examples: 5 ft sides → 30 ft perimeter; 8 ft sides → 48 ft perimeter; 10 ft sides → 60 ft perimeter. Use this for ordering border trim, edging, or fencing around a hexagonal space.
How does a hexagon compare to a circle of the same width? +
A regular hexagon with side s fits inside a circle of radius s (the circumradius equals the side length). That circle has area π × s². The hexagon covers about 82.7% of that circle's area (2.598 × s² ÷ 3.14159 × s² = 0.827). So a hexagonal gazebo is slightly smaller than its circumscribed circle.
Where are hexagons used in real life? +
Hexagonal shapes appear in: gazebo floors, hexagonal tile patterns (bathroom and kitchen), honeycomb garden beds, outdoor paving stones, decorative pool surrounds, barn designs, hot tub decks, and architectural floor plans. Hexagons tile a plane perfectly with no gaps, making them ideal for flooring.
How do I measure a hexagonal room or patio for the side length? +
Measure from one corner to the adjacent corner (not across the full width). That is the side length s. Alternatively, measure the long diagonal (corner to opposite corner) and divide by 2 — that equals the side length for a regular hexagon. Or measure the full width across the flats (2 × apothem) and use apothem = width/2, then s = apothem ÷ 0.866.
Can I use this for hexagonal pavers or stepping stones? +
Yes. Calculate the hexagon area to know the total coverage. For individual hexagonal pavers: find the paver side length, calculate one paver's area (2.59808 × s²), then divide the total project area by one paver's area. Add 10–15% for edge cuts where the hexagonal pattern meets the project boundary.