About the Hexagonal Prism Calculator
A regular hexagonal prism has two identical regular hexagons as its ends and six rectangular side faces. It is the shape of a hex nut or bolt head, a pencil, many honeycomb cells, hexagonal planters and pavers, and the columns of basalt at the Giant’s Causeway.
Enter the length of one side of the hexagon and the height (length) of the prism, and this hexagonal prism calculator returns the volume, the area of each hexagonal base, the lateral area of the six sides, the total surface area, the apothem and the long diagonals. Choose a length unit to see the capacity in litres and US gallons — useful for hexagonal planters, tanks and aquariums.
The tool assumes a right, regular prism: all six base edges are equal and the sides meet the base at 90°. If you know the distance across the flats (the wrench size of a nut) instead of the side, divide it by √3 to get the side length.
With the default inputs, the volume is 415.6922. Change any value above to recalculate instantly.
How to use the hexagonal prism calculator
- 1Measure one side of the hexagonal end (or divide the across-flats width by √3).
- 2Measure the height or length of the prism.
- 3Pick a length unit if you want the capacity in litres and gallons.
- 4Read the volume, surface areas and diagonals.
Formula and method
A regular hexagon splits into six equilateral triangles of side a, each with area (√3/4)a², so the base area is (3√3/2)a² ≈ 2.598a². Like every right prism, the volume is base area × height.
The six side faces are rectangles a wide and h tall, giving a lateral area of 6ah; the total surface area adds the two hexagonal ends. The apothem (centre to the middle of a side) is (√3/2)a, so the width across the flats is √3·a, the width across the corners is 2a, and the longest space diagonal, from a top corner to the opposite bottom corner, is √(4a² + h²).
- a
- Base edge (side length of the hexagon)
- h
- Height or length of the prism
- A_base
- Area of one hexagonal end
- V
- Volume
Worked examples
Side 4, height 10
The base area is 2.598 × 4² ≈ 41.57, so V = 41.57 × 10 ≈ 415.69 cubic units. The six sides add 6 × 4 × 10 = 240, and with both hexagons the total surface is about 323.14. The longest diagonal is √(8² + 10²) ≈ 12.81.
Hexagonal planter: 20 cm sides, 35 cm tall
Each hexagon is 2.598 × 400 ≈ 1,039.2 cm², so the planter holds 1,039.2 × 35 ≈ 36,373 cm³ — about 36.4 litres or 9.6 US gallons of soil. It measures about 34.6 cm across the flats and 40 cm across the corners.
Pencil: 4 mm sides, 175 mm long
A standard hexagonal pencil about 6.9 mm across the flats has 4 mm sides. V = 41.57 × 175 ≈ 7,275 mm³ and the painted outer surface (sides plus both ends) is about 4,283 mm².
Frequently asked questions
What is the formula for the volume of a hexagonal prism?+
V = (3√3/2) × a² × h ≈ 2.598 × a² × h, where a is the hexagon side and h the prism height. For a = 4 and h = 10 the volume is about 415.7 cubic units.
How do I find the surface area of a hexagonal prism?+
Add the six rectangular sides (6 × a × h) and the two hexagonal ends (2 × 2.598 × a²). That simplifies to 6ah + 3√3 a². For a = 4 and h = 10 it is 240 + 83.14 ≈ 323.1 square units.
How many faces, edges and vertices does a hexagonal prism have?+
A hexagonal prism has 8 faces (2 hexagons and 6 rectangles), 18 edges and 12 vertices, which satisfies Euler’s formula F + V − E = 8 + 12 − 18 = 2.
How do I get the side length from the width of a hex nut?+
The wrench size is the distance across the flats, which equals √3 × side. Divide by 1.732 to get the side: a 13 mm nut has sides of about 7.51 mm. The distance across the corners is twice the side.
Does this work for irregular hexagonal prisms?+
No — it assumes all six sides are equal. For an irregular hexagonal base, find the base area with the shoelace formula and multiply by the height; the volume of any right prism is base area × height.