Hexagonal Pyramid Calculator — Volume and Surface Area
Enter the base side length and height of a right hexagonal pyramid to get the volume, total surface area, lateral area, slant height, lateral edge length and base apothem instantly.
V = (√3/2) × a² × h
V = 173.21
- 1
Square the base side
a² = 5² = 25 - 2
Apply √3 ÷ 2 factor
(√3 ÷ 2) × 25 = 21.6506√3/2 ≈ 0.866025 is the area coefficient for a regular hexagonal base divided by 3 - 3
Volume V = (√3/2) × a² × h
21.6506 × 8 = 173.2051
How does this calculator work?
For a hexagonal pyramid with base side a and height h: Volume = (√3/2)a²h, Total surface area = (3√3/2)a² + 3al, where the slant height l = √(h² + 3a²/4). The six triangular lateral faces each have base a and height l.
Formula
How this is calculated
A right hexagonal pyramid has a regular hexagon as its base and an apex directly above the centre. The base has side length a, and the perpendicular (vertical) height from base to apex is h.
The base area is the standard regular hexagon formula: (3√3/2)a². The base apothem (perpendicular from the centre of the base to the midpoint of a base edge) is (√3/2)a. The slant height l is the distance from the apex to the midpoint of a base edge, measured along the triangular face: l = √(h² + ap²) = √(h² + (3a²/4)). The lateral surface comprises six congruent isosceles triangles, each with base a and height l, giving lateral area = 6 × (1/2)al = 3al. Total surface area is base area plus lateral area.
Volume equals one-third of base area times height: V = (1/3) × (3√3/2)a² × h = (√3/2)a²h. The lateral edge e (from apex to a base vertex) is √(h² + a²), because the distance from the base centre to a vertex equals the side length a for a regular hexagon.
Frequently asked questions
The slant height l is the distance from the apex to the midpoint of a base edge, measured along the sloping face. It equals √(h² + ap²), where ap = (√3/2)a is the base apothem. This is different from the lateral edge e = √(h² + a²), which runs from the apex to a base vertex.
Lateral area covers only the six triangular sloping faces: LA = 3al. Total surface area adds the hexagonal base: SA = (3√3/2)a² + 3al. Use lateral area when painting only the sides; use total surface area when covering the entire solid including the base.
A hexagonal pyramid has six triangular faces and a hexagonal base, while a square pyramid has four triangular faces and a square base. The hexagonal pyramid has a larger base area relative to the same "radius" and a higher volume for the same height and base size.
Also known as
TG we-Calculate Editorial Team. (2026). Hexagonal Pyramid Calculator — Volume and Surface Area [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hexagonal-pyramid-calculator
TG we-Calculate Editorial Team. "Hexagonal Pyramid Calculator — Volume and Surface Area." TG we-Calculate. 2026. https://we-calculate.com/calculator/hexagonal-pyramid-calculator.
TG we-Calculate Editorial Team, "Hexagonal Pyramid Calculator — Volume and Surface Area," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hexagonal-pyramid-calculator
@misc{wecalculate_hexagonal_pyramid_calculator, title = {Hexagonal Pyramid Calculator — Volume and Surface Area}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hexagonal-pyramid-calculator}}, year = {2026}, note = {TG we-Calculate} }
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