Volume of a Hexagonal Pyramid Calculator
Find the volume and all surface areas of a regular hexagonal pyramid — six equal triangular faces meeting at one apex above a regular hexagonal base. Enter the base side length and perpendicular height.
units
units
V = (√3/2) × a² × h — one-third of a hexagonal prism
V = (√3/2)a²h
173.2051 units³- 1
Base area (regular hexagon)
(3 × √3 ÷ 2) × 5² = 64.9519Area of a regular hexagon = (3√3/2) × a². - 2
Volume = (1/3) × base area × height
(1 ÷ 3) × 64.9519 × 8 = 173.2051
How does this calculator work?
Volume of a regular hexagonal pyramid: V = (√3/2) × a² × h, where a is the base side length and h is the perpendicular height. Base area = (3√3/2)a². Slant height l = √(h² + 3a²/4); lateral surface area = 3al; total surface area = (3√3/2)a² + 3al.
Formula
How this is calculated
A regular hexagonal pyramid has a regular hexagon as its base — six equal sides and six equal angles — and six congruent isosceles triangular lateral faces that meet at the apex directly above the base centre. The volume follows the universal pyramid rule: V = (1/3) × base area × perpendicular height.
The base area of a regular hexagon with side a equals (3√3/2) × a². Substituting into the pyramid formula gives V = (1/3) × (3√3/2) × a² × h = (√3/2) × a² × h. For the slant height — the distance from the apex to the midpoint of a base edge measured along the face — you need the apothem of the hexagon (perpendicular distance from centre to the midpoint of a side), which is (√3/2) × a. Slant height l = √(h² + apothem²) = √(h² + 3a²/4).
Each of the six triangular lateral faces has base a and height l, giving face area (1/2)al. Total lateral area = 6 × (1/2)al = 3al. Total surface area = hexagonal base + lateral = (3√3/2)a² + 3al. All inputs must share the same length unit — the volume is in cubic units and areas in square units of that measure.
Frequently asked questions
The apothem is the perpendicular distance from the hexagon's centre to the midpoint of one of its edges, equal to (√3/2) × a. For a = 5 units the apothem is about 4.330 units. It appears in the slant height formula l = √(h² + apothem²).
A hexagonal pyramid with the same base and height as a prism has exactly one-third of the prism's volume — V_pyramid = V_prism / 3. This is the universal "one-third" rule for all pyramids versus their corresponding prisms.
The perpendicular height h is the vertical distance from base to apex. The slant height l is the distance along a triangular face from apex to the midpoint of a base edge — always longer than h. It equals √(h² + apothem²) and is used to compute lateral face area.
Also known as
TG we-Calculate Editorial Team. (2026). Volume of a Hexagonal Pyramid Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/volume-hexagonal-pyramid-calculator
TG we-Calculate Editorial Team. "Volume of a Hexagonal Pyramid Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/volume-hexagonal-pyramid-calculator.
TG we-Calculate Editorial Team, "Volume of a Hexagonal Pyramid Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/volume-hexagonal-pyramid-calculator
@misc{wecalculate_volume_hexagonal_pyramid_calculator, title = {Volume of a Hexagonal Pyramid Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/volume-hexagonal-pyramid-calculator}}, year = {2026}, note = {TG we-Calculate} }
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