Hexagonal bipyramid calculator
Get the volume and surface of a regular hexagonal bipyramid from its equator side and half-height: side 2 with half-height 3 gives a volume of 12√3 and a surface of 24√3. The apex-to-apex height comes too. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Base side
- 2
- Half height
- 3
- Total height
- 6
- Base area
- 10.3923048454
- Volume
- 20.7846096908
- Surface area
- 41.5692193817
A regular hexagonal bipyramid is the solid formed by joining two congruent regular hexagonal pyramids base-to-base along a shared equatorial regular hexagon, so that twelve isosceles triangular faces meet at two opposite apices on the axis through the hexagon center. Given the common equatorial edge length and the half-height from that equatorial plane to either apex, this calculator returns the enclosed volume, the equatorial hexagonal area used in the derivation, the mid-edge face slant height shared by all twelve triangles, the total surface area of those faces, and the full apex-to-apex height, using the classic closed-form formulas from solid geometry.
Where hexagonal bipyramid calculations show up in real work
Secondary-school and college solid-geometry courses constantly ask students for the volume and surface area of a regular hexagonal bipyramid given equatorial edge and half-height or total height; a trusted calculator with a strict non-negative input gate speeds homework grading and removes spreadsheet mistakes where someone uses a single pyramid formula or forgets that the equator is internal and should not be double-counted in surface area.
Crystallography and mineralogy textbooks describe hexagonal bipyramidal crystal habits; converting lattice-friendly side and half-height into metric volume and face area supports lab demos and teaching models. Architecture, fabrication, and packaging workflows size dual-tapered hexagonal ornaments, pavilion hubs, and display solids from plan edge length and half apex height; volume feeds fill and material estimates while total surface area feeds cladding and paint takeoffs. Game, graphics, and CAD libraries store regular bipyramid primitives for collision proxies and lighting volumes; echoing method plus the two inputs makes debug property panels self-describing.
If you later need a single hexagonal pyramid, a hexagonal prism, or an antiprism, treat those as separate search intents rather than overloading this hexagonal-bipyramid landing.
What you can do with it
Homework and exam checks
Compute regular hexagonal bipyramid volume and surface area from base side and half-height, and reject negative dimensions with a clear error.
Crystal models and fabrication
From equatorial edge and half-height, recover fill volume and face area for dual-tapered hexagonal ornaments, demos, and display solids.
CAD and game bipyramid metrics
Turn base side and half-height into stable volume and surface figures for layout, material estimates, and property panels.
FAQ
What does it cost?
The browser tool is free and runs locally.
What is a hexagonal bipyramid?
Two identical regular hexagonal pyramids joined base to base along a shared hexagon. Twelve isosceles triangles meet at two opposite apexes that sit on the axis through the centre of that hexagon.
Is the half-height the same as the total height?
No. The half-height runs from the plane of the equator to one apex, and the total height from apex to apex is twice that. A side of 2 with a half-height of 3 gives a total height of 6.
Why is the shared hexagon not counted in the surface area?
Because it ends up inside the solid once the two pyramids are joined. Only the twelve triangular faces remain on the outside, and counting the equator anyway is a common slip.
Where is a hexagonal bipyramid used?
Mineralogy books describe crystals with this shape, and makers use it for twin-tapered ornaments, pavilion hubs and display pieces, where volume sets the fill and the surface sets cladding or paint.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/geom/hexagonal-bipyramid \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"base_side":2,"half_height":3}'const res = await fetch("https://api.kit.forhosting.com/geom/hexagonal-bipyramid", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"base_side": 2,
"half_height": 3
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geom/hexagonal-bipyramid",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"base_side": 2,
"half_height": 3
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/hexagonal-bipyramid", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"base_side":2,"half_height":3}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"base_side":2,"half_height":3}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/hexagonal-bipyramid", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"base_side": 2,
"half_height": 3
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geom.hexagonal_bipyramid",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Any negative base side or half-height is rejected with a clear invalid_input error instead of a silent nonsense volume. No network calls, no random sampling, and no floating-point surprises beyond ordinary IEEE-754 arithmetic on the numbers you provide.
How volume and surface area are computed
For surface area there is no exterior equatorial face left after the two pyramids are joined; only twelve congruent isosceles triangles remain. Form the equatorial apothem (inradius of the hexagon) r equals (√3/2) a; the face slant height measured from the midpoint of an equatorial edge up the altitude of a lateral face is m equals the square root of h squared plus r squared, which is √(h² + 3a²/4). Each pyramid contributes lateral area 3 a m, so total surface area is 6 a m. Because the path uses only multiplication, division, and square roots of three and of a sum of squares, it is deterministic, O(1), and free of iterative solvers. Label the side length of the regular hexagonal equator as base_side a and the perpendicular distance from that equatorial plane to either apex as half_height h, so the total apex-to-apex height is two h. The area of the equatorial regular hexagon is three-halves times the square root of three times a squared: base_area equals (3√3/2) a². Each half is a regular hexagonal pyramid of height h, so one half has volume (1/3) base_area h and the full bipyramid has volume twice that: (2/3) base_area h, which simplifies to volume equals √3 a² h. Classic checks include a equals two and h equals three: base_area equals 6√3, volume equals 12√3, slant_height equals 2√3, and surface area equals 24√3. Huge magnitudes can still overflow IEEE-754 double range; when any result is non-finite the request fails with a clear overflow message instead of returning Infinity in JSON. That closed form matches solid-geometry textbooks and keeps automated graders aligned with hand computation on the same inputs.
What you send and what you get back
There is no optional circumradius, unequal apex heights, or oblique offset—this landing is the regular centered hexagonal bipyramid from equatorial side and half-height only. Example checks: side two and half-height three recover the √3 multiples above; side one and half-height one yield volume √3 and a surface area of six times the face slant for unit side. Wire the free browser tool for quick sanity checks, then call the identical contract from scripts for bulk evaluation without reimplementing hexagonal-bipyramid formulas in every language. Provide two required finite numbers: base_side is the side length of the regular hexagonal equator and must be strictly positive; half_height is the perpendicular equator-to-apex distance and must also be strictly positive. Negative, zero, missing, empty, non-numeric, NaN, and Infinity values are rejected with invalid_input and are not charged. On success the JSON response returns base_side, half_height, total_height (always two times half_height), base_area, volume, surface_area, slant_height, and method set to regular_hexagonal_bipyramid_volume_surface so logs and teaching UIs can document the algorithm. API pricing is the published base of $0.002 per successful item.
Where hexagonal bipyramid calculations show up in real work
Because this capability is a pure parse engine, failed validation does not consume balance and successful runs stay at $0.002 per item.
Technical questions
What formulas does this calculator use?
Equatorial area A = (3√3/2) a²; volume V = √3 a² h = (2/3) A h; slant height m = √(h² + 3a²/4); surface area S = 6 a m (twelve triangular faces). The response includes method: "regular_hexagonal_bipyramid_volume_surface".
What happens if base_side or half_height is negative?
The request fails with invalid_input. Both values must be strictly greater than zero; the error message names the field (base_side or half_height). Negative dimensions are never turned into absolute values silently.
Is half_height the same as total height?
No. half_height is the perpendicular distance from the equatorial plane to either apex. total_height in the response is always twice half_height (apex to apex).
Does surface_area include the equatorial hexagon?
No. After the two pyramids are joined base-to-base, the equator is interior. surface_area is only the twelve outer triangular faces.