Worked example: a 13-block dome over a round room
A diameter-13 dome is the classic roof for a small round tower, an observatory or a greenhouse. It is 7 courses tall, adds about 6 blocks of height above the wall top, and the hollow shell costs 225 blocks (3 × 64 + 33). Here is the whole thing course by course:
| Course | Height above base | Hollow shell | Solid | Running total (hollow) |
|---|---|---|---|---|
| 1 (base) | +0 | 36 | 137 | 36 |
| 2 | +1 | 36 | 137 | 72 |
| 3 | +2 | 32 | 121 | 104 |
| 4 | +3 | 32 | 101 | 136 |
| 5 | +4 | 32 | 89 | 168 |
| 6 | +5 | 36 | 57 | 204 |
| 7 (cap) | +6 | 21 | 21 | 225 |
| Total | 225 | 663 |
Two things to notice. The courses do not shrink smoothly — they hold at 36 for the first two, drop to 32 for three courses, then climb back to 36 in the course just below the top, because the shell is flattening out there. And the cap itself is 21 blocks — a flat disc, not a point:
............. ............. ............. ............. .....XXX..... ....XXXXX.... ....XXXXX.... ....XXXXX.... .....XXX..... ............. ............. ............. .............
That flat top is correct for a hemisphere. A sphere's surface is nearly horizontal at the pole, so the last course of a shell is a broad shallow disc. A dome that tapers to a single block is not a dome, it is a cone — if you want a spire, build the hemisphere and put the spire on top of the cap.
The base course is just a circle — exactly
This is worth knowing before you start, because it saves a whole planning step: the base course of a hollow dome is identical, block for block, to the flat circle outline of the same diameter. Not similar — identical. We check this in the test suite for every diameter from 3 to 64, and the "dome base" and "circle ring" columns below are computed independently and come out the same every time.
| Diameter | Courses | Dome base course | Flat circle ring | Hollow dome total | Solid dome total |
|---|---|---|---|---|---|
| 9 | 5 | 24 | 24 | 105 | 229 |
| 11 | 6 | 28 | 28 | 153 | 418 |
| 13 | 7 | 36 | 36 | 225 | 663 |
| 15 | 8 | 40 | 40 | 285 | 984 |
| 17 | 9 | 48 | 48 | 369 | 1,389 |
| 21 | 11 | 56 | 56 | 569 | 2,647 |
| 25 | 13 | 68 | 68 | 809 | 4,353 |
| 31 | 16 | 84 | 84 | 1,233 | 8,132 |
The practical consequence: build your round wall using the ring from the circle generator, and the dome will land on it perfectly with no fudging at the junction. It also means you can check your dome is on-plan before you leave the ground — if the base course does not match the flat circle, something is already off.
How tall is the dome, and how much headroom do you get?
A hemisphere of diameter d rises about d/2 above its base, so the 13-block dome above adds roughly 6 blocks of height. That is the clearance at the very centre only; at the rim the ceiling meets the wall. If you need usable standing room across the whole floor, add a straight wall section underneath and let the dome sit on top of it — a 21-block dome on a 4-block wall gives you a room that is comfortable everywhere, not just in the middle.
Cost scales fast. Going from a 13-block dome (225 blocks) to a 31-block one (1,233 blocks) is roughly a 5.5× increase in material for a 2.4× increase in diameter. Surface area grows with the square of the diameter, so budget accordingly before you start a stadium.
Building order for a dome
- Build the base course on the ground or on the wall top. It is the flat circle ring — easy to verify.
- Work up one course at a time, centring each new ring on the one below using the flat runs at top, bottom, left and right as alignment marks.
- Support the overhang. From the second or third course onward every ring overhangs; use scaffolding or a temporary central pillar with arms.
- Place the cap disc last, then remove the supports from the inside working outward.
Related tools
- Need the full ball rather than a roof? The Minecraft sphere generator slices a complete sphere, including the lower half this page leaves out.
- Building the wall or floor under the dome? The Minecraft circle generator gives you the matching ring and the filled disc for the floor.
- Choosing a diameter? The circle chart compares every size from 5 to 32 with previews and counts, which is the fastest way to pick a footprint.
- For an elongated roof over a rectangular hall, start from the oval generator and build a barrel vault from repeated arcs instead of a dome.