What this calculator does
A Minecraft arch, the kind used over a doorway, bridge or tunnel entrance, is built by stacking a different number of blocks in each column so the top edge curves rather than running flat or at a sharp angle. Working that shape out by eye tends to produce a lopsided result, especially past a handful of blocks wide.
This calculator treats the arch as a semicircle: for a chosen width, it works out how tall each column needs to be so the tops trace a smooth curved profile, then lays the whole thing out as a block grid you can build from directly.
The formula
The arch is treated as the top half of a circle of diameter equal to the arch width. For each column, the height is the rounded distance from the centre line to the circle's edge at that column's position, using height = round(square root of (radius squared minus distance-from-centre squared)). Columns near the centre get the tallest stacks, and columns near the edges taper down.
| Term | Meaning |
|---|---|
| Arch width | The number of blocks the arch spans, edge to edge, at its base. |
| Radius | Half the arch width, used as the radius of the semicircle the arch traces. |
| Column height | How many blocks tall a given column in the arch needs to be. |
The inputs explained
| Field | What to enter |
|---|---|
| Arch width (blocks) | The width of the arch opening in blocks. Odd widths give a single tallest centre column; even widths give two matching tallest columns. |
When to use it
Building a doorway or gate arch
A narrower arch, roughly 5 to 9 blocks wide, suits a doorway or small gate opening where you want a curved top without an overly tall structure.
Building a bridge or tunnel entrance
A wider arch spans a bridge deck or tunnel mouth, and the same column-height layout scales up cleanly to those larger widths.
Matching an arch to an existing circle build
If you have already used a full circle elsewhere in a build, using the same width here keeps the curvature visually consistent between the two structures.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does arch height change with width?
The tallest column height for a range of arch widths.
| Arch width | Arch height at centre | Total blocks needed |
|---|---|---|
| 5 blocks | 3 blocks | 11 |
| 7 blocks | 4 blocks | 20 |
| 9 blocks | 5 blocks | 31 |
| 11 blocks | 6 blocks | 48 |
| 15 blocks | 8 blocks | 90 |
| 21 blocks | 11 blocks | 173 |
Questions
Why is my arch not perfectly symmetric?
It should be. The height formula is applied symmetrically around the centre column, so any width should produce a mirror-image profile either side of the middle. If it looks off, double check the width entered matches what you intend to build.
What is the difference between this and a full circle generator?
A circle generator fills or outlines a complete ring or disc shape. This tool only lays out the top curved half as a set of column heights, which is the shape actually needed for a doorway, bridge or tunnel arch rather than a full circle.
Can I build a pointed arch instead of a rounded one with this?
No, this generates a semicircular profile specifically. A pointed (Gothic-style) arch uses a different geometric construction and is not what this tool calculates.
Why is there a maximum width limit?
The block pattern is shown as a text grid on the page, and very wide arches would produce a grid too large to display or read usefully, so the width is capped to keep the output practical.
For a full circle layout instead of an arch, see the Minecraft Circle Generator.