SimCity 2000 (1993)
The blueprint for the dimetric city-builder. Each zone tile is twice as wide as tall, so the two ground axes land at 26.57° — measurable everywhere, identical wherever it sits on the map.
Perspective · two equal axes, one different · Pohlke 1853
The dimetric grid
A dimetric grid draws three parallel axes in which two are foreshortened equally and one differently — most often two ground axes climbing at the same shallow angle plus an emphasised vertical, with no vanishing point. Where isometric carries one scale across every axis, dimetric carries two: two faces share a measurement and one face is deliberately set apart. It is the quietly dominant projection of video games — the famous 2:1 tile is dimetric at 26.57°, not the 30° most people assume. Here is what the overlay does, the two-scale math behind it, the engineering standard that codified it, and when one face deserves the emphasis only dimetric gives.
- First documented
- 1853 (Pohlke, as a family)
- Popularised in
- Engineering & pixel-art games
- Origin culture
- German/British axonometry
- Difficulty
- Intermediate
- Axis scales
- 2 equal : 1 different
- Also known as
- Two-scale axonometric
See the dimetric grid on five built subjects
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A tall facade is where dimetric earns its keep: the two receding ground planes share one shallow scale while the vertical runs at full height. Drag the handle and watch which storeys and string-courses ride the emphasised vertical lines.
What the overlay shows
The dimetric overlay lays down three families of parallel lines: two ground families climbing at the same shallow angle — left-to-right and its mirror — and a set of true verticals drawn at a different, heavier weight. Those three directions are the projected images of the object's width, depth, and height. What makes the grid dimetric rather than isometric is that two of the three carry one scale and the third carries another. In the live tool the angle pair, the cell size, and the line weight are all adjustable, so you can set the classic 2:1 ratio or any engineering pair you need.
The defining property is selective emphasis. Like every parallel projection, dimetric has no vanishing point, so parallel edges never converge and the drawing stays measurable.4 But because one axis is set to a separate scale, dimetric lets you weight a single face above the other two — a top panel, a tall front, a long flank — without abandoning the measurability that distinguishes axonometric work from perspective. It is the game-art projection you reach for when isometric's perfect even-handedness is the wrong answer, and the form most often mislabelled when people compare dimetric vs isometric tiles.
The math, briefly
Isometric obeys one constraint: all three axes foreshorten equally. Dimetric relaxes that to a single, looser rule:
two axes share one scale · the third takes another · e.g. 2:1 ground ratio → arctan(0.5) ≈ 26.57°
Two things follow from that one constraint:
- Two scales, not one. Where isometric measures one unit per cell on every axis, dimetric carries two units — a shared scale on the equal pair and a separate scale on the odd axis. Pohlke's 1853 theorem is what guarantees that any such triple of axis directions is a valid parallel projection of three mutually perpendicular axes.7
- The 26.57° ground angle. The most common dimetric in practice is the 2:1 pixel ratio: a cell twice as wide as it is tall puts the two ground axes at arctan(0.5) ≈ 26.57° above horizontal — close to isometric's 30° but reached for an entirely different reason, integer pixel stepping rather than equal foreshortening.
Engineering practice tends to a different pair. A common dimetric standard uses scale ratios of roughly 1 : 1 : 0.5 with a defined angle pair, so the two full-scale faces stay easy to dimension while the half-scale axis recedes — a convention recorded among the axonometric methods of ISO 5456-3.5 The relationship between such parameters and the underlying parallel-projection geometry is laid out in Carlbom and Paciorek's survey.4 The grid keeps the two scales consistent for you — open it in the live tool and set the angle pair to match your standard.
History — what is real and what is myth
Verified history (with primary sources)
1822 — the axonometric idea arrives. William Farish formalised the equal-axis case in his 1822 paper On Isometrical Perspective, giving engineers a way to draw machines so measurements survived on every axis.1 Dimetric is the natural neighbour of that idea: keep the parallel-projection logic, but let one axis differ.
1853 — Pohlke generalises the families. The German geometer Karl Pohlke stated the fundamental theorem of axonometry, which showed that any three line segments from a point can stand for three equal, mutually perpendicular axes. That single result splits parallel projection into the three families we still name today — isometric (all equal), dimetric (two equal), and trimetric (all different) — and so dimetric exists as a defined category from this point on.7
19th–20th century — the engineer's option. As industrial drawing matured, dimetric took its place beside isometric in the draughtsman's repertoire, a lineage traced in Peter Booker's A History of Engineering Drawing.2 It was eventually written into ISO 5456-3 as one of the recognised axonometric methods, and remains a standard notation in references such as Francis Ching's Architectural Graphics when one face of a form deserves emphasis.56 Patrick Maynard's study of graphic expression situates these projection choices as deliberate acts of depiction rather than mere convention.8
Confusions that won't die
"Game isometric is isometric." Most of it is dimetric. The tile that defined a genre — the 2:1 cell of the classic city-builders and dungeon-crawlers — sits at 26.57°, not 30°. Two equal ground axes plus a vertical is the textbook description of dimetric, so the look an entire industry calls "isometric" is, by the geometry, the most-drawn dimetric projection in history. The misnomer stuck because the visual difference from true isometric is small and the word "isometric" had already entered the vernacular.3
"Dimetric is just bad isometric." It is a deliberate choice, not a degraded one. Selecting two equal axes and one different is how you tell the viewer which face matters — the emphasised axis becomes the subject's dominant dimension. An engineer reaching for a 1:1:0.5 dimetric is not failing to hit isometric; they are choosing to keep two faces measurable while letting the third recede.
"It's a kind of perspective." Dimetric is a parallel projection, the opposite limit of linear perspective. Carlbom and Paciorek's survey places both on one continuum: perspective has a finite centre of projection, axonometric pushes that centre to infinity, so the converging lines of perspective become the strictly parallel lines of every axonometric family — dimetric included.4
When to use it (and when not)
| If you want to... | Use dimetric | Don't use it for... | Difficulty |
|---|---|---|---|
| Build tile-based game art in the classic look | The 2:1 ratio tiles at integer pixel steps — the genre's native grid | Subjects where all three faces matter equally (use isometric) | Intermediate |
| Emphasise one face of a part or product | The odd-scale axis weights the dominant face while two stay measurable | Hero renders that need depth and drama (use 2-point perspective) | Intermediate |
| Draw an engineering view to a defined standard | A 1:1:0.5 pair keeps two faces dimensioned and one foreshortened | Quick neutral three-quarter views (isometric is simpler) | Advanced |
| Show a tall facade or stacked assembly | The emphasised vertical reads at full height against shallow ground axes | Organic or curved subjects with no rectilinear structure | Intermediate |
| Match a retro pixel-art aesthetic exactly | 26.57° carries the visual signature of an entire era of games | Floating-point vector pipelines that gain nothing from integer steps | Beginner |
Famous examples of the projection at work
Six works and products where dimetric — usually the 2:1 ratio, sometimes the engineering pair — is demonstrably the chosen system.
Diablo II (2000)
The dungeon-crawler standard. Its 2:1 floor tiles are dimetric, letting hand-painted sprites repeat across vast levels while a tall doorway or column reads cleanly on the vertical.
Q*bert (1982)
An early pyramid of stacked cubes rendered with two equal ground axes and a vertical hop. No camera, no convergence — just a parallel projection chosen so the platformer logic stays legible.
Fallout 1–2 (1997–98)
The wasteland's "isometric" overhead view is dimetric in practice — a 2:1 tile grid that let the team author dense ruined towns with consistent, walkable cell geometry.
Engineering dimetric part drawings
A 1:1:0.5 dimetric keeps two faces of a casting full-scale and dimensionable while the third recedes — the documented use the standard preserves for emphasis without losing measure.
Pixel-art tile sets
Modern retro-styled games keep the 2:1 dimetric ratio on purpose — it tessellates at integer pixels and carries the era's visual signature that true 30° isometric would quietly break.
Common mistakes
1
Calling a 2:1 tile set "isometric"
The 2:1 ratio sits at 26.57°, not 30°, which makes it dimetric. The label is harmless in conversation but causes real trouble when a collaborator authors true-30° assets to match your "isometric" set and the tiles refuse to align.
Fix: state the actual ratio in your asset spec — "2:1 dimetric, 26.57°" — so everyone builds to the same grid.
2
Letting the two scales drift
Dimetric only stays measurable if the two equal axes truly share one scale and the third holds its own. Eyeballing the odd axis differently from object to object turns a clean two-scale drawing into a guess.
Fix: lock the cell size on the equal pair and pick one fixed ratio for the odd axis before you start, then keep both for the whole drawing.
3
Emphasising the wrong axis
The point of dimetric is to weight one face. Putting the different scale on an axis the subject doesn't care about wastes the projection's only advantage over isometric and leaves the drawing looking simply lopsided.
Fix: decide which face is the subject's headline — tall front, wide top, long flank — and assign the odd scale to that axis before blocking in.
4
Adding a vanishing point "to help"
Letting the parallel axes converge even slightly defeats the entire purpose — the two-scale relationship stops being readable and the drawing becomes a weak perspective with no measurement at all.
Fix: keep every axis strictly parallel. If you want convergence, you want perspective — switch tools rather than bending the grid.
How different disciplines use it
For game artists
Dimetric is the genre grid. Settle on the 2:1 ratio before a single tile is drawn — it dictates the whole asset pipeline, and tile engines (Unity Tilemap, Godot, Phaser) expect a consistent cell so sprites stack without gaps. The reward is that depth-sorting collapses to a back-to-front cell order rather than a z-buffer, and a tile authored once reads correctly anywhere on the map. Keep one tab on the 2:1 ratio and another on true 30° isometric if you need to compare the two looks side by side.
For technical illustrators
When a diagram has a hero face — the labelled front of a device, the top of an assembly — dimetric lets you give it the larger scale while the other two faces stay measurable for callouts and dimensions. Block the form on the grid first, commit every edge to one of the three axes, then reserve your annotation density for the emphasised face. The parallel axes mean exploded parts drift apart without losing alignment.
For product designers
Dimetric is the choice when one dimension carries the design intent — a tall bottle, a slim remote, a packaging net whose front panel is the brand. Put the emphasised scale on that axis and the product reads as itself rather than as a neutral three-quarter box. Width and depth still share one scale, so a caliper measurement on those two faces maps straight to the drawing; pair it with a consistent ellipse treatment for bores and fillets.
For architects
For a tall, narrow building the architect's axonometric can be tuned dimetric so the vertical reads at full height against shallower ground axes — useful for slender towers, stair cores, and section studies where height is the story. As with all axonometric notation, covered as a core skill in Ching's Architectural Graphics, it stays measurable, so a massing study communicates proportion without hiding dimensions behind perspective foreshortening.
"Since the 1920s axonometry, or parallel perspective, has provided an important graphic technique for artists, architects, and engineers and has taken on a new significance with the advent of visual computing."
Jan Krikke, Axonometry: A Matter of Perspective, IEEE Computer Graphics & Applications (2000)3
Frequently asked questions
What is a dimetric grid?
A parallel-projection drawing guide in which two of the three principal axes are foreshortened equally and the third differently. There is no vanishing point, so parallel edges stay parallel, but unlike isometric the drawing carries two scales rather than one — two faces share a measurement and one face is set apart for emphasis.
Is video-game "isometric" actually dimetric?
Usually yes. The 2:1 pixel ratio in SimCity 2000, Diablo II, and most pixel-art tile engines makes the two ground axes climb at arctan(0.5) ≈ 26.57°, not the true isometric 30°. Two axes equal, one different is the definition of dimetric, so the games most people call isometric are dimetric. The 2:1 ratio was chosen because integer pixel steps tiled cleanly and rendered fast on 1990s hardware.
How is dimetric different from isometric?
Isometric foreshortens all three axes by the same factor, so one cell measures one unit on every axis — a single scale. Dimetric keeps two axes equal and sets the third apart, so the drawing carries two scales. Isometric is the most balanced of the three axonometric families; dimetric trades a little of that balance to emphasise one face.
What angle is the 2:1 dimetric ratio?
The classic 2:1 tile — twice as wide as it is tall — puts the two ground axes at arctan(0.5) ≈ 26.57° above horizontal. That is the most common dimetric in the world by sheer volume of pixels drawn, because it underpins decades of tile-based game art. True isometric would be 30°; the 26.57° choice keeps every step an integer number of pixels.
Is dimetric a standard in engineering drawing?
Yes. Dimetric is one of the recognised axonometric methods codified in ISO 5456-3, alongside isometric. Engineering dimetric typically uses scale ratios such as 1:1:0.5 with a defined angle pair, so a part can be shown with one face — often the most detailed — emphasised while the other two stay measurable.
Who established the dimetric family?
No single person invented dimetric. Karl Pohlke's 1853 fundamental theorem of axonometry generalised parallel projection into the isometric, dimetric, and trimetric families, and engineering-drawing practice — later codified in standards — singled dimetric out as a useful method when one face deserves emphasis.
Does dimetric show real depth?
No. Like every parallel projection, dimetric has no perspective convergence, so distant objects are the same size as near ones. It trades atmospheric depth for measurability and for the ability to weight one face above the others. Use linear perspective when you need a genuine sense of distance.
What software supports dimetric grids?
Tile-based game engines (Unity Tilemap, Godot, Phaser) handle the 2:1 dimetric ratio natively, and vector tools (Illustrator, Affinity Designer, Inkscape) can be set to any axis pair. Grid Maker Pro overlays an adjustable dimetric grid over any reference image in the browser, with PNG, SVG, and PDF export.
References
- Farish, W. "On Isometrical Perspective." Transactions of the Cambridge Philosophical Society, Vol. 1, pp. 1–20 (1822).
- Booker, P.J. A History of Engineering Drawing. Chatto & Windus, London (1963).
- Krikke, J. "Axonometry: A Matter of Perspective." IEEE Computer Graphics and Applications 20(4), 7–11 (2000). DOI: 10.1109/38.851742.
- Carlbom, I. & Paciorek, J. "Planar Geometric Projections and Viewing Transformations." ACM Computing Surveys 10(4), 465–502 (1978). DOI: 10.1145/356744.356750.
- International Organization for Standardization. ISO 5456-3:1996 — Technical drawings — Projection methods — Part 3: Axonometric representations. Geneva (1996).
- Ching, F.D.K. Architectural Graphics (6th ed.). Wiley (2015). ISBN 978-1-118-73948-1.
- Pohlke, K. Fundamental theorem of axonometry (1853). See Monge, G. Géométrie descriptive, Baudouin, Paris (1799), for the descriptive-geometry foundation it generalises.
- Maynard, P. Drawing Distinctions: The Varieties of Graphic Expression. Cornell University Press (2005). ISBN 978-0-8014-4263-6.
Other Perspective overlays
Notes from the studio · Three practitioners on the dimetric grid
Illustrative composites of how the tool gets used in practice — not quotes from named individuals.
Our whole tile library is 2:1 dimetric, and I keep the overlay pinned to that exact ratio. Authoring against a true 26.57° grid stops the seam-hunting we used to do every milestone.
For device cutaways I want one face loud and two faces measurable. Dimetric does that in a single view, and the bookmarkable URL reopens with my angle pair already set.
A bottle is all about its height, so I put the odd scale on the vertical and let width and depth share the rest. Free and browser-only means I test a packaging render in seconds.
Open the dimetric grid overlay
Drop a reference image. The dimetric grid overlay applies in one click — set the 2:1 ratio or your own angle pair. Free, in your browser.
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