21:9 Is Never Exactly 21:9
At every width from 640 to 3840, a 21:9 frame needs a fractional height, so no whole-pixel frame is exactly 21:9. At 1920 wide the exact height is 822.857 pixels. Round to 823 and the real ratio is 2.3329:1, off by 0.0174%.
Direct answer: 0 of 8 common widths hit 21:9 exactlyWhy whole pixels matter
A frame has an integer number of pixels on each side. Ratios like 16:9, 4:3 and 2:1 are built from small integers, so they land on whole numbers at friendly widths: 1920 × 1080 is exactly 16:9, and 3840 × 2160 is exactly 16:9 again.
21:9 is a marketing name for roughly 2.33:1, and 2.39:1 is a cinema ratio inherited from anamorphic projection. Neither is a small-integer fraction. Divide 1920 by 21/9 and you get 822.857, which is not a pixel count anybody can render.
The rounding is small enough that no viewer will notice it. It still matters in three places: when a tool refuses to accept a frame as 21:9, when two pieces of software disagree about whether a clip is "true" ultrawide, and when a chain of conversions accumulates error.
The error table
Each cell gives the rounded height and, in brackets, how far the resulting ratio sits from the target. "Exact" means the height came out whole.
| Ratio | 1080 wide | 1920 wide | 3840 wide |
|---|---|---|---|
| 16:9 | 608 (0.0822%) | 1080 (exact) | 2160 (exact) |
| 4:3 | 810 (exact) | 1440 (exact) | 2880 (exact) |
| 3:2 | 720 (exact) | 1280 (exact) | 2560 (exact) |
| 1:1 | 1080 (exact) | 1920 (exact) | 3840 (exact) |
| 9:16 | 1920 (exact) | 3413 (0.0098%) | 6827 (0.0049%) |
| 21:9 | 463 (0.0309%) | 823 (0.0174%) | 1646 (0.0174%) |
| 2.39:1 | 452 (0.0259%) | 803 (0.0432%) | 1607 (0.0190%) |
| 1.85:1 | 584 (0.0370%) | 1038 (0.0156%) | 2076 (0.0156%) |
Across all eleven ratios and eight widths tested (640, 720, 1080, 1280, 1440, 1920, 2560, 3840), 55 of 88 combinations land exactly and 33 need rounding. The worst case is not at 4K: it is 21:9 at 720 wide, where 308.571 rounds to 309 and the ratio misses by 0.1387%, eight times the error at 1920.
Three ratios that never land
21:9, 2.39:1 and 1.85:1 fail at every width tested. Their decimals do not terminate in a way that produces an integer height at any power-of-two width, so there is always a remainder.
16:9 has the opposite problem in only one place: a 1080-wide frame needs 607.5 pixels of height. Rounding to 608 makes the frame 1.7763:1, off by 0.0822%. That is why "1080 wide, 16:9" is a description rather than a specification.
9:16 is exact at 720, 1080 and 1440 wide and nowhere else in the tested set. Vertical delivery is usually specified at one of those three, which is why phone video rarely shows this problem.
What to do about it
Pick the width first and let the height follow, then state the ratio as a rounded decimal rather than as a promise. A 1920 × 823 frame is honest as "2.333:1" and dishonest as "21:9 exact".
When two tools disagree, compare cross products instead of decimals: a frame is exactly 21:9 only if width × 9 equals height × 21. For 1920 × 823, 1920 × 9 = 17,280 and 823 × 21 = 17,283, so the answer is no by three pixels of cross product.
When chaining conversions, round once at the end rather than at every step. Two roundings of 0.1% can turn into a visible shift in a stack of overlays or a title-safe guide that no longer lines up.
Pixel accuracy questions
Is 3440 × 1440 exactly 21:9?
No. 3440 ÷ (21/9) = 1474.3, so 21:9 at that width would need 1474 pixels of height. The real ratio of 3440 × 1440 is 2.3889:1, which is closer to 2.39:1 than to 21:9.
Which common resolution is exactly 21:9?
None in the tested set. 2560 × 1080 is 64:27 (2.3704:1). 5120 × 2160 is also 64:27. The 21:9 label is a family name, not a pixel-exact specification.
Does a 0.02% error matter visually?
No. It matters to software that validates ratios, to overlay alignment, and to chains where errors add up. For a single encode, 823 and 822 pixels are both fine.
Why is the error larger at 720 than at 1920?
Rounding moves the height by up to half a pixel. Half a pixel is a larger fraction of 309 than of 823, so the same absolute rounding produces a bigger relative error at small widths.
Method note
Heights were computed as width × 9 ÷ 21 for 21:9, width ÷ 2.39 for 2.39:1, and so on, then rounded to the nearest integer. Errors are the relative difference between the rounded ratio and the target ratio. No outside data is used; the table is reproducible with a calculator, and the calculator above repeats it live.
Related
Chained crop loss: why 4:3 → 16:9 → 9:16 costs 76.3%, not 93.4%