9:16 Aspect Ratio
Every exact whole-pixel 9:16 frame is 9k × 16k. But an exact portrait crop is not always an equally centered crop. From 3840 × 2160, the exact crop is 1215 × 2160; the 2625 discarded columns are odd, so the closest whole-pixel center removes 1312 on one side and 1313 on the other.
The two conditions for a perfect centered 9:16 crop
Suppose a landscape source is W × H and you keep its full height. The exact portrait crop width is C = 9H ÷ 16. A clean raster crop needs C to be a whole number. Because 9 and 16 share no factor, that first condition is simple: H must be divisible by 16.
Equal left and right removal adds another condition. The discarded width D = W − C must be even. Only then can each side remove D ÷ 2 whole columns.
Whole-pixel centered-crop test
C = 9H ÷ 16
D = W − C
Pass only if C is an integer and D is even.
Equivalently: H mod 16 = 0 and (W − 9H/16) mod 2 = 0.
| Landscape source | Exact 9:16 crop | Discarded width | Whole-pixel center |
|---|---|---|---|
| 1280 × 720 | 405 × 720 | 875 | 437 / 438 — unequal |
| 1920 × 1080 | 607.5 × 1080 | 1312.5 | No exact raster crop |
| 2560 × 1440 | 810 × 1440 | 1750 | 875 / 875 — exact |
| 3840 × 2160 | 1215 × 2160 | 2625 | 1312 / 1313 — unequal |
Why 1920 × 1080 cannot yield an exact full-height 9:16 raster crop
The formula gives 1080 × 9 ÷ 16 = 607.5. A crop boundary can be positioned between pixel columns, but the exported rectangle cannot be 607.5 physical pixels wide. Choosing 607 gives 607:1080; choosing 608 gives 608:1080. Neither cross-multiplies to 9:16.
You therefore have three honest choices: resample the image into a true 9:16 output, crop to a nearby exact 9:16 height such as 1072, or accept a near-ratio 607- or 608-column crop. Label the choice; do not call a rounded width mathematically exact.
Generate exact 9:16 sizes without reversing the ratio
In 9:16, width is the short side and height is the long side. Pick any positive whole number k and multiply: width = 9k, height = 16k. This creates the complete whole-pixel sequence, not just a list of popular presets.
| k | Exact size | Cross-check |
|---|---|---|
| 40 | 360 × 640 | 360 × 16 = 640 × 9 = 5760 |
| 45 | 405 × 720 | 405 × 16 = 720 × 9 = 6480 |
| 60 | 540 × 960 | 540 × 16 = 960 × 9 = 8640 |
| 80 | 720 × 1280 | 720 × 16 = 1280 × 9 = 11520 |
| 120 | 1080 × 1920 | 1080 × 16 = 1920 × 9 = 17280 |
| 240 | 2160 × 3840 | 2160 × 16 = 3840 × 9 = 34560 |
If a width is given, height = width × 16 ÷ 9. An integer height is guaranteed when the width is divisible by 9. If a height is given, width = height × 9 ÷ 16; an integer width is guaranteed when the height is divisible by 16.
Centering rule: one odd discarded column has to go somewhere
For 3840 × 2160, keeping 1215 columns is exact 9:16. The source has 2625 columns outside that crop. Since 2625 ÷ 2 = 1312.5, an integer crop box must choose either left = 1312 and right = 1313, or the reverse. The crop center shifts by half a source pixel relative to the geometric center.
This is not a visible disaster and it does not make the retained frame inexact. It only means “perfectly symmetric removal in whole source pixels” is impossible for that source. Choose which side loses the extra column based on the subject, or resample if subpixel centering is a requirement.
- 1Test the crop width
Calculate 9H ÷ 16. If it is fractional, a full-height exact raster crop is impossible.
- 2Test the remainder
Subtract the crop width from W. An odd remainder cannot split equally into whole columns.
- 3Verify the retained frame
Check crop width × 16 = crop height × 9 before export.
- 4Record the one-column choice
When the remainder is odd, state which edge loses the extra column.
9:16 calculation questions
What is the formula for a 9:16 size?
Use width = 9k and height = 16k for any positive whole number k. With one known side, calculate height = width × 16 ÷ 9 or width = height × 9 ÷ 16.
Is 607 × 1080 exactly 9:16?
No. 607 × 16 = 9712, while 1080 × 9 = 9720. The exact mathematical width at height 1080 is 607.5, which is not a whole-pixel raster width.
Can 3840 × 2160 be cropped to exact 9:16?
Yes. The retained frame is 1215 × 2160. However, the 2625 removed columns cannot be divided equally, so a whole-pixel crop removes 1312 from one edge and 1313 from the other.
Which common landscape size gives an exact symmetric 9:16 crop?
2560 × 1440 does: retain 810 × 1440 and remove 875 columns from both the left and right.
Calculation scope
This guide treats pixels as square and analyzes crop geometry only. It does not assume a platform’s safe areas, interface overlays, encoding limits, or automatic reframing. For a general missing-side calculation, use the image aspect ratio calculator. For the different problem of placing a vertical video inside a fixed landscape frame, see the vertical-video fit ledger.
All dimensions and parity results above were recalculated from 9:16 and verified by cross multiplication. The center-crop parity test is the distinguishing calculation: exact ratio and equal whole-pixel centering are related, but they are not the same claim.