Math Tables
Aspect Ratio Table
An aspect ratio is width divided by height, and everything else follows from that one number. Given a width you can compute the height, given a diagonal you can compute both sides, and given an original frame you can compute what a crop keeps. The arithmetic is simple; the confusion comes from labels that do not match their values.
Last updated
The worst offender is 21:9. As a fraction it is 2.333, but the ultrawide monitors sold under that name are usually 3440 × 1440, which is 2.389. True 21:9 at that height would be 3360 × 1440. The label is a marketing category, not a measurement, and the 2.5% difference shows up when you try to fit two windows side by side expecting a particular split.
The second trap is that aspect ratio says nothing about size. A 16:9 phone screen and a 16:9 cinema screen have the same ratio and wildly different areas. That is why screen specifications need both: the ratio tells you the shape, the diagonal tells you the scale, and only together do they determine the pixel density or the physical dimensions.
The last table is the one photographers reach for. A 3:2 sensor at 24 megapixels does not deliver 24 megapixels at every output ratio — cropping to 16:9 keeps 20.25, and cropping to the 32:9 of a super-wide banner keeps 11.25. Knowing that before composing a shot is the difference between a usable crop and a soft one.
Common aspect ratios at a fixed 1920 pixel width
| Ratio | Decimal | Height at 1920 wide | Megapixels |
|---|---|---|---|
| 1:1 | 1.0000 | 1,920 | 3.69 |
| 5:4 | 1.2500 | 1,536 | 2.95 |
| 4:3 | 1.3333 | 1,440 | 2.76 |
| 3:2 | 1.5000 | 1,280 | 2.46 |
| 16:10 | 1.6000 | 1,200 | 2.30 |
| 16:9 | 1.7778 | 1,080 | 2.07 |
| 1.85:1 | 1.8500 | 1,038 | 1.99 |
| 2:1 | 2.0000 | 960 | 1.84 |
| 2.35:1 | 2.3500 | 817 | 1.57 |
| 21:9 | 2.3333 | 823 | 1.58 |
| 32:9 | 3.5556 | 540 | 1.04 |
21:9 is 2.333 as a decimal, but the common 3440 × 1440 panel is 2.389. The label rounds the ratio, and the difference is visible when comparing side by side.
16:9 screens by diagonal, in centimetres
| Diagonal (in) | Width (cm) | Height (cm) | Area (cm²) |
|---|---|---|---|
| 24 | 53.1 | 29.9 | 1,588 |
| 27 | 59.8 | 33.6 | 2,010 |
| 32 | 70.8 | 39.8 | 2,823 |
| 40 | 88.6 | 49.8 | 4,411 |
| 55 | 121.8 | 68.5 | 8,339 |
| 65 | 143.9 | 80.9 | 11,647 |
| 75 | 166 | 93.4 | 15,507 |
| 85 | 188.2 | 105.8 | 19,918 |
Doubling the diagonal quadruples the area, which is why a 65 inch television is not twice the screen of a 32 inch one — it is more than four times the area.
What survives when a 6000 × 4000 photo is cropped
| Crop ratio | Cropped pixels | Megapixels | Share of the original |
|---|---|---|---|
| 1:1 | 4,000 × 4,000 | 16.00 | 66.7% |
| 5:4 | 5,000 × 4,000 | 20.00 | 83.3% |
| 4:3 | 5,333 × 4,000 | 21.33 | 88.9% |
| 3:2 | 6,000 × 4,000 | 24.00 | 100.0% |
| 16:10 | 6,000 × 3,750 | 22.50 | 93.8% |
| 16:9 | 6,000 × 3,375 | 20.25 | 84.4% |
| 1.85:1 | 6,000 × 3,243 | 19.46 | 81.1% |
| 2:1 | 6,000 × 3,000 | 18.00 | 75.0% |
| 2.35:1 | 6,000 × 2,553 | 15.32 | 63.8% |
| 21:9 | 6,000 × 2,571 | 15.43 | 64.3% |
| 32:9 | 6,000 × 1,688 | 10.13 | 42.2% |
The original is 24 megapixels at 3:2. Cropping to 16:9 keeps 20.25, and cropping to 32:9 keeps only 11.25 — less than half the frame.
How to Use These Tables
- Computing a height: divide the width by the ratio. A 1200 px wide 16:9 image is 675 px tall.
- Computing a diagonal: square the ratio parts, add, take the root, then scale. For 16:9 the diagonal is 18.36 units, so a 55 inch screen is 47.9 inches wide.
- Checking a label: divide the actual pixels. 3440 / 1440 = 2.389, so a panel sold as 21:9 is really 43:18.
- Planning a crop: multiply the short side by the ratio to get the long side. Cropping a 4000 px tall frame to 16:9 gives 7111 px wide, which exceeds a 6000 px sensor, so the height becomes the limiting side.
- Matching platforms: 16:9 for video, 4:5 or 1:1 for social feeds, 2:1 for banners. Shooting at 3:2 leaves room to crop to any of them.
Common Questions
Is 21:9 the same as 2.35:1?
No. 21:9 is 2.333 and 2.35:1 is 2.35, and the common 3440 × 1440 panel is 2.389. Cinema scope is 2.39:1, which is closer to the panel than either label.
How do I find the width from the diagonal?
Divide the diagonal by the square root of the sum of the squared ratio parts, then multiply by each part. For 16:9 the divisor is 18.358.
Does cropping change the aspect ratio of the file?
Yes, that is the point. Cropping removes pixels from the edges, so the remaining rectangle has a new ratio. The megapixels drop by the area of the discarded region.
Why are camera sensors 3:2?
It is inherited from 35 mm film, which was 36 × 24 mm. The ratio carried over to full-frame digital sensors, and most lenses are designed around it.
What is the aspect ratio of a phone screen?
Most modern phones are between 19.5:9 and 20:9, taller than 16:9. That is why video shot in 16:9 leaves black bars at the top and bottom.
Is a wider aspect ratio always better for video?
No. Wider frames suit landscapes and action; 4:3 suits faces and dialogue. The ratio should follow the subject, not the specification sheet.
More Math Tables
Sources
- SMPTE ST 2046-1 — 2.39:1 scope aspect ratio for digital cinema — Society of Motion Picture and Television Engineers
- ISO 12233 — photography, electronic still picture imaging, resolution — International Organization for Standardization
- ITU-R BT.709 — parameter values for HDTV production — International Telecommunication Union
Filed with Math calculations.