# Aspect ratio calculator (16:9, 4:3, 21:9)

> Find the aspect ratio of any resolution, such as 1920 × 1080 = 16:9, resize it to a new width or height, or fit it in a screen with letterbox bars.

Interactive version: https://www.calcopenly.com/programming/aspect-ratio-resolution-calculator
Subject: Programming and tech calculators

The aspect ratio is the width divided by the height, written in lowest terms by dividing both sides by their greatest common divisor: 1920 ÷ 120 = 16 and 1080 ÷ 120 = 9, so 1920 × 1080 is 16:9. Resizing keeps that quotient fixed, so the new height is the new width × H ÷ W. Fitting a picture inside another frame uses the largest scale that fits both ways, s = min(frame width ÷ W, frame height ÷ H), and the leftover space becomes bars.

Scaling 1920 × 1080 to 1280 wide gives 1280 × 720. Showing that 16:9 picture on a 1024 × 768 screen gives a 1024 × 576 picture with 96 px letterbox bars above and below, so the picture uses 75% of the screen.

Sizes stay exact fractions until the end. Scaled sizes are then rounded to whole pixels, which can shift the ratio slightly.

## Inputs

- **I want to** (options: Find the ratio, Resize keeping the ratio, Fit inside another frame)
- **Source ratio** (options: Use the width and height below, 16:9 (HD video, most monitors), 4:3 (older TVs, iPad), 21:9 (ultrawide, as marketed), 9:16 (vertical phone video), 1:1 (square), 3:2 (35 mm photo), 16:10 (laptops), 4:5 (portrait social post), 1.85:1 (flat cinema), 2.39:1 (scope cinema), 32:9 (super ultrawide))
- **Width**
- **Height**
- **New size is given as** (options: Width, Height)
- **New width or height**
- **Frame width**
- **Frame height**

## Results

- Result
- Simplified ratio — main result
- Width ÷ height
- Closest common ratio
- New width (px)
- New height (px)
- Picture width in frame (px)
- Picture height in frame (px)
- Bars
- Each bar (px)
- Frame area used by the picture

## Formula

$$
\begin{aligned} W{:}H &= \frac{W}{\gcd(W,H)} : \frac{H}{\gcd(W,H)} \\[4pt] s &= \min\!\left(\frac{W_f}{W}, \frac{H_f}{H}\right)\end{aligned}
$$

## Worked examples

### Full HD

- I want to: Find the ratio
- Width: 1920 px
- Height: 1080 px
- **Simplified ratio: 16:9**
- **Width ÷ height: 1.7778**
- **Closest common ratio: 16:9**
- Checked against: Python 3.8: fractions.Fraction(1920, 1080) = 16/9

### Ultrawide 2560 × 1080

- I want to: Find the ratio
- Width: 2560 px
- Height: 1080 px
- **Simplified ratio: 64:27**
- **Width ÷ height: 2.3704**
- Checked against: Python 3.8: fractions.Fraction(2560, 1080) = 64/27 = 2.37037…

### 1366 × 768 laptop is not exactly 16:9 (edge)

- I want to: Find the ratio
- Width: 1366 px
- Height: 768 px
- **Simplified ratio: 683:384**
- **Width ÷ height: 1.7786**
- **Closest common ratio: 16:9 (0.05% wider)**
- Checked against: Python 3.8: Fraction(1366, 768) = 683/384; (683/384) / (16/9) − 1 = 0.0488%

### Decimal cinema ratio

- I want to: Find the ratio
- Width: 2.39 px
- Height: 1 px
- **Simplified ratio: 239:100**
- Checked against: Python 3.8: Fraction('2.39') / 1 = 239/100

### Scale 1920 × 1080 to 1280 wide

- I want to: Resize keeping the ratio
- Source ratio: Use the width and height below
- Width: 1920 px
- Height: 1080 px
- New size is given as: Width
- New width or height: 1280 px
- **New width: 1,280 px**
- **New height: 720 px**
- **Result: 1280 × 720 px**
- Checked against: Python 3.8: 1280 × Fraction(1080, 1920) = 720

### 4:3 at 1080 tall

- I want to: Resize keeping the ratio
- Source ratio: 4:3 (older TVs, iPad)
- New size is given as: Height
- New width or height: 1080 px
- **New width: 1,440 px**
- **New height: 1,080 px**
- Checked against: Python 3.8: 1080 × Fraction(4, 3) = 1440

## Questions

### What is the aspect ratio of 1920 × 1080?

1920 × 1080 is 16:9: both sides divide by their greatest common divisor, 120, to give 16 and 9, and the width is 1.7778 times the height. ITU-R BT.709 defines 1920 × 1080 as the HDTV picture format, and the same 16:9 shape covers 1280 × 720, 2560 × 1440 and 3840 × 2160 (4K UHD).

### Is a 21:9 ultrawide monitor really 21:9?

No. Ultrawide monitors sold as 21:9 are 2560 × 1080 (64:27, 2.370), 3440 × 1440 (43:18, 2.389) or 3840 × 1600 (12:5, 2.4), while 21:9 itself is 2.333. The label is rounded marketing, and the gap shows up in practice: true 21:9 video on a 3440 × 1440 panel fills 3360 × 1440 and leaves a 40 px pillarbox bar on each side.

### How do I calculate the new height when resizing an image?

Multiply the new width by the original height over the original width: new height = new width × H ÷ W. Scaling 1920 × 1080 to 1280 wide gives 1280 × 1080 ÷ 1920 = 720. The other way round, new width = new height × W ÷ H, so a 4:3 picture 1080 tall is 1440 wide. Round to whole pixels at the end, and to even numbers for most video encoders.

### What is the difference between letterbox and pillarbox?

Letterboxing adds bars above and below when the picture is wider than the screen, such as 16:9 video on a 1024 × 768 display, which gets 96 px bars. Pillarboxing adds bars on the left and right when the picture is narrower, such as 4:3 content on a 1920 × 1080 screen, which leaves 240 px on each side. Zooming to fill removes the bars but crops the picture, by 25% in that 4:3 case.

### What aspect ratios do cinema films use?

Digital cinema uses two DCI container shapes: flat at 1.85:1 (1998 × 1080 in the 2K container) and scope at 2.39:1 (2048 × 858). On a 1920 × 1080 TV, a 2.39:1 film shows letterbox bars of about 138 px above and below, and a 1.85:1 film bars of about 21 px, because both are wider than the TV's 16:9 (1.78:1).

### How accurate is the aspect ratio calculator (16 calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 9 worked examples whose answers come from independent sources; for example, “Full HD” is checked against Python 3.8: fractions.Fraction(1920, 1080) = 16/9.

### Where does the method come from?

ITU-R BT.709-6 — HDTV picture format 1920 × 1080 at 16:9; DCI Digital Cinema System Specification — flat 1998 × 1080 (1.85:1) and scope 2048 × 858 (2.39:1) containers.

## Sources

- [ITU-R BT.709-6 — HDTV picture format 1920 × 1080 at 16:9](https://www.itu.int/rec/R-REC-BT.709)
- [DCI Digital Cinema System Specification — flat 1998 × 1080 (1.85:1) and scope 2048 × 858 (2.39:1) containers](https://www.dcimovies.com/specification)