Why films have black bars
Tonight's idea
A screen's aspect ratio is its width compared with its height, written width : height. Old televisions were 4:3, which means 4 units wide for every 3 tall. Most modern screens are 16:9. Many cinema films are wider still, roughly 21:9.
A picture must keep its shape, or faces look stretched. So when the picture and the screen have different shapes, the picture is shrunk until it just fits, and the leftover screen stays black.
How much is black? Make one side match. A 4:3 screen is the same shape as 16:12 (multiply both numbers by 4). A 16:9 film fills the 16 across but only 9 of the 12 up. The bars take the other 3, so \(\tfrac{3}{12} = \tfrac14\) of the screen is black.
Now the other way round. Write 4:3 as 12:9. On a 16:9 screen the show fills the 9 up and only 12 of the 16 across. The bars take \(\tfrac{4}{16} = \tfrac14\) again.
Watch one: an old show on a new TV
A 16:9 TV is 96 cm wide and 54 cm tall. An old 4:3 show plays on it.
The show fills the height, 54 cm. Its width is 4 units for every 3 of height: \(54 \div 3 = 18\) and \(18 \times 4 = 72\) cm.
That leaves \(96 - 72 = 24\) cm of width, so there is a 12 cm bar on each side.
Check with the ratios: \(\tfrac{24}{96} = \tfrac14\) of the screen is black, as before.
Your turn
- Write each as an aspect ratio in simplest form: (a) a screen of 1920 by 1080 pixels; (b) 640 by 480; (c) a phone held upright, 1080 wide by 1920 tall; (d) 1080 by 1080.
- A 4:3 screen is 64 cm wide and 48 cm tall. It shows a 16:9 film. (a) How tall is the picture? (b) How tall is each black bar? (c) What fraction of the screen is black?
- A 21:9 film is shown on a 16:9 screen. What fraction of the screen is black? (Hint: write both ratios with a width of 336.)
- There are two ways to get rid of the bars when a 4:3 show plays on a 16:9 screen. (a) Zoom in until the show fills the whole width. The top and bottom are cut off. What fraction of the picture is lost? (b) Or stretch the show sideways only, until it fills the screen. How many times wider does everything look? (c) Why can no method show the whole picture, with its true shape, and no bars?
Stretch: the upright video
A video shot on a phone held upright is 9:16. It is shown whole, with its true shape, on a 16:9 TV. What fraction of the screen is black? Give the exact fraction, then a rough percentage.
Answers
- (a) Divide both by 120: 16:9. (b) Divide both by 160: 4:3. (c) 9:16. (d) 1:1, a square.
- (a) The picture fills the width, 64 cm. \(64 \div 16 = 4\) and \(4 \times 9 = 36\) cm tall. (b) \(48 - 36 = 12\) cm is left, so each bar is 6 cm. (c) \(\tfrac{12}{48} = \tfrac14\).
- \(21:9 = 336:144\) (multiply by 16) and \(16:9 = 336:189\) (multiply by 21). The film fills the width and 144 of the 189 up. The bars take \(189 - 144 = 45\), and \(\tfrac{45}{189} = \tfrac{5}{21}\), a little under a quarter.
- (a) Write 4:3 as 16:12. The screen shows 9 of the 12 rows, so \(\tfrac{3}{12} = \tfrac14\) of the picture is lost. (b) Write 4:3 as 12:9. The width must grow from 12 to 16, so everything looks \(\tfrac{16}{12} = \tfrac43\) times as wide. (c) Shrinking or enlarging a picture never changes its shape. A 4:3 shape and a 16:9 shape are different, so either some screen is left over, or some picture is, or the shape is changed.
Stretch. Give both the same height. The screen is 16:9. The video is 9:16; multiply both numbers by \(\tfrac{9}{16}\) to get \(\tfrac{81}{16} : 9\). So the video covers \(\tfrac{81}{16}\) of the 16 units of width, which is \(\tfrac{81}{256}\) of the screen. The black part is \(\tfrac{175}{256}\), about 68%. More than two thirds of the screen is bars.