Ratio Calculator
Find the missing number in a proportion (A : B = C : ?) or reduce a ratio to its simplest form, with the working shown.
16 : 9 = 1,920 : x, so x =
1,080
16 : 9 = 1,920 : 1,080. Both sides scale by 120.
- Simplest form of a : b
- 16 : 9
How this works: Method, 2 sources, Checked against 1 worked example,
How this works
Method
A proportion says two ratios are equal, a : b = c : x. The cross products of a proportion are equal, a × x = b × c, so x = b × c ÷ a. For a 16:9 screen 1,920 pixels wide: x = 9 × 1,920 ÷ 16 = 1,080 pixels high. Another way to see it: 1,920 is 120 times 16, so the height is 120 times 9. Full method
Sources
How it’s tested
One worked example for this page is checked by automated tests before every release: given the inputs, the tool must show the expected answer.
Privacy
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Changes
- First published, with nine pages: adding, subtracting, multiplying, dividing and simplifying fractions, fraction to decimal and back, mixed numbers and ratios.
How to solve and simplify ratios
A proportion says two ratios are equal, a : b = c : x. The cross products of a proportion are equal, a × x = b × c, so x = b × c ÷ a. For a 16:9 screen 1,920 pixels wide: x = 9 × 1,920 ÷ 16 = 1,080 pixels high. Another way to see it: 1,920 is 120 times 16, so the height is 120 times 9.
To simplify a ratio, divide every part by their greatest common factor. 12 : 18 : 30 share a factor of 6, giving 2 : 3 : 5. If a part is a decimal or a fraction, multiply everything by the same number first to make them whole: 1.5 : 2.25 becomes 150 : 225 (× 100), which simplifies to 2 : 3.
A ratio compares amounts; a fraction compares a part with the whole. In a 2 : 3 mix of cement and sand, the cement is 2 parts of 5, so it is 2/5 (40%) of the mix, not 2/3.
a : b = c : x ⇒ x = b × c ÷ a
- Ratios and rates are introduced in US grade 6, including using ratio reasoning to solve problems with tables of equivalent ratios (6.RP.A.3). Source: Common Core State Standards, Grade 6 Ratios and Proportional Relationships.
- Full HD video is 1,920 × 1,080 pixels, an aspect ratio of 16:9. Source: ITU-R Recommendation BT.709 (HDTV).
Screen and photo sizes as simplified ratios
Common resolutions reduced by their greatest common factor; the last column is the width per unit of height.
| Size | Simplest ratio | Width : 1 | Where you see it |
|---|---|---|---|
| 1920 : 1080 | 16 : 9 | 1.778 | Full HD video |
| 1280 : 720 | 16 : 9 | 1.778 | HD video |
| 3840 : 2160 | 16 : 9 | 1.778 | 4K UHD |
| 2560 : 1440 | 16 : 9 | 1.778 | QHD monitors |
| 1024 : 768 | 4 : 3 | 1.333 | older monitors, iPad |
| 1280 : 1024 | 5 : 4 | 1.25 | older office monitors |
| 1440 : 900 | 8 : 5 | 1.6 | 16:10 laptops |
| 2560 : 1080 | 64 : 27 | 2.37 | “21:9” ultrawide |
| 6000 : 4000 | 3 : 2 | 1.5 | DSLR photos |
| 4032 : 3024 | 4 : 3 | 1.333 | phone photos |
Show all 12 rowsShow fewer
| 1080 : 1920 | 9 : 16 | 0.563 | vertical video |
| 1080 : 1350 | 4 : 5 | 0.8 | portrait social posts |
Frequently Asked Questions
How do I split an amount in a ratio?
Add the parts to get the total number of shares, divide the amount by it, then multiply by each part. Splitting 120 in the ratio 2 : 3 gives 5 shares of 24, so 48 and 72.
Is 2560 × 1080 really 21:9?
Not exactly: it simplifies to 64 : 27, about 2.37 : 1, while 21 : 9 (7 : 3) is about 2.33 : 1. “21:9” is a marketing name for this family of ultrawide screens.
Can a ratio have more than two parts?
Yes. A recipe might use flour, sugar and butter in the ratio 3 : 2 : 1. Simplify all the parts by their common factor, and scale them all by the same number.