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 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.