What a ratio says, and what it does not
A ratio such as 3:2 compares two amounts by size: for every 3 of the first, there are 2 of the second. It says nothing about the actual quantities, so 3 kg to 2 kg, 30 mL to 20 mL and 3,000 people to 2,000 people all have the ratio 3:2.
A ratio is closely related to a fraction, but the two are easy to mix up. The ratio 3:2 has 3 + 2 = 5 parts in total, so the first amount is 3/5 of the whole and the second is 2/5. It does not mean “3/2 of the total”. Comparing the two amounts directly, the first is 3/2, or 1.5 times, the second.
The calculator has three sections: simplify a ratio, solve a proportion, and split a total.
Simplifying a ratio
Simplifying means dividing every term by their greatest common factor until no whole number above 1 divides them all. 1920:1080 has a GCF of 120, and 1920 ÷ 120 = 16, 1080 ÷ 120 = 9, so the ratio is 16:9. Three terms work the same way: 6:9:12 shares the factor 3 and becomes 2:3:4. Separate the terms with colons; “16 to 9” and 16/9 are read the same way. Under the result, the calculator also gives each term as a fraction of the whole (16/25 and 9/25) and the ratio in 1 : n form (1 : 0.5625).
Decimals are allowed. The calculator first multiplies every term by the same power of ten to make them whole (1.5:2.5 becomes 15:25), then divides by the GCF to give 3:5.
Solving a proportion
A proportion states that two ratios are equal, A:B = C:x. Since A/B = C/x, cross-multiplying gives A × x = B × C, and the missing value follows.
The first line solves A:B = C:x; the second splits a total in a ratio. A ratio with a zero first term cannot be scaled this way, because the formula would divide by zero. Results that do not divide evenly are shown as decimals, so round money or counts to a sensible unit yourself.
Splitting a total in a ratio
To share an amount in 3:2:1, add the terms (6 parts), find the size of one part (total ÷ 6), and multiply by each term. The shares always add back to the total, which is a quick check that nothing went wrong.
Worked examples
- The greatest common factor of 1920 and 1080 is 120.
- 1920 ÷ 120 = 16 and 1080 ÷ 120 = 9.
- The result is 16:9. ITU-R Recommendation BT.709, the international HDTV standard, specifies exactly this picture: a 16:9 aspect ratio with 1,920 samples per line and 1,080 active lines. 1280 × 720 and 3840 × 2160 also simplify to 16:9.
- To find the water for 250 mL of concentrate, solve 1:4 = 250:x. x = 4 × 250 ÷ 1 = 1,000 mL.
- To make 2 L (2,000 mL) of finished mix instead, split 2,000 in the ratio 1:4. There are 5 parts of 400 mL each.
- Concentrate: 1 × 400 = 400 mL. Water: 4 × 400 = 1,600 mL.
- Total parts: 3 + 2 + 1 = 6.
- One part: 120 ÷ 6 = 20.
- Shares: 3 × 20 = 60, 2 × 20 = 40, 1 × 20 = 20. Check: 60 + 40 + 20 = 120.
- Set up 16:9 = 1200:x.
- x = 9 × 1200 ÷ 16 = 675.
Ratio mistakes worth avoiding
- Treating the ratio terms as fractions of the total. In a 1:4 mix, the concentrate is 1/5 of the bottle, not 1/4. Using 1/4 makes the mix stronger than intended.
- Swapping the order. 1:4 concentrate to water and 4:1 concentrate to water are very different mixes. Keep the terms in the order the label or recipe gives them.
- Mixing units inside one ratio. 2 cups to 300 mL is not 2:300. Put both amounts in the same unit before simplifying or solving.
- Expecting marketing names to be exact. A 2560 × 1080 monitor simplifies to 64:27, about 2.37:1. It is usually sold as 21:9 (about 2.33:1), which is a rounded name, not the exact shape.
Shares that do not divide evenly, such as 500 in 3:2:1 (250, 166.67, 83.33 after rounding), may need a cent or a unit moved by hand so the rounded parts still add up to the total.
Questions people ask
Can a ratio have more than two parts?
Yes. Ingredient, concrete and paint mixes often use three-part ratios. The calculator simplifies and splits ratios such as 2.4:3.6:1.2, which becomes 2:3:1.
Is 16:9 the same as 1.78:1?
16 ÷ 9 is 1.777…, so 1.78:1 is the same shape rounded to two decimals. Writing ratios as “something to 1” is common for cinema formats and makes different shapes easy to compare.
Sources
- Ratio, Wolfram MathWorld.
- Recommendation ITU-R BT.709, Parameter values for the HDTV standards for production and international programme exchange, International Telecommunication Union.