What a ratio is
A ratio compares two or more quantities: 2:3 means that for every 2 parts of the first, there are 3 parts of the second. Ratios are used in recipes, mixtures, maps, screen formats, financial analysis and sharing money or work. This calculator simplifies a ratio of two or three terms, converts it to the form 1:n and splits a total amount accordingly.
The formulas
- Simplify: divide every term by the greatest common divisor (GCD) of all the terms.
- 1:n form: n = second term ÷ first term.
- Share of each part: total × term ÷ sum of the terms.
- Percentage: term ÷ sum of the terms × 100.
Decimal terms are first multiplied by 1,000 to make whole numbers, then simplified.
Worked example
Two partners invested $12,000 and $18,000, and want to share a profit of $1,000 in the same ratio.
- The ratio is 12:18. The GCD of 12 and 18 is 6, so it simplifies to 2:3.
- In 1:n form: 18 ÷ 12 = 1.5, so the ratio is 1:1.5.
- The sum of the parts is 2 + 3 = 5. The first partner gets $1,000 × 2 ÷ 5 = $400, the second $600.
- The first partner’s share is 40% of the total.
With three terms, 2:3:5 splits $1,000 into $200, $300 and $500.
Common ratios
| Use | Typical ratio |
|---|---|
| Widescreen video | 16:9 |
| Concrete, cement:sand:gravel | 1:2:3 |
| Rice to water (white rice) | 1:2 |
| Coffee to water (drip) | about 1:16 |
| Map scale | 1:24,000 (USGS topographic) |
Ratios, fractions and percentages
A ratio of 2:3 between two parts means the first part is 2/5 of the whole, not 2/3. That is a common mistake: the denominator of the fraction is the sum of the parts. The ratio of the first part to the second, on the other hand, is 2/3.
Equivalent ratios
Multiplying or dividing every term by the same number gives an equivalent ratio: 2:3, 4:6 and 20:30 all describe the same proportion. To find a missing term, such as 2:3 = 7:x, cross-multiply: x = 3 × 7 ÷ 2 = 10.5. The rule of three calculator handles that kind of problem directly.
Tips
Keep the order of the terms consistent with the order of the things you compare, and use the same unit for all of them: comparing 1 cup with 300 ml requires converting one of them first.