Ratio calculator: solve proportions, simplify and split totals
Pick what you need. To solve 3 : 5 = 12 : ?, the missing term is 12 × 5 ÷ 3 = 20. To simplify 12 : 20, divide both by 4 to get 3 : 5. To split 800 in the ratio 3 : 5, each part is 100, so the shares are 300 and 500.
Inputs used by this calculator
Ratio Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| What do you need? | Solve A : B = C : ? | Solve A : B = C : ? · Simplify A : B · Split a total in the ratio A : B | Chooses which Ratio Calculator method or unknown the engine evaluates. |
| A | 3 | 0 or greater | Supplies the a quantity used by the published equation or result breakdown. |
| B | 5 | 0 or greater | Supplies the b quantity used by the published equation or result breakdown. |
| C | 12 | 0 or greater | Supplies the c quantity used by the published equation or result breakdown. |
| Total to split | 800 | 0 or greater | Selects the unit or conversion path used by Ratio Calculator. |
What a ratio says
A ratio compares two quantities: 3 : 5 means 3 of one for every 5 of the other. It does not say how many there are in total, only the proportion. Recipes, maps, screen shapes, paint mixes and dosage instructions all use ratios.
Solving a proportion
A proportion states that two ratios are equal. To find the missing term in A : B = C : ?, multiply C by B and divide by A. Scaling a recipe from 3 cups of flour to 12 cups multiplies every ingredient by 4.
A : B = C : DD = C × B ÷ ASimplifying a ratio
Divide both terms by their greatest common factor. 12 : 20 shares a factor of 4, so it simplifies to 3 : 5. Ratios with decimals are first scaled to whole numbers: 1.5 : 2.5 becomes 15 : 25 and then 3 : 5.
Splitting a total in a ratio
Add the terms to find how many equal parts there are, divide the total by that number and multiply by each term. Splitting $800 in the ratio 3 : 5 gives 8 parts of $100, so $300 and $500. The same method shares costs, profits or ingredients.
one part = total ÷ (A + B)share of A = one part × ARatios, fractions and percents
In 3 : 5, the first quantity is 3 of 8 parts, or 37.5% of the whole, and the ratio of the first to the second is 3/5 = 0.6. Keep the difference in mind: a part-to-part ratio is not the same as a part-to-whole fraction.
Checking the answer
Cross-multiplying checks a proportion: in 3 : 5 = 12 : 20, 3 × 20 equals 5 × 12. Split shares should add back to the total. The detail rows show these checks for each mode.
Common ratios and equivalents
| Ratio | × 3 | × 10 | Shares of the whole |
|---|---|---|---|
| 1 : 2 | 3 : 6 | 10 : 20 | 33.3% and 66.7% |
| 2 : 3 | 6 : 9 | 20 : 30 | 40% and 60% |
| 3 : 4 | 9 : 12 | 30 : 40 | 42.9% and 57.1% |
| 3 : 5 | 9 : 15 | 30 : 50 | 37.5% and 62.5% |
| 4 : 5 | 12 : 15 | 40 : 50 | 44.4% and 55.6% |
| 16 : 9 | 48 : 27 | 160 : 90 | 64% and 36% |
Frequently asked questions
How do I solve a ratio with a missing number?
Multiply across and divide: for A : B = C : ?, the answer is C × B ÷ A.
How do I simplify a ratio?
Divide both terms by their greatest common factor, for example 12 : 20 ÷ 4 = 3 : 5.
How do I split an amount in a ratio?
Divide the total by the sum of the terms, then multiply by each term.
Can a ratio have decimals?
Yes. The calculator scales decimals to whole numbers before simplifying.
Is 3 : 5 the same as 3/5?
3/5 is the ratio of the first quantity to the second; as a share of the whole, the first is 3/8.
What is a 16 : 9 ratio?
A common screen shape: 16 units wide for every 9 units tall, such as 1920 × 1080 pixels.
How do I check a proportion?
Cross-multiply: the two products must be equal.
What to keep in mind
This scales equivalent ratios; it does not calculate financial debt-to-income ratios.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.