Solved proportion
Missing value
Simplified ratio
Equivalent fraction
As a decimal
Table of Contents
What is a ratio?
A ratio compares two quantities of the same kind. Written as A:B (read "A to B"), it expresses how much of one thing there is relative to another. Ratios appear everywhere — recipes (2 cups flour to 1 cup sugar), maps (a 1:50,000 scale), aspect ratios in photography (16:9), and finance (a 4:1 debt-to-equity ratio). This calculator handles the three most common ratio operations: solving a proportion for a missing value, simplifying a ratio to lowest terms, and scaling a ratio.
Solving a proportion
A proportion is a statement that two ratios are equal: A:B = C:D. The fundamental property of proportions is that the cross-products are equal:
A × D = B × C
If three of the four values are known and one is unknown, you can rearrange to solve for the missing value. To use the calculator, just leave that one box blank.
Example: Solve 3:4 = 6:?. Cross-multiply: 3 × ? = 4 × 6 = 24. So ? = 24 / 3 = 8.
Simplifying a ratio
To simplify a ratio, divide both numbers by their greatest common factor (GCF). The result is the equivalent ratio in its lowest terms — the ratio cannot be reduced further while keeping the proportion the same.
Example: Simplify 12:18. The GCF of 12 and 18 is 6. Divide both by 6 to get 2:3.
Simplifying ratios is useful for clearer communication ("the soil mix is 2:3 sand-to-loam" reads better than "12:18") and for spotting equivalences ("18:24 and 12:16 are both equivalent to 3:4").
Scaling a ratio
To scale a ratio up or down, multiply both sides by the same factor. The proportion stays the same but the absolute quantities change. This is how recipes get scaled to feed more people, or how scale models are produced from real-world measurements.
Example: The original recipe uses a 2:1 flour-to-sugar ratio (2 cups flour, 1 cup sugar). To triple it, multiply both by 3: now you need 6 cups flour and 3 cups sugar — still a 2:1 ratio.
Ratios, fractions, and percentages
A ratio A:B can be expressed as a fraction A/B (the relative amount of A compared to B) or as a part-to-whole percentage A/(A+B) × 100% (the share of A in the total).
For 3:4: the fraction is 3/4 = 0.75; the percentage of A in the total is 3/(3+4) = 3/7 ≈ 42.9%.
This calculator returns both the fraction (A divided by B) and the decimal equivalent so you can switch between formats easily.
Where ratios show up
Cooking: A 1:1 ratio of vinegar to oil is the basis of a vinaigrette. Bread doughs are described by hydration (water:flour ratio).
Finance: The price-to-earnings (P/E) ratio compares a stock's price to its annual earnings. The debt-to-income ratio is critical when applying for a mortgage.
Maps and models: A scale of 1:50,000 means 1 cm on the map represents 50,000 cm (500 m) in the real world.
Photography and design: Aspect ratios (16:9 for HDTV, 3:2 for DSLR photos, 1:1 for Instagram) describe the proportions of an image or screen.
Chemistry and mixing: Two-part epoxies often specify mix ratios like 4:1 by volume. Concrete is mixed in ratios such as 1:2:4 (cement:sand:gravel).
Three-part ratios
Some ratios involve three or more parts, written as A:B:C — for example, the 1:2:4 cement:sand:gravel ratio for concrete. To simplify a multi-part ratio, divide every number by the GCF of all of them. To scale, multiply every number by the same factor. Use the simplify form above for two-part ratios; for three-part ratios, simplify pairs at a time or use the GCF calculator directly.
FAQs
A ratio compares two quantities of the same kind, expressed as A:B (read 'A to B'). It tells you how much of one thing there is relative to another. For example, a recipe with a 2:1 flour-to-sugar ratio uses twice as much flour as sugar. Ratios are used everywhere — in cooking, scale models, finance, photography, and chemistry.
When you see two equivalent ratios written as A:B = C:D, the cross-products are equal: A × D = B × C. If one of the four values is unknown, rearrange the equation to solve for it. For example, if 3:4 = 6:?, then 3 × ? = 4 × 6, so ? = 24 / 3 = 8.
Find the greatest common factor (GCF) of both numbers and divide each by it. For example, to simplify 12:18, the GCF is 6, so the simplified ratio is 12/6 : 18/6 = 2:3. A ratio is in its simplest form when its two numbers share no common factor greater than 1.
A ratio compares two quantities (e.g. 3:4). A proportion is a statement that two ratios are equal (e.g. 3:4 = 6:8). Solving a proportion typically means finding a missing value that makes the equation true.
Convert the ratio to a fraction (A:B becomes A/(A+B) for the share of A in the total), then multiply by 100. For example, 3:7 means 3 parts out of 10 total, which is 3/10 = 30%. If you want B's share, that is 7/10 = 70%.
Multiply both numbers in the ratio by the same scaling factor. To double the recipe ratio 2:1, multiply both sides by 2 to get 4:2 (which simplifies back to 2:1, since the proportion has not changed). To triple it, multiply by 3 to get 6:3. Scaling preserves the proportion.