--- title: "Ratio Calculator | Method Calculator" description: "Simplify a ratio, solve a proportion (A:B = C:D) for the missing value, or scale a ratio up or down." canonical_url: "https://methodcalculator.com/ratio-calculator" meta: "og:description": "Simplify a ratio, solve a proportion (A:B = C:D) for the missing value, or scale a ratio up or down." "og:image": "https://methodcalculator.com/_og/s/o_1108f32fe9103cfa.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Ratio Calculator – Free Online Tool" "twitter:image": "https://methodcalculator.com/_og/s/o_1108f32fe9103cfa.png" --- > Index of every page on this site: [llms.txt](https://methodcalculator.com/llms.txt) # **Ratio Calculator** Reduce a ratio to its simplest form, solve a proportion for a missing value, or scale a ratio up or down to a new size. ## **Result** 6 : 8 simplifies to **3 : 4**
As a fraction (A ÷ B)
0.75
A as a share of the total
42.86%
B as a share of the total
57.14%
Equivalent ratios
6 : 8, 9 : 12, 30 : 40
## What is a ratio? A ratio expresses how much of one thing there is compared with another. A recipe that calls for 2 cups of flour to 3 cups of water has a flour-to-water ratio of 2 : 3. Ratios are used for mixing paint and concrete, scaling recipes, map scales, screen resolutions (16 : 9) and financial measures such as the debt-to-income ratio. The order matters: 2 : 3 is not the same as 3 : 2. ## Formulas **Simplifying:** divide both terms by their greatest common divisor (GCD). 6 : 8 → GCD is 2 → **3 : 4**. **Proportion:** if A : B = C : D then A × D = B × C. For 2 : 3 = C : 9, C = (2 × 9) ÷ 3 = 6. **Scaling:** multiply both terms by the same factor. 3 : 4 scaled by 2.5 is 7.5 : 10; the ratio is unchanged because both parts grew together. *Worked example:* a photo is 6 inches by 8 inches. Simplifying 6 : 8 gives 3 : 4, so the picture has the classic 4 : 3 landscape proportions turned on its side. To enlarge it so the short side becomes 9 inches, solve 6 : 8 = 9 : D, giving D = 8 × 9 ÷ 6 = 12 inches. ## How to use this calculator 1. **Simplify:** enter A and B. Decimals are converted to whole numbers before reducing. 2. **Solve a proportion:** fill in three of A, B, C and D and leave the unknown blank; the calculator finds it by cross-multiplying. 3. **Scale:** enter the ratio and a multiplier such as 2 (double) or 0.5 (halve). ## Tips - To compare more than two quantities, simplify them pairwise or divide all of them by their common GCD. - A ratio of a part to the whole is a fraction; convert it to a percentage with the [percentage calculator](https://methodcalculator.com/percentage-calculator). - Ratios with the same simplified form are equivalent: 3 : 4, 6 : 8 and 75 : 100 all describe the same relationship. - For arithmetic on fractions themselves, see the [fraction calculator](https://methodcalculator.com/fraction-calculator). ## **Frequently asked questions ** ### **What is a ratio?** A ratio compares two quantities by division. "3 : 4" (read "three to four") means that for every 3 of the first thing there are 4 of the second. Ratios can be written with a colon, as a fraction (3/4) or with the word "to". ### **How do I simplify a ratio with decimals?** Multiply both parts by a power of ten until they are whole numbers, then divide both by their greatest common divisor. 1.5 : 2 becomes 15 : 20, and dividing by 5 gives 3 : 4. The calculator does this automatically. ### **How do I solve a proportion?** Cross-multiply. If a : b = c : d then a × d = b × c. Solve that equation for the unknown. For 2 : 3 = x : 9, cross-multiplying gives 3x = 18, so x = 6. ### **What is the difference between a ratio and a fraction?** A fraction is a part compared with the whole, whereas a ratio usually compares one part with another part. If a class has 3 boys for every 4 girls the ratio of boys to girls is 3 : 4, but boys are 3/7 of the class. ## **Related calculators ** - [**Fraction Calculator**](https://methodcalculator.com/fraction-calculator) - [**Percentage Calculator**](https://methodcalculator.com/percentage-calculator) - [**Area Calculator**](https://methodcalculator.com/area-calculator) ```json {"@context":"https://schema.org","@graph":[{"@id":"https://methodcalculator.com/#website","@type":"WebSite","description":"Free online calculators for finance, health and fitness, math and everyday life. 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