Ratio Calculator
A ratio calculator simplifies ratios to their lowest terms and finds equivalent or missing values in proportion problems. Ratios appear everywhere — map scales, recipe scaling, mixing solutions, resizing images, and financial analysis. This tool handles three common ratio tasks: simplifying a given ratio, finding a missing value in equivalent ratios, and scaling a ratio by a multiplier.
Ratio Bar Visual
How to Use
- Choose Simplify when you have a ratio like 12:18 and want the lowest whole-number form.
- Choose Find Missing when you know A:B = C: and need the fourth proportional value.
- Choose Scale when you want to multiply both parts of a ratio by the same factor, such as doubling a recipe.
- Enter A and B as positive numbers. For missing and scale modes, enter C as the known value or multiplier.
- Click Calculate and read both the result cards and the ratio bar. The bar shows the relative size of A and B visually.
Ratio Formula
Equivalent ratio: A/B = C/D, so D = (B × C) / A
Scale ratio: A:B scaled by N = (A × N):(B × N)
A ratio compares two quantities by division. Simplifying a ratio does not change the comparison; it only divides both sides by their greatest common divisor. For example, 12:18 and 2:3 describe the same relationship because both 12 and 18 can be divided by 6. Equivalent ratio problems use cross multiplication. If A/B equals C/D, then A × D equals B × C, so D is found by B × C divided by A. Scaling is different from simplifying because it intentionally increases or decreases both parts by the same factor. This is useful in recipes, drawings, maps, concrete mixes, and screen sizes. The key rule is that whatever operation is applied to one side must also be applied to the other side.
Worked Example
Simplify 12:18. First find the greatest common divisor of 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common factor is 6. Divide both parts by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3. The simplified ratio is 2:3. This means that for every 2 parts of the first quantity, there are 3 parts of the second quantity. If the original numbers represented cups of cement and sand, 12:18 and 2:3 produce the same mix.
Common Ratio Mistakes
The most common ratio mistake is adding the same number to both sides instead of multiplying or dividing both sides by the same number. For example, 2:3 is equivalent to 4:6 because both parts are multiplied by 2. It is not equivalent to 3:4, even though one was added to both parts. Another mistake is reversing the order. A width-to-height ratio of 16:9 is different from 9:16. Always keep labels attached to the numbers. In recipes, maps, and image resizing, swapping the order changes the meaning of the answer. For three-part ratios such as 1:2:4, every part must be scaled together; changing only one part changes the mixture. Labelled units prevent most ratio interpretation errors.
Real-World Ratio Reference
| Use case | Ratio | Meaning |
|---|---|---|
| HD video | 16:9 | Width to height |
| A4 paper | 1:√2 | Width to height |
| Golden ratio | 1:1.618 | Aesthetic proportion |
| Map scale 1:50000 | 1:50000 | 1 cm = 500 m |
| Standard brick | 2:1:0.5 | Length:width:height |
| Concrete mix | 1:2:4 | Cement:sand:gravel |
| Fuel-oil mix | 50:1 | Petrol to 2-stroke oil |
| Blood sugar | 70:130 | Normal fasting mg/dL range |
Ratio Calculator FAQ
What is a ratio
A ratio compares two or more quantities using division. The ratio 2:3 means that for every 2 parts of the first quantity there are 3 parts of the second quantity. Ratios can describe physical sizes, recipes, map distances, financial relationships, image dimensions, or mixing instructions. Unlike a single number, a ratio is about relationship and proportion. If both sides are multiplied by the same number, the relationship stays the same. That is why 2:3, 4:6, and 20:30 are equivalent ratios.
How do I simplify a ratio
To simplify a ratio, divide every part by the greatest common divisor shared by the parts. For a two-part ratio such as 24:36, the greatest common divisor is 12. Dividing both parts by 12 gives 2:3. The simplified ratio expresses the same comparison with smaller whole numbers. If the two parts have no common divisor other than 1, the ratio is already in simplest form. Simplified ratios are easier to read, compare, and use in later calculations.
How do equivalent ratios work
Equivalent ratios describe the same proportional relationship. They are created by multiplying or dividing every part by the same nonzero number. For example, 3:5 is equivalent to 6:10 and 30:50. In missing-value questions, cross multiplication is used. If 3:5 = 12:, then 3/5 = 12/D. Multiply 5 by 12 and divide by 3 to get D = 20. So 3:5 equals 12:20. This is the same reasoning used in map scales and recipe scaling.
Can ratios have decimals
Ratios can include decimals, but they are often converted to whole-number ratios for clarity. If a ratio is 1.5:2.5, multiply both parts by 10 to get 15:25, then simplify to 3:5. Decimal ratios appear in design, finance, chemistry, and measurement. The important rule is to apply the same multiplication to every part. If the decimal values represent measured quantities, keep enough precision so rounding does not change the intended relationship too much.
Where are ratios used in real life
Ratios are used in recipes, construction mixes, map scales, screen sizes, photography, financial analysis, chemistry, and sports statistics. A recipe might use a 2:1 ratio of flour to sugar. A map might use 1:50000 to show that one unit on paper equals fifty thousand units in real distance. A phone screen may use a 20:9 width-to-height ratio. Ratios make it possible to scale quantities up or down while preserving the same relationship between parts.