Ratio Calculator
Simplify 2-part or 3-part ratios, work with whole numbers or decimals, see equivalent ratios, and scale a ratio while keeping the same proportion.
Simplify a Ratio
Enter two or three numerical terms. Decimal values are converted to an equivalent integer ratio before the ratio is reduced.
Enter your values to simplify the ratio.
Scale This Ratio
After simplifying, choose one ratio part and enter the value you want that part to become. The other terms are scaled by the same factor.
What Is a Ratio?
A ratio compares quantities by showing their relative sizes. It is commonly written with a colon, such as 2:3.
The ratio 2:3 means that for every 2 parts of the first quantity, there are 3 corresponding parts of the second quantity.
These ratios use different numbers, but they represent the same proportion because both terms have been multiplied by the same factor.
How to Simplify a Ratio
For whole-number ratios, simplification works much like reducing a fraction. Find the greatest common divisor (GCD) of all the terms, then divide every term by that same number.
12 ÷ 6 = 2
18 ÷ 6 = 3
Simplified ratio = 2 : 3
Simplifying Ratios With Decimals
A ratio can contain decimals. Before reducing it, the decimal terms can be multiplied by a power of 10 so that all terms become whole numbers.
× 10 → 15 : 25
÷ 5 → 3 : 5
This calculator follows that approach automatically. It first converts the entered finite decimal values into a common integer scale and then reduces the resulting integers.
The calculator interprets the decimal digits you enter. For example, 1.25 is treated as the exact entered decimal 1.25 for the purpose of ratio simplification rather than being silently rounded to 1.
Two-Part and Three-Part Ratios
A ratio is not limited to two quantities. Three-part ratios are useful when three quantities need to remain in the same relative proportion.
When simplifying a three-part ratio, every term must be divided by the same common factor. Reducing only two of the three terms would change the proportion.
How to Scale a Ratio
Scaling changes the numerical size of a ratio without changing its proportion. Every term must be multiplied by the same scale factor.
For example, suppose the ratio is 2:3 and you want the first part to equal 10:
2 × 5 = 10
3 × 5 = 15
Scaled ratio = 10 : 15
The Scale This Ratio section above performs this calculation after you simplify your ratio.
Ratios as Fractions and Percentages
For a two-part ratio a:b, there are two common interpretations, and it is important not to confuse them.
One quantity compared with the other
The expression a ÷ b compares the first quantity directly with the second.
Each part as a share of the total
If the two quantities together form one total, the total number of parts is a + b. For 2:3, there are five total parts.
Second share = 3 ÷ 5 = 60%
So saying “2 is 66.67% of 3” is different from saying “the first part represents 40% of the combined total.”
Practical Ratio Examples
| Situation | Original Ratio | Simplified | Meaning |
|---|---|---|---|
| Red to blue items | 12:18 | 2:3 | 2 red for every 3 blue |
| Recipe quantities | 500:250 | 2:1 | 2 parts of one ingredient to 1 part of another |
| Three-color mix | 6:9:12 | 2:3:4 | Three quantities remain in the same proportion |
| Equal groups | 20:20 | 1:1 | The two quantities are equal |
Ratios are commonly used in recipes, mixtures, scale drawings, classroom mathematics, maps, dimensions and quantity comparisons. Whether a ratio is appropriate depends on what the numbers represent and whether their units are compatible.
Units, Zero and Negative Values
Keep units consistent
A ratio can compare values expressed in different units, but they normally need to be converted to compatible units before numerical simplification is meaningful.
For example, the ratio 1 meter : 50 centimeters should not simply be entered as 1:50. Convert 1 meter to 100 centimeters first:
Zero terms
A ratio may contain a zero term in some mathematical contexts. For example, 0:5 reduces to 0:1. However, 0:0 does not provide a meaningful proportional relationship and this calculator rejects a ratio in which every term is zero.
Negative terms
The calculator can mathematically reduce ratios containing negative values. In many everyday ratio applications—such as recipes, lengths or item counts—negative quantities may not make practical sense, so interpret the result according to the situation being measured.
Equivalent Ratios
Equivalent ratios describe the same relative relationship. Starting from a simplified ratio, multiply every term by the same number.
| Base Ratio | ×2 | ×3 | ×5 |
|---|---|---|---|
| 2:3 | 4:6 | 6:9 | 10:15 |
| 1:4 | 2:8 | 3:12 | 5:20 |
| 2:3:4 | 4:6:8 | 6:9:12 | 10:15:20 |
Dividing every term by the same non-zero factor works in the opposite direction and can reduce an equivalent ratio back toward its simplest form.
Browser-Based Calculation
The ratio calculations on this page are designed to run with JavaScript in your browser. The numerical values entered into the calculator do not need to be sent to a separate calculation service solely to simplify or scale the ratio.
Normal website technologies such as hosting, analytics, security, consent systems or advertising may operate separately according to ToolZippy’s applicable site policies.
Ratio Calculator FAQs
How do I simplify a ratio?
For whole-number terms, find their greatest common divisor and divide every term by that number. For example, 12:18 divided by 6 becomes 2:3.
Can this calculator simplify decimal ratios?
Yes. It converts the entered finite decimals to a common integer scale and then reduces the resulting integer ratio.
Can I calculate a three-part ratio?
Yes. Select 3-Part Ratio and enter all three values. The calculator finds a common reduction factor for all three terms.
What does a ratio of 2:3 mean?
It means that for every 2 parts of the first quantity there are 3 corresponding parts of the second quantity.
Are 2:3 and 4:6 the same ratio?
Yes. Dividing 4 and 6 by 2 gives 2:3, so the ratios are equivalent.
How do I scale a ratio?
Find the scale factor by dividing the target value by the corresponding ratio term, then multiply every term by that same factor.
Can a ratio contain zero?
Yes in some mathematical contexts. For example, 0:5 can simplify to 0:1. A ratio in which every term is zero does not define a useful proportional relationship.
Can a ratio contain negative numbers?
The calculator can reduce negative numerical terms mathematically, although negative ratios may not have a practical interpretation for quantities such as lengths, ingredients or item counts.
How do I convert a ratio to percentages?
If the ratio parts represent shares of one total, add the parts and divide each part by that total. For 2:3, the total is 5, so the shares are 40% and 60%.
Do I need to convert units before calculating a ratio?
When the quantities represent the same type of measurement, convert them to compatible units first. For example, 1 meter to 50 centimeters should first become 100 centimeters to 50 centimeters, which simplifies to 2:1.