Ratio Converter

The Ratio Convertor is a simple ratio calculator that allows you to convert a ratio to a fraction, percentage, decimal amount, physical amount or simplified ratio. When calculating Math formula (and Physics, Engineering, Chemistry and other formulas for that matter), we will often encounter ratios and need to calculate the value of that ratio. When you encounter a ratio within a formula, the best practice for working with the ratio is normally to convert it to a value from which you can calculate the remaining formula with greater ease. This ratio calculator allows you to convert a ratio into a format better suited for calculating and completing formulas (whether math or any other discipline which uses mathematics).

Ratio Converter
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Ratio Calculator Precision (Decimal Places)
Ratio Numerator : Ratio Denominator
:
Convert Ratio to
Factor Amount

Ratio Converter Results (detailed calculations and formula below)
Ratio Expressed as a Fraction

Please note that the ratio formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each ratio converter calculation, the Ratio Converter Calculator will automatically calculate the results and update the formula elements with each element of the ratio converter calculation. You can then email or print this ratio converter calculation as required for later use.

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Ratio Converter. This image shows the properties and ratio converter formula for the Ratio Converter

How to convert Ratios

Ratio conversion is a key math function as it enables us to turn an indicative value into an amount from which we can calculate and compute math formula. Converting ratios also allows us to display the information and relative value in a way that is more relevant. For example, if you wish to present a business report, converting a ratio to a percentage will provide a figure that more people will be familiar with. Another example is a math student completing their math homework, they need to answer a math question that includes a question with a ratio within it, by changing the ratio to a decimal they can complete the math calculation and answer the math homework question set.

Converting ratios is a very simple math process once you are familiar with it, the Ratio Convertor provided by iCalculator™ allows you to learn how to convert ratios by providing ratio conversion formula and a ratio convertor calculator to check and test your answers. Let's take a look at each ratio conversion formula used in the ratio converter.

before we look at each ratio conversion formula, lets first recap on the lessons covered in the Ratio Comparison Calculator and guide.

Understanding the structure of a ratio with two numbers

Most ratios you encounter will compose two numbers separated by a Colon (:), for example 2:3. In these instances we can refer to the numbers within the ratio in the same manner that we refer to the numbers within fractions, the numerator and the denominator:

3 : 4
= a : b
= numerator : denominator

Understanding the structure of a ratio with more than two numbers

When ratios are expressed with more than two numbers separated by a Colon (:) this indicates that the ratio is in fact a shorthand ratio which composes many ratios, typically used for share ratio calculations. If you are interested you can use the Values to Ratios Calculator to see how a group of numbers can be turned into a ratio and expressed in terms of the total share of an amount of money (for example).

When we encounter these multiple value ratios, we need to take an additional step before we can define the ratio numerator and ratio denominator for each value. We need to do this as each value expressed within a ratio with more than two numbers is in fact a numerator, the ratio denominator for a ratio with more than two numbers is the sum of all numbers expressed in the ratio, lets take a look at an example of a ratio with more than two numbers:

Step 1: calculate the denominator of a ratio with more than two numbers

3:4:5:6:7
Ratio Denominator = 3+4+5+6+7
Ratio Denominator = 25

Step 2: express a ratio with more than two numbers as paired ratios

3:4:5:6:7
= 3:25, 4:25, 5:25, 6:26. 7:25
= 3:25, 4:25, 1:5, 6:26. 7:25

In our example above, in the first step we calculated the ratio denominator of a ratio with more than two numbers by adding each ratio value to calculate the total sum of each ratio. In step two, we broke the ratio with more than two numbers down into its component paired ratios (referred to as paired ratios as they belong together - see the tutorial in the Sharing Ratio Calculator for more details.) Our final action was to simplify each ratio where practicable, in this example the ratio 5:25 was simplified to the ratio 1:5.

We hope that the recap covering ratio structure was useful, remember you can visit any of the supporting ratio calculators to expand your knowledge or ratios further as required. Know that we understand the ratio numerator and ratio denominator structure we can easily convert our ratios into more friendly workable formats to support our requirements.

In our ratio conversion formulas we will use the following key structure:

r_n = Ratio Numerator
r_d = Ratio Denominator
f_n = Fraction Numerator
f_d = Fraction Denominator

How to convert a ratio to a fraction

Converting a ratio to a fraction is a very simple process now that we understand the ratio numerator and denominator structure:

Ratio to Fraction Formula and Calculation

a:b = a/b
= : = /
where:
a = r_n = f_n
b = r_d = f_d

How to convert a ratio to a decimal amount

Converting a ratio to a decimal is a lot easier for some when they have converted the ratio to a fraction as a lot of people are more familiar with converting fractions. With this in mind we convert our ratio to a fraction and then to a decimal to support those who prefer to convert ratios in this way.

Ratio to Decimal Formula and Calculation

a:b = a/b = a ÷ b
= : = / = ÷
=

How to convert a ratio to a percentage

Once we have converted our ratio to a decimal number, it is a simple step to the convert the decimal to a percentage and thereby complete the conversion of the ratio to a percentage:

Ratio to Percentage Formula and Calculation

a:b = a/b = a ÷ b = (a ÷ b) * 100
= : = / = ÷
( ÷ ) × 100 =

Ratio Summary

In summary, ratios are a great way of expressing related numbers for simplicity of expression but we will often encounter times when we need to convert a ratio into a format that is more practical for computation or for communicating information to a wider audience. We hope that your found this ratio conversion guide and Ratio Convertor useful, our final point is to highlight that you can expand your working knowledge of ratios by reviewing the ratios tutorials and guides which accompany our other ratio calculators, we also kindly request that you leave us a rating for the ratio calculator and guides to we can review and improve where required.