Type each term on its own line, in the same order as in your ratio, and select “Calculate”. The result shows the original ratio, the common denominator, the whole-number terms, the GCD and the simplest ratio, which reads as the parts of the first quantity for every part of the second. If you want to know what fraction of the total each part is, use ratio to fraction.
Worked example: 1/2 : 3/4
A banner is 1/2 yard wide and 3/4 yard tall. What is the width : height ratio in whole numbers?
- Find the LCM of the denominators. The denominators are 2 and 4, and their LCM is 4.
- Multiply every term by that number. 1/2 × 4 = 2 and 3/4 × 4 = 3.
- Find the GCD of the whole numbers. GCD(2, 3) = 1, so it cannot be reduced further.
The result is 1/2 : 3/4 = 2 : 3.
Check. 1/2 ÷ 3/4 = 2/3 and 2 ÷ 3 = 2/3. The banner has 2 parts of width for every 3 parts of height.
Multiplying by the LCM does not change the relationship, because every term is scaled the same way. To see how that common divisor is found, see the greatest common divisor page.
What changes depending on the data
Real data does not always come as whole numbers. The table gathers four cases with the step that takes each one to whole numbers.
| Case | Ratio | Step | Result |
|---|---|---|---|
| Three terms | 12 : 18 : 30 | ÷ 6 | 2 : 3 : 5 |
| Decimals | 0.5 : 2 | × 2 | 1 : 4 |
| Mixed number | 1 1/2 : 2 | 3/2 : 2; × 2 | 3 : 4 |
| Screen | 1920 : 1080 | ÷ 120 | 16 : 9 |
In the first three cases the same factor is applied to every term. For the screen, it is enough to divide width and height by their GCD, which is why a 1920 by 1080 image and a 1280 by 720 image have the same shape.
When to use this ratio and what to do next
Simplifying helps you compare recipes, mixtures, scales or formats using the same small numbers. A simplified ratio keeps the order of its terms, so 2 : 3 is not equal to 3 : 2.
You can continue in several ways with the reduced ratio. To find what fraction of the total each part is, use ratio to fraction. To split an amount according to the ratio, the proportional sharing calculator does the work. If one term is missing in an equality between ratios, solve it with proportions or the rule of three. When you only have a fraction, simplify fractions applies the same method, and the guide to ratio, proportion and fraction explains how the three ideas differ.
Sources
In the OpenStax chapter Ratios and Rate, a ratio compares two quantities in the same unit and is written as a fraction, and ratios with decimals are turned into whole numbers by moving the decimal points the same number of places (accessed October 17, 2026). The calculations on this page come from the calculator engine and are checked with the GCD and the LCM, not with that chapter.
Frequently asked questions
What is the difference between a ratio and a fraction?
A ratio compares two quantities and is written with a colon; a fraction is a quotient. With 3 red chips and 5 blue chips, the ratio is 3 : 5, the red chips are 3/5 of the blue ones and 3/8 of the total. Simplifying the ratio changes none of those readings. To move from one to the other, use ratio to fraction.
How do I enter a decimal or a mixed number in the calculator?
Type each term on its own line. A decimal uses a point, like 0.75, and a mixed number has a space between the whole number and the fraction, like 2 1/4. The calculator accepts whole numbers, fractions, decimals and mixed numbers, from 2 to 10 terms. With 0.75 and 2.25 the ratio becomes 1 : 3.
What happens with a zero or negative term?
A zero is valid if another term is positive: 0 : 14 becomes 0 : 1, because the GCD of 0 and 14 is 14. The ratio 0 : 0 describes no relationship, and the calculator rejects it. Negative terms are rejected too, because the tool works with nonnegative quantities.