How to simplify a ratio
A ratio compares two quantities. To simplify a whole-number ratio, divide both values by their greatest common divisor.
For example, the greatest common divisor of 12 and 18 is 6. Dividing both values by 6 reduces 12:18 to 2:3.
Ratio calculation example
For a ratio of 12:18, the simplified ratio is 2:3. That simplified ratio contains five total parts.
The first quantity represents 2 out of 5 parts, or 40% of the combined total. The second quantity represents 3 out of 5 parts, or 60%.
How to simplify decimal ratios
Decimal ratios can first be converted to equivalent whole-number values by multiplying both sides by the same power of ten.
For example, 1.5:2.25 can be treated as 150:225. Reducing both values by 75 gives the simplified ratio 2:3.
How to calculate an equivalent ratio
Equivalent ratios preserve the same relationship between both quantities. Multiply both parts by the same scale factor.
If the original ratio is 12:18 and the first value must become 10, the scale factor is 10 ÷ 12. Applying that same factor to 18 gives 15, so the equivalent ratio is 10:15.
Ratio as a percentage
A two-part ratio can also be expressed as each part's percentage of the combined total.
For a 2:3 ratio, the first part is 40% of the total and the second part is 60%.
Ratio vs. fraction
A ratio such as 2:3 compares one quantity with another. It can also be written as 2/3 when expressing the first quantity relative to the second.
That is different from saying the first quantity is 2/3 of the combined total. In a 2:3 ratio, the combined total is five parts, so the first share of the total is 2/5.
Ratios and proportions
A proportion states that two ratios are equivalent. For example, 2:3 and 10:15 form the same proportion because both parts were multiplied by five.
The scale mode lets you enter a target value for either side and calculates the matching value on the other side.
Ratios with units
When both quantities use the same unit, that unit cancels when the ratio is simplified. If the quantities use different units, convert them to compatible units first when appropriate.
For example, comparing 1 meter with 50 centimeters directly as 1:50 would mix units. Converting 1 meter to 100 centimeters gives the meaningful ratio 100:50, which simplifies to 2:1.
Ratio vs. aspect ratio
General ratios can compare many kinds of quantities. An aspect ratio specifically describes the proportional width and height of an image, screen or rectangle.
For image dimensions and resizing, use the Aspect Ratio Calculator.
This calculator accepts positive ratio values and simplifies decimal inputs up to six decimal places. For measurements with units, convert quantities to compatible units before comparing them when needed.
Frequently asked questions
What is 12:18 simplified?
12:18 simplifies to 2:3 because both values can be divided by 6.
Can a ratio contain decimals?
Yes. Decimal ratios can be converted to equivalent whole-number ratios and then reduced to lowest terms.
How do I find an equivalent ratio?
Multiply or divide both parts by the same scale factor. For example, 2:3 multiplied by 5 becomes 10:15.
What percentage is each part of a 2:3 ratio?
There are five total parts. The first part is 40% and the second part is 60% of the total.
Is a ratio the same as an aspect ratio?
An aspect ratio is a specific type of ratio used to compare width and height. A general ratio can compare many other kinds of quantities.
Using this calculator effectively
The Ratio Calculator simplifies two-part ratios, calculates equivalent scaled ratios and shows how each part compares with the combined total. Decimal inputs can also be reduced to equivalent whole-number ratios.
Common uses
- Reducing ratios to lowest terms for everyday comparisons, recipes, mixtures and proportions.
- Scaling a known ratio when one side needs to reach a specific target value.
- Converting the two parts of a ratio into percentage shares of the combined total.
Tips for a better estimate
- Use quantities expressed in compatible units when the ratio compares physical measurements.
- Enter positive values for both parts of the ratio and use the same scale factor when creating equivalent ratios.
- Remember that a ratio such as 2:3 means the first part is 2 out of 5 total parts, not 2/3 of the combined total.
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