📐 Math
Ratio Calculator
Use this free ratio calculator to get fast, accurate results.
📝 Your Assumptions
A ratio calculator compares two numbers to find their relative size, simplifying the relationship into a single number. Whether you're mixing paint, adjusting a recipe, or analyzing financial ratios, this tool gives you the simplified ratio in seconds. Just enter two values and see the ratio instantly.
How to Use This Calculator
Follow these steps to calculate any ratio quickly and accurately.
1
Enter the first value
Type the first number of your ratio into the 'Value' field. For example, if you're comparing 15 apples to 20 oranges, enter 15.
2
Enter the second value
Type the second number into the 'Percentage' field. In the apple example, you would enter 20.
3
Click the calculate button
Press the 'Calculate' button to process your numbers. The calculator will immediately compute the simplified ratio.
4
Read the result
The result appears as a simplified ratio, such as 3:4. This means for every 3 units of the first value, there are 4 units of the second.
5
Reset for a new calculation
Click 'Reset' to clear the fields and enter new numbers. This lets you quickly compare multiple ratios without reloading the page.
What Your Results Mean
Understanding your ratio result helps you apply it correctly in real situations.
Simplified ratio
The result shows the ratio in its simplest form, like 2:3. This means the two quantities are in a 2-to-3 relationship, regardless of the actual sizes.
Equivalent ratios
A simplified ratio like 2:3 is equivalent to 4:6, 6:9, or 20:30. All these ratios represent the same proportional relationship between two numbers.
Part-to-part vs part-to-whole
If you compare 5 boys to 10 girls, the part-to-part ratio is 1:2. The part-to-whole ratio of boys to total students is 5:15, which simplifies to 1:3.
Scaling recipes
A recipe with a flour-to-sugar ratio of 3:1 means for every 3 cups of flour, use 1 cup of sugar. If you use 6 cups of flour, you need 2 cups of sugar.
Financial ratios
In finance, a debt-to-income ratio of 1:3 means your debt is one-third of your income. Lenders often look for ratios below 1:2.5 for mortgage approval.
Aspect ratios
A 16:9 aspect ratio means for every 16 units of width, there are 9 units of height. This is common for widescreen displays and video content.
Key Terms
Ratio
A ratio compares two quantities, showing how many times one value contains or is contained within the other. It can be written as a:b, a/b, or 'a to b'.
Simplified ratio
A ratio reduced to its smallest whole numbers by dividing both terms by their greatest common divisor. For example, 10:15 simplifies to 2:3.
Proportion
An equation stating that two ratios are equal, such as 1/2 = 2/4. Proportions are used to solve for unknown quantities in ratio problems.
Part-to-part ratio
A ratio that compares one part of a whole to another part, like comparing the number of cats to dogs in a pet store. It does not include the total.
Part-to-whole ratio
A ratio that compares a part to the total, such as the number of red marbles to all marbles in a jar. It is often expressed as a fraction or percentage.
❓ Frequently Asked Questions
To calculate a ratio between two numbers, divide both numbers by their greatest common divisor (GCD). For example, to find the ratio of 18 to 24, the GCD is 6. Divide both by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so the ratio is 3:4. If the numbers are decimals, multiply both by 10, 100, or another power of 10 to make them whole numbers before simplifying. For instance, 0.5 to 1.5 becomes 5 to 15 after multiplying by 10, which simplifies to 1:3. Our ratio calculator automates this process, giving you the simplified ratio instantly. After getting the ratio, you might want to convert it to a percentage using our percentage calculator to express the relationship as a fraction of 100.
A ratio of 1:2 means that for every 1 unit of the first quantity, there are 2 units of the second quantity. For example, if you have a ratio of 1:2 for blue to red marbles, and you have 5 blue marbles, you must have 10 red marbles. The total number of marbles would be 15, and the blue marbles make up 1/3 of the total. This ratio can be scaled up or down while maintaining the same relationship. If you have 100 blue marbles, you would need 200 red marbles. In terms of fractions, the first quantity is 1/3 of the total and the second is 2/3. To convert this ratio to a percentage, the first part is 33.33% and the second is 66.67%. You can use our percentage calculator to verify these conversions quickly.
To simplify a ratio like 10:15, find the greatest common divisor (GCD) of both numbers and divide each by it. The GCD of 10 and 15 is 5. Divide 10 by 5 to get 2, and 15 by 5 to get 3, resulting in the simplified ratio 2:3. This means the relationship between the two quantities is the same as 10:15, but expressed in the smallest possible whole numbers. Simplifying ratios makes them easier to compare and use in calculations. For example, a recipe that calls for a 10:15 ratio of sugar to flour is the same as a 2:3 ratio. If you need to scale the recipe, using 2:3 is simpler. Our ratio calculator automatically simplifies any ratio you input, saving you the step of finding the GCD manually. If you need to convert the ratio to a decimal or percentage, our percentage calculator can help.
A ratio compares two quantities, while a fraction represents a part of a whole. For example, if a class has 12 boys and 16 girls, the ratio of boys to girls is 12:16, which simplifies to 3:4. This ratio compares boys to girls directly. However, the fraction of boys in the class is 12/28 (since the total is 28), which simplifies to 3/7. So, the ratio is 3:4 (boys:girls), but the fraction is 3/7 (boys:total). Ratios can be part-to-part or part-to-whole, while fractions are always part-to-whole. In everyday use, ratios are often written with a colon (:) and fractions with a slash (/). Our ratio calculator helps you find the simplified ratio, and our percentage calculator can convert fractions to percentages for easier comparison.
Yes, ratios are perfect for scaling recipes. Suppose a recipe calls for a flour-to-sugar ratio of 3:1. If you want to use 6 cups of flour, you need to maintain the ratio. Since 6 cups is twice the original 3 cups, you double the sugar to 2 cups. The ratio remains 3:1, but the quantities are scaled. Similarly, if you want to use 9 cups of flour, you multiply both parts by 3, giving 9 cups flour and 3 cups sugar. To find the multiplier, divide your desired amount of one ingredient by its original amount in the ratio. For example, if you have 4.5 cups of flour and the ratio is 3:1, the multiplier is 4.5 ÷ 3 = 1.5, so sugar needed is 1×1.5 = 1.5 cups. Our ratio calculator can simplify the ratio first, making scaling easier. If you need to convert the ratio to a percentage for a different recipe, use our percentage calculator.
To calculate a ratio from a percentage, first convert the percentage to a decimal by dividing by 100, then express it as a fraction, and finally simplify. For example, if you have 40%, that's 40/100, which simplifies to 2/5. So the ratio is 2:5 (part-to-whole) or 2:3 (part-to-part, since the remaining part is 3). If you have two percentages, like 30% and 70%, the ratio is 30:70, which simplifies to 3:7. To find the ratio of two numbers given as percentages of a whole, simply write the percentages as a ratio and simplify. For instance, if a survey shows 60% prefer option A and 40% prefer option B, the ratio is 60:40, simplifying to 3:2. Our ratio calculator can simplify any ratio you input, and our percentage calculator can convert ratios back to percentages. This is useful in finance, where debt-to-income ratios are often expressed as percentages.
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