Ratio Calculator
Simplify ratios, solve for missing values, scale ratios up or down, and convert between ratio formats — with step-by-step solutions.
The Ratio Calculator is a free online tool designed to help you calculate and analyze simplify ratios solve proportions and scale ratios up or down with step-by-step solutions. Planning details accurately is crucial for making smart personal or financial decisions, and this calculator provides instant clarity with downloadable PDF reports.
This tool is built to benefit students, teachers, parents, and home cooks who need to verify numerical operations. By showing the complete mathematical formulas and steps, it helps you understand the process rather than just giving a raw final answer. By evaluating these key calculations, you can determine exactly how different inputs affect your results and align them with your direct planning requirements.
Before using this tool, make sure you have your details ready, such as your numbers, fractions, or ratios in the designated input boxes and select your desired calculation method. This ensures the most accurate calculations.
Examples
18:24 → simplified 3:4 | 75%:25% | decimal 0.75
3:4 = x:20 → missing value x = 15
3:4 scaled by a factor of 5 → 15:20
Frequently Asked Questions
What is a ratio and how is it written?
A ratio is a mathematical comparison of two numbers or quantities. It shows the relative size of one value compared to another. Ratios can be written using a colon (e.g., 3:4), as a fraction (3/4), or using the word "to" (3 to 4).
How do you simplify a ratio?
To simplify a ratio, you find the Greatest Common Divisor (GCD) of the numbers in the ratio and divide each number by that divisor. For example, to simplify 18:24, the GCD is 6. Dividing both terms by 6 results in the simplified ratio of 3:4.
What is a proportion?
A proportion is an equation stating that two ratios are equal, written as A:B = C:D or A/B = C/D. If you know three of the values, you can solve for the missing fourth value using cross-multiplication: A × D = B × C.
How do you scale a ratio up or down?
To scale a ratio, you multiply or divide all terms in the ratio by the same positive number, known as the scale factor. For example, scaling the ratio 3:5 up by a factor of 4 yields 12:20, which represents the exact same relationship on a larger scale.
Can ratios compare more than two values?
Yes, ratios can compare three or more values (called a continued ratio). For example, a recipe might call for a ratio of 1 part oil, 2 parts vinegar, and 3 parts water, which is written as 1:2:3. Our simplify tool works with two-part ratios, but the scaling rules apply to any number of parts.
How do ratios relate to fractions and percentages?
A ratio like 3:5 means there are 3 parts of one component for every 5 parts of another, totaling 8 parts. As a fraction of the whole, the first component is 3/8 (37.5%) and the second is 5/8 (62.5%). The decimal value of the ratio itself is 3 ÷ 5 = 0.6.