How to simplify a ratio
To simplify a ratio, divide every term by the greatest common divisor (GCD) of all the terms. This produces the smallest whole-number terms that represent the same proportion.
Divide every term by the GCD Example: 8:12 GCD of 8 and 12 = 4 8 ÷ 4 : 12 ÷ 4 = 2:3 The same idea is used when simplifying a fraction: divide by the greatest common divisor without changing the underlying value or proportion. For ratios with three or more terms, divide every term by the same GCD. For example, 100:250:50 simplifies to 2:5:1.
How to solve a ratio
A proportion is an equation showing that two ratios are equal. If three values are known, you can solve for the missing value by cross-multiplying.
A:B = C:D Example: 2:5 = 6:x 2x = 5 × 6 x = 30 ÷ 2 = 15 This is useful for scale, recipes, measurements, maps, and other situations where two quantities need to remain proportional. Enter three known values in the calculator and leave the unknown value blank.
How to divide a quantity in a ratio
To divide a total according to a ratio, first add the ratio terms together. Divide the total by that sum to find the value of one part, then multiply by each ratio term.
Part = (Ratio term ÷ Sum of ratio terms) × Total Example: split 100 in a 2:3 ratio 2 + 3 = 5 parts First part = (2 ÷ 5) × 100 = 40 Second part = (3 ÷ 5) × 100 = 60 The resulting amounts always have the same ratio as the original terms. This can be used to divide money, quantities, budgets, workloads, or other totals proportionally.
Ratio vs. fraction
Ratios and fractions can represent similar relationships, but they are written and used differently. A ratio compares quantities, such as 2:3, while a fraction represents one quantity relative to another, such as 2/3.
For example, a ratio of 2:3 means that for every 2 parts of one quantity there are 3 parts of another. If you need to perform arithmetic directly with fractions, use the Fraction Calculator.
Ratio vs. percentage
A ratio describes how quantities compare, while a percentage expresses a quantity as a fraction of 100. You can convert a ratio into percentages when the ratio represents parts of a whole.
Total parts = 2 + 3 = 5 First part = 2 ÷ 5 × 100 = 40% Second part = 3 ÷ 5 × 100 = 60% If you need to calculate percentages directly, use the Percentage Calculator.
Using ratios in real-world calculations
Ratios are useful whenever two or more quantities need to maintain a fixed relationship. For example, a business might divide a $10,000 budget between marketing and operations in a 2:3 ratio. The total number of parts is 5, so marketing receives $4,000 and operations receives $6,000.
For calculations involving business revenue, costs, or profitability, see the Profit Margin Calculator.
Frequently asked questions
How do you simplify a ratio?
Divide every term in the ratio by their greatest common divisor (GCD). 8:12 has a GCD of 4, so it simplifies to 2:3 — the same proportion, written with smaller numbers.
How do you solve a ratio for an unknown value?
Set up a proportion (A:B = C:D) with the unknown in one position, then cross-multiply and solve. For 2:5 = 6:?, the missing value is (5 × 6) ÷ 2 = 15.
How do you split a number into a ratio?
Divide the total by the sum of the ratio's terms, then multiply that result by each term individually. Splitting 100 in a 2:3 ratio: the sum is 5, so each "part" is worth 20, giving 40 and 60.
What does a ratio mean?
A ratio compares two or more quantities. A ratio of 2:3 means that for every 2 parts of one quantity, there are 3 parts of another. Ratios can be simplified as long as every term is divided by the same nonzero number.
How do you convert a ratio to a percentage?
Add the terms of the ratio to find the total number of parts, then divide each term by that total and multiply by 100. For a 2:3 ratio, there are 5 parts, so the percentages are 2 ÷ 5 × 100 = 40% and 3 ÷ 5 × 100 = 60%.
Can a ratio have more than two numbers?
Yes. Ratios can compare three or more quantities. For example, 2:5:1 compares three parts. To simplify it, divide every term by the greatest common divisor of all the terms.