Ratio Calculator
Simplify a ratio and see it as a decimal and percentage.
Updates as you type.
What a Ratio Represents
A ratio compares two quantities, showing how much of one thing there is relative to another. Written as A:B, it tells you that for every A units of the first quantity there are B units of the second. Ratios appear everywhere: mixing paint, scaling recipes, reading maps, setting screen resolutions, and splitting profits among partners.
A ratio is closely related to a fraction. The ratio 3:4 carries the same information as the fraction 3/4, and both can be scaled up or down without changing their meaning. This calculator handles the two most common ratio tasks: reducing a ratio to its simplest form and solving a proportion to find a missing value.
Unlike a fraction, a ratio is often left in colon form because it can compare more than two parts and because it emphasizes the relationship rather than a single numeric value.
Simplifying a Ratio to Lowest Terms
To simplify a ratio, divide both sides by their greatest common divisor (GCD), the largest whole number that divides both terms evenly:
A : B = (A ÷ GCD) : (B ÷ GCD)
The result is the smallest whole-number ratio with the same relationship. For example, 18:24 has a GCD of 6, so dividing both sides by 6 gives 3:4. You cannot reduce 3:4 any further because 3 and 4 share no common factor other than 1.
If the ratio contains decimals, first multiply both terms by a power of ten to make them whole numbers, then reduce. For instance, 1.5:2 becomes 15:20 after multiplying by 10, which simplifies to 3:4. A ratio is in lowest terms when its two numbers are coprime, meaning their only shared factor is 1.
Solving Proportions: A:B = C:D
A proportion states that two ratios are equal. When three of the four numbers are known, you can find the fourth using cross-multiplication. From A:B = C:D, the cross products are equal:
A × D = B × C
Rearranging lets you solve for whichever term is missing. To find D, for example, multiply B by C and divide by A:
D = (B × C) / A
This is the engine behind scaling recipes, converting units, resizing images while keeping their shape, and reading map scales. As long as the relationship between the two quantities stays constant, the proportion holds and cross-multiplication gives the exact answer.
Equivalent Ratios and Worked Examples
Equivalent ratios are produced by multiplying or dividing both terms by the same number. The ratios 2:3, 4:6, and 10:15 are all equivalent because each reduces to 2:3. Generating equivalent ratios is how you scale a recipe up or down while keeping the flavor balance identical.
Example 1 — Simplify: Reduce 45:60. The GCD of 45 and 60 is 15. Dividing both by 15 gives 3:4.
Example 2 — Solve a proportion: A recipe uses 2 cups of flour for every 3 cups of milk. How much milk do you need for 5 cups of flour? Set up 2:3 = 5:x. Cross-multiply: 2x = 3 × 5 = 15, so x = 7.5 cups of milk.
Example 3 — Map scale: If 1 cm on a map equals 50 km, how far is a 6 cm distance? Set up 1:50 = 6:x, giving x = 6 × 50 = 300 km.
Frequently Asked Questions
Find the greatest common divisor (GCD) of both terms and divide each term by it. For example, 12:18 has a GCD of 6, so it simplifies to 2:3. A ratio is fully simplified when the two numbers share no common factor other than 1.
A ratio compares two quantities, such as 3:4. A proportion is a statement that two ratios are equal, such as 3:4 = 6:8. Proportions are what you solve when three of the four values are known and you need to find the missing one.
In a proportion A:B = C:D, the cross products are equal, so A × D = B × C. If one value is unknown, substitute the three known numbers and solve the resulting equation. For example, in 2:3 = x:9, cross-multiplying gives 3x = 18, so x = 6.
Yes, but it is usually clearer to convert it to whole numbers. Multiply both terms by a power of ten to clear decimals, or by a common denominator to clear fractions, then simplify. For example, 0.5:1.5 becomes 5:15, which reduces to 1:3.
Equivalent ratios express the same relationship using different numbers. You create them by multiplying or dividing both terms by the same value. For instance, 1:2, 3:6, and 5:10 are all equivalent because each one reduces to 1:2.
A two-part ratio A:B can be written as the fraction A/B and carries the same information. Simplifying a ratio uses the same process as reducing a fraction. The main difference is presentation: ratios use a colon and can compare more than two parts, while fractions express a single value.