Ratio Calculator
Simplify a ratio such as 12:18:24, scale it to a new size, find a missing number in a proportion, or split a total into shares.
Simplify a ratio
Scale a ratio
Solve a proportion
Fill in three boxes and leave one empty. The ratio a : b = c : d means a divided by b equals c divided by d.
Share a total in a ratio
Worked examples
Simplifying a ratio
12:18
2:3
The highest common factor of 12 and 18 is 6, and dividing both parts by it gives 2:3.
Missing value in a proportion
2:3 equals 8:x
x = 12
Both ratios must scale by the same amount, and 8 is four times 2, so x is four times 3, which is 12.
About Ratio Calculator
A ratio compares two or more amounts, such as the cups of flour to cups of sugar in a recipe, or the number of boys to girls in a class. Ratios can look complicated when the numbers are large, so simplifying them makes the relationship clear. This calculator divides every part by their highest common factor to give the simplest form. For example, 12:18:24 becomes 2:3:4, because 6 is the largest number that divides all three parts evenly. Ratios with decimals, such as 1.5:2, are converted into whole numbers first so the working stays easy to follow.
Ratios are also useful for scaling, which means changing the size of a mix while keeping its proportions the same. Multiply each part by the same number to make a larger batch, or scale to a total to find how much of each ingredient or share you need. Solving a proportion finds one missing term when three are known, using the rule that the cross products are equal. You can also share a total in a ratio to split money, time or materials fairly, such as dividing 250 in a 2:3 ratio into 100 and 150.
How to use Ratio Calculator
- Enter a ratio with colons between the parts to simplify it, such as 12:18:24.
- Enter a ratio and a multiplier, or a new total, to scale it up or down.
- Fill in three of the four boxes in a proportion and leave the fourth empty.
- Enter a total and a ratio to share the total into parts, then read each share.
Common uses
- Scaling a recipe up or down for more or fewer people
- Mixing paint, concrete or squash in the correct proportions
- Splitting a shared prize or bill in an agreed ratio
- Converting a map scale or model size into real measurements
Frequently asked questions
How do you simplify a ratio?
Divide every part of the ratio by the highest common factor of all the parts. For 15:25, the highest common factor is 5, so the simplest form is 3:5. If the ratio contains decimals, multiply every part by a power of ten first, so 0.5:1.5 becomes 5:15 and then 1:3. Keep the parts in the same order as the original ratio.
What is a proportion?
A proportion says that two ratios are equal, written a:b = c:d. Multiplying across gives a times d equals b times c, so any missing term can be found by rearranging. For example, if 3:4 equals 9 to a missing number, the missing number is 12, because 3 times 12 equals 4 times 9. Proportions are used for scaling recipes, reading maps and converting between units.
How do you share an amount in a ratio?
Add the parts of the ratio together to find the total number of shares, then work out each person's share of the total. For 250 shared in a 2:3 ratio there are five shares, so each share is 50. The first person gets two shares, which is 100, and the second gets three shares, which is 150. The parts always add back up to the full total.
Can a ratio have more than two parts?
Yes. A ratio can have as many parts as you need, such as 2:3:5 for three ingredients or three groups. Enter each part separated by a colon. The simplifier works on every part together, so the common factor must divide all of them. The three parts of 12:18:24 simplify to 2:3:4, but 2:3:5 is already in its simplest form.
Do scaled and shared results round to whole numbers?
The simplified ratio is always exact, because it only divides the parts by a common factor. Scaled and shared values are shown to two decimal places, so a total of 100 shared in a 1:2 ratio gives 33.33 and 66.67 rather than exact fractions. Round the figures yourself where the context needs whole items, such as people, pieces or bags.