What is a ratio?
A ratio is a way to compare two or more quantities by describing their relative size. The notation A : B is read as “A to B.” A ratio can also be written as a fraction, A/B, when the two forms are being used to describe the same relationship.
For example, a recipe with 2 cups of flour for every 3 cups of water has a flour-to-water ratio of 2 : 3. The important idea is not the absolute size of the numbers; it is the relationship between them.
2 : 3 as parts
5 total parts. Two belong to A and three belong to B.
Part-to-whole
A represents 2/5 = 40% of the whole; B represents 3/5 = 60%.
Equivalent ratios
Two ratios are equivalent when they express the same relationship. If 3 : 8 is multiplied by 3, the result is 9 : 24. The numbers change, but the comparison does not.
The same idea works in the opposite direction. If both terms can be divided by the same non-zero factor, the ratio can be reduced without changing its value.
3 : 82 ×
6 : 163 ×
9 : 244 ×
12 : 325 ×
15 : 406 ×
18 : 48
How to find a missing ratio value
When two ratios are equal, they form a proportion. Write the ratios as fractions and cross-multiply. This turns the comparison into an equation that can be solved for the missing term.
- Write the known ratio and the target ratio as a proportion.
- Cross-multiply to form an equation.
- Divide by the coefficient of the unknown.
- Check the answer by substituting it back into the original ratio.
How to simplify a ratio
A ratio is in simplest form when its terms have no common factor greater than 1. For whole-number ratios, find the greatest common factor (GCF), then divide every term by it.
- GCF
- greatest common factor shared by the ratio terms
- A, B
- the original ratio terms
24 : 36 → 2 : 3
The GCF of 24 and 36 is 12.
1.5 : 2.5 → 3 : 5
Multiply both terms by 10 first to remove decimals, then reduce by 5.
Splitting a total by ratio
A part-to-part ratio can also tell you how a total amount should be divided. Add the ratio terms to find the total number of parts. Each share is the total multiplied by that term divided by the sum.
Example · 1 : 2 split of 180
There are 3 total parts. One part is 180 ÷ 3 = 60.
Check
The shares add back to the original total, while their ratio remains 1 : 2.
Three-term ratios
The same rules apply to A : B : C. To simplify, divide every term by the same common factor. To scale, multiply every term by the same factor. To split a total, divide the total into the sum of all three ratio parts.
| Ratio | Total parts | Shares of whole | Equivalent example |
|---|---|---|---|
| 1 : 2 : 3 | 6 | 1/6, 2/6, 3/6 | 2 : 4 : 6 |
| 2 : 3 : 5 | 10 | 20%, 30%, 50% | 4 : 6 : 10 |
| 3 : 4 : 5 | 12 | 25%, 33.33%, 41.67% | 6 : 8 : 10 |
Everyday uses of ratios
Ratios appear whenever quantities need to stay in proportion. Recipes use ingredient ratios, maps use scale ratios, mixtures use component ratios, and screen dimensions use width-to-height ratios.
Recipes
Keep ingredient proportions constant when changing the batch size.
Maps
Use a scale ratio to connect a map distance with real distance.
Mixtures
Describe how much of each component belongs in a blend.
Displays
Width-to-height ratios describe the shape of screens and images.
Screen and video aspect ratios
An aspect ratio is a width-to-height comparison. A 16 : 9 display is wider than a 4 : 3 display even when both are scaled to different physical sizes.
Ratio formulas
These formulas cover the main operations used by the calculator. The same relationship can be expressed using colon notation or fraction notation.
- A, B, C, D
- the four terms in an equivalent-ratio problem
- g
- the greatest common factor of the ratio terms
- k
- a non-zero scale factor applied to every term
Ratio calculator examples
The examples below show the same ideas from different angles: finding an unknown, simplifying a ratio, and dividing a total.
3 : 8 = x : 72
Cross-multiply and solve for x.
x = 216 ÷ 8
45 : 60
The GCF is 15.
2 : 5 × 4
Multiply every term by 4.
2 : 3 of 250
There are 5 total parts.
250 × 3/5 = 150
Ratio calculator FAQ
A ratio compares quantities by showing their relative size, such as 2 : 3. It can be read as “2 to 3.”
For whole-number terms, divide every term by the greatest common factor. For example, 24 : 36 becomes 2 : 3 after dividing both terms by 12.
Set the ratios equal as a proportion, cross-multiply, and divide to isolate the unknown. For 3 : 8 = x : 72, the answer is x = 27.
Two ratios are equivalent when one can be obtained from the other by multiplying or dividing every term by the same non-zero factor.
Add the ratio parts, then multiply the total by each term divided by that sum. For 1 : 2 and a total of 180, the shares are 60 and 120.
Yes. The calculator accepts decimal inputs. A decimal ratio can often be converted to whole-number terms by multiplying every term by the same power of 10 and then simplifying.
Part-to-part compares one quantity with another, such as apples : oranges. Part-to-whole compares a part with the total, such as apples : all fruit.