Enter the two terms of the ratio, choose whether you are comparing one group with the other or with the whole, and the calculator returns the simplified fraction. If you only want to reduce a ratio, use simplify ratios; for the difference between a ratio and a fraction, see the guide to ratio, proportion, and fraction.
| Question | Fraction | Result |
|---|---|---|
| The red compared with the blue | a/b | 2/3 |
| What part of all the counters is red | a/(a + b) | 2/5 |
| What part of all the counters is blue | b/(a + b) | 3/5 |
The difference is only in the denominator, which is b or a + b.
Worked example with 2 red counters and 3 blue
A bag has 2 red counters for every 3 blue, a ratio of 2:3. What fraction are the red counters of the blue, and what fraction are they of the total?
- Group to group. Red over blue, 2/3.
- Count the whole. There are 2 + 3 = 5 counters.
- Part of the whole. Red over all, 2/5.
- Part of the whole that is blue. The blue counters are 3/5 of the total.
The answer is that, compared with the blue, the fraction is the one in step 1, and compared with all the counters, the one in step 3.
Check. with 2 + 3 = 5, the two parts of the whole complete the five fifths, that is, one whole. The group-to-group fractions do not complete the whole, because they compare the groups with each other.
Why the denominator changes
In a ratio, the first term is called the antecedent and the second the consequent, and the ratio is read “a over b.” That reading is the group-to-group fraction, a/b. For the part of the whole, b is replaced by the total, a + b, because the first group is already part of what you are counting.
| Ratio | Group to group | First part of the whole |
|---|---|---|
| 1:1 | 1 | 1/2 |
| 1:4 | 1/4 | 1/5 |
| 3:2 | 3/2 | 3/5 |
| 16:9 | 16/9 | 16/25 |
The part-of-the-whole column stays between 0 and 1, and the group-to-group column goes above 1 when the first term is larger than the second. The aspect ratio of a screen, 16 to 9, is the typical case: the width is 16/9 of the height, and that fraction is not the part of any total.
From fraction to ratio
Again, the ratio depends on what the fraction describes. If 5/12 is the part of a total, the rest is 12 − 5 = 7 twelfths and the smallest ratio is 5 to 7. If 5/12 compares two groups, the ratio is 5 to 12. The fraction alone does not say which of the two readings you want, so it is best to settle that first.
A fraction greater than 1 can only come from comparing groups. The fraction 7/6 is written as the ratio 7 to 6, and it does not work as a part of the total because the rest would be negative.
Cases with zero
The ratio 1 to 0 has a part-of-the-whole fraction, 1/(1 + 0) = 1, but no group-to-group fraction, because that would require dividing by zero. The ratio 0 to 4 equals 0 in both readings. The ratio 0 to 0 has no fraction in either, and negative terms are not accepted.
Where to go next
If you know a part and the total instead of two parts, what fraction one number is of another calculates the fraction directly. To find the missing term in an equality of ratios, solve a proportion. To express the part of the whole as a percent, see the percentages page.
According to Wikipedia’s article Ratio, a ratio can be given by the quotient of its terms, written as a fraction with the first term as numerator and the second as denominator. The part-of-the-whole reading is not stated as a formula in that source; it is the total of the parts described above (accessed October 17, 2026).
Frequently asked questions
How do I turn a three-term ratio into fractions?
Put each term over the total number of parts. In 6:8:9 there are 6 + 8 + 9 = 23 parts, so the fractions are 6/23, 8/23, and 9/23, and all three together make 1.
How does “4 out of every 11” differ from 4:11?
“4 out of every 11” already describes the whole, with 11 in total, and is written 4/11, leaving 7. The ratio 4:11 compares two groups and has 15 parts in total, so the first group is 4/15 of the whole. If the wording says “out of every,” do not add the terms.
How do I turn a ratio into a percent?
Convert the ratio into the part of the whole, then into a percent. In 3:17 there are 20 parts, so the first term is 3/20 of the whole, which is 15%, and the second is 85%. If you already have the fraction, use fraction to percent.
What happens if the terms are in different units?
Both terms must be in the same unit before you turn them into a fraction, because a ratio compares quantities of the same kind. The ratio 3 hours : 40 minutes is not 3:40 but 180:40, and group to group it is written 9/2.