Relative frequency is the count of a value divided by the total number of data points: f = n / N. If 6 of 20 answers say “bus,” the relative frequency is 6/20, which simplifies to 3/10 and equals 0.30, or 30%. All the relative frequencies in a set add up to 1.
The tool that tells you what fraction one quantity is of another gives you each quotient already simplified. This guide explains how to build the full table, how to accumulate it, and how to convert to percents. For the theoretical model, see probability with fractions.
The complete frequency table
Every row uses the same denominator, the total number of data points, and is then simplified separately.
| Way to school | Absolute frequency | Relative frequency | Simplified | Percent |
|---|---|---|---|---|
| Bus | 6 | 6/20 | 3/10 | 30% |
| Bicycle | 5 | 5/20 | 1/4 | 25% |
| Walking | 7 | 7/20 | 7/20 | 35% |
| Car | 2 | 2/20 | 1/10 | 10% |
| Total | 20 | 20/20 | 1 | 100% |
The last row works as a check: the counts add up to 20, the fractions add up to 1, and the percents add up to 100%. If any of the three sums fails, a data point is missing or a count was copied wrongly.
Worked example: how 20 students get to school
In a survey of 20 answers, 6 students come by bus, 5 by bicycle, 7 on foot, and 2 by car. What is the relative frequency of the bus?
- Count the total. 6 + 5 + 7 + 2 = 20 answers.
- Divide the count by the total. 6/20.
- Simplify with the GCD. The GCD of 6 and 20 is 2, so 6/20 = 3/10.
- Convert to a decimal and a percent. 3/10 = 0.30 = 30%.
Result: 3/10, or 30%.
Check: 0.30 × 20 = 6, the count we started with.
Why relative frequencies add up to 1
Each answer belongs to one category only, and the categories together cover all the answers. When you add 6/20 + 5/20 + 7/20 + 2/20, the numerator counts each answer once and comes to 20, the same as the denominator. The result is 20/20 = 1, no matter how many categories there are. The condition is that the categories do not overlap and leave no data out; with missing data, state how many there are and decide whether they count in the total.
Cumulative relative frequency
The cumulative frequency of a category adds its relative frequency to those of all the earlier ones, in an order that makes sense. It answers “what fraction of the data is at or below this point?” It is used only with ordered values, such as number of siblings or test scores, and not with unordered categories like the way students get to school.
Example with 25 answers about how many siblings each person has. There are 5 people with 0 siblings, 10 with 1, 7 with 2, and 3 with 3.
| Siblings | Absolute frequency | Relative | Cumulative |
|---|---|---|---|
| 0 | 5 | 1/5 | 1/5 |
| 1 | 10 | 2/5 | 3/5 |
| 2 | 7 | 7/25 | 22/25 |
| 3 | 3 | 3/25 | 1 |
The cumulative 22/25 says that 22 of the 25 people have 2 siblings or fewer, and it always ends at 1. To find a segment you subtract cumulative values, so the fraction with exactly 3 siblings is 1 − 22/25 = 3/25.
For the mean of the table, multiply each value by its absolute frequency, add, and divide by the total, which gives (0 + 10 + 14 + 9)/25 = 33/25 = 1.32 siblings. With relative frequencies you get the same thing, 0 × 1/5 + 1 × 2/5 + 2 × 7/25 + 3 × 3/25 = 33/25. The average of fractions calculator computes this kind of mean with fractional values.
Fraction, decimal, and percent
A percent is the relative frequency with a denominator of 100, for example 7/20 = 35/100 = 35%. It terminates when the simplified fraction has only the factors 2 and 5 in the denominator, as in 1/8 = 12.5%. With other factors, such as 1/3, the decimal does not end and is rounded. The fraction to percent converter does the step for you, and the fraction, decimal, and percent table collects the most common equivalents. If you would rather see it in a circle, the pie chart with fractions splits the 360° according to these same fractions.
Rounded percents that add up to 99%
Three categories of 1/3 each give 33.33…% per category. Rounded to whole numbers, 33 + 33 + 33 = 99. Since the fractions add up to 1 and the total must be 100%, add the missing point to one of the categories and state the adjustment in a note. Show the fractions first, which add up to 1, and present the percents as a rounded reading.
When to use fractions and when to use percents
With few categories and small counts, simplified fractions are convenient and the sum can be checked by hand. With twenty categories they become unwieldy and percents read better. In that case keep the counts for the check. Relative frequency describes only the data that were observed: it cannot speak for people who did not answer or for other groups. To carry these ideas into more contexts, the applications hub collects uses such as unit price.
Sources
Wikipedia, article Frequency (statistics): defines relative frequency as the ratio of absolute frequency to the sample size, and cumulative frequency as the total of the absolute frequencies of all events at or below a certain point in an ordered list (accessed October 17, 2026).