Relative Frequency Calculator
Convert raw counts into relative frequencies. Enter the frequency of each category separated by commas and get each category’s share as a decimal and a percentage, plus the cumulative relative frequency and the total number of observations.
Example: with Frequencies (comma separated counts) 12, 18, 20, 10 → Relative frequencies: 0.2, 0.3, 0.333, 0.167.
- As percentages20%, 30%, 33.3%, 16.7%
- Cumulative relative frequency0.2, 0.5, 0.833, 1 — the last value is always 1
- Total observations60 observations across 4 categories
Computed by the calculator below using its default values. Change any input to see your own numbers.
Relative frequency = category count ÷ total count. It is the experimental (observed) probability of that category, and the full column always sums to 1.
Relative frequency is observed probability
A frequency table counts how often each outcome happened; relative frequency divides each count by the total, turning counts into shares. If 20 of 60 surveyed students chose pizza, the relative frequency is 20/60 ≈ 0.333 — pizza captured a third of the responses. Shares are what let you compare groups of different sizes fairly.
Relative frequency is also the empirical estimate of probability: flip a tack 60 times, get point-up 20 times, and 0.333 is your best experimental estimate of the true chance. The cumulative column adds shares in order and must end at exactly 1 — a quick integrity check for any frequency table you build by hand.
How it’s calculated
Relative frequency of category i = fᵢ ÷ Σf. Percentage = relative frequency × 100. Cumulative relative frequency of category i = (f₁ + … + fᵢ) ÷ Σf, computed from running count totals so the final value is exactly 1. Decimals are rounded to 3 places, percentages to 1.
Counts are taken at face value — the tool does not know your sampling method, so shares describe the data you collected, not necessarily the population.
Worked example: 60 survey responses
| Category | Frequency | Relative frequency | Cumulative |
|---|---|---|---|
| A | 12 | 0.200 | 0.200 |
| B | 18 | 0.300 | 0.500 |
| C | 20 | 0.333 | 0.833 |
| D | 10 | 0.167 | 1.000 |
Computed with f ÷ 60; rounding makes the column sum 1.000 within a thousandth.
Common mistakes
- Dividing by the number of categories instead of the total count — 12 of 60 is 0.2, not 12/4.
- Entering percentages or measurements instead of raw counts; the inputs should be how many times each category occurred.
- Expecting the rounded decimals to sum to exactly 1 — 0.333 style rounding can leave the printed column at 0.999 or 1.001.
- Confusing relative frequency (share of all observations) with cumulative relative frequency (running total of shares).
Frequently asked questions
What is the relative frequency formula?
Relative frequency = frequency of the category ÷ total of all frequencies. If a value occurred 18 times out of 60 observations, its relative frequency is 18/60 = 0.3, or 30%.
What is the difference between frequency and relative frequency?
Frequency is a raw count (18 students). Relative frequency is that count as a share of the whole (0.3). Shares let you compare distributions from samples of different sizes.
What is cumulative relative frequency?
The running total of relative frequencies through each category in order. It answers "what share falls at or below this point" and always reaches 1 at the last category.
Is relative frequency the same as probability?
It is the experimental estimate of probability — what fraction actually happened in your data. As the number of trials grows, relative frequency tends toward the true probability (the law of large numbers).