Ratios, fractions, decimals, probabilities and percentages are five notations for the same underlying value. Here's how to move between them cleanly, plus how to combine probabilities and build distributions.
Convert between ratios, fractions, decimals, and percentages; express probability as a percentage; multiply independent probabilities; and build percentage frequency distributions for charts.
See also: Percentage calculator · Formula cheat sheet
Every ratio, fraction, decimal and percentage is the same number wearing different clothes. Take the ratio 3:2:
| Form | Value | How you got there |
|---|---|---|
| Ratio | 3 : 2 | Two parts, total of 5 |
| Fraction | 3/5 and 2/5 | Each part over the total (3 + 2) |
| Decimal | 0.60 and 0.40 | Divide top by bottom |
| Percentage | 60% and 40% | Multiply the decimal by 100 |
The one trap: a ratio's parts are shares of the total of the parts. 3:2 is not "3 out of 2" — it's 3 out of 5 (60%) and 2 out of 5 (40%), which correctly sum to 100%.
A probability is favorable outcomes over total possible outcomes, expressed on a 0–100% scale:
Probability % = Favorable outcomes ÷ Total outcomes × 100
Drawing any heart from a 52-card deck: 13 ÷ 52 = 0.25 = 25%. A probability is just a percentage bounded between 0% (impossible) and 100% (certain).
For two independent events that must both happen, you multiply their probabilities — you don't add or average them:
P(A and B) = P(A) × P(B)
If a production step succeeds 90% of the time and the next succeeds 95%, both succeeding in a row is 0.90 × 0.95 = 0.855 = 85.5%. Note the combined chance is lower than either step alone — chaining requirements always drives the joint probability down. (This only holds when the events are truly independent; if one affects the other, you need conditional probability instead.)
To turn a messy count table into clean, chart-ready percentages, divide each category by the grand total:
| Category | Count | % of total |
|---|---|---|
| A | 45 | 45% |
| B | 30 | 30% |
| C | 15 | 15% |
| D | 10 | 10% |
| Total | 100 | 100% |
Each slice is count ÷ total × 100, and a correct distribution always sums to 100% — which is exactly what a pie chart needs (each category becomes a wedge of 360° proportional to its percentage). If your percentages don't total 100 (allowing for rounding), a category is missing or double-counted.
Add the parts to get the total, then divide each part by that total and multiply by 100. For 3:2, the total is 5, so the parts are 3/5 = 60% and 2/5 = 40%. A ratio's parts are shares of the combined total, not of each other.
Divide favorable outcomes by total possible outcomes and multiply by 100. Drawing a heart from a deck is 13/52 = 25%. Probabilities always land between 0% and 100%.
For independent events that must both occur, multiply them: 90% and 95% give 0.90 x 0.95 = 85.5%. The combined chance is always lower than either event alone.
Divide each category's count by the grand total and multiply by 100. The percentages should sum to 100%, and each becomes a wedge of the pie proportional to its share.
Links point to primary sources and standards bodies. Tax rates and official formulas change over time — verify against the source for current figures.