Ratio to Decimal & Fraction Calculator
Turn a ratio into its decimal value, a simplified fraction, a mixed number and the 1 : n form — both directions.
Open → Ratio to Decimal & Fraction CalculatorConvert a ratio of two to six parts into percentages. You get each part as a share of the whole — which always sums to 100% — and separately A as a percentage of B, because those are different questions with different answers.
Formula part ÷ total × 100
You get two different percentages, and which you need depends on the
question. Share of the whole divides by the total of all parts.
A as a % of B divides by B alone. For 3 : 5 those are 37.5% and
60% respectively.
| Part | Value | Fraction of whole | % of whole | Exact % |
|---|
Nearly every wrong answer in this topic comes from using the wrong denominator. Here is how to tell which you need.
Share of the whole
part ÷ total × 100
A as a percentage of B
A ÷ B × 100
Add every part to get the total
For 3 : 5 the total is 8; for 2 : 3 : 5 it is 10. This is
the number of equal parts the whole has been divided into, and it becomes the
denominator for every share.
Divide each part by that total
3 ÷ 8 = 0.375 and 5 ÷ 8 = 0.625. Keeping these as
fractions — 3/8 and 5/8 — is worth doing, because it makes
recurring percentages exact rather than approximate.
Multiply by 100
0.375 × 100 = 37.5%. A percentage is just a fraction with a
denominator of 100, so this step is a change of units rather than a calculation.
Confirm the total is 100%
37.5 + 62.5 = 100. If your percentages do not sum to 100 (allowing for
rounding), you divided by the wrong thing. This check takes two seconds and catches
the mistake reliably.
For a direct comparison, divide by B instead
3 ÷ 5 × 100 = 60%. Note this is greater than 37.5% because the
denominator is smaller. Both numbers describe the same ratio; they answer different
questions about it.
Share of the whole. Works for any number of parts and always totals 100%.
A as a percentage of B. A two-quantity comparison. Reversing it gives
a different number: B/A × 100.
1 : 2 gives 33.333…% and 66.666…%. Exactly,
those are 100/3 and 200/3 percent. Rounded to one place they
become 33.3% and 66.7%, which sum to 100.0% — but at two places, 33.33 + 66.67 = 100.00
only because the rounding happened to go opposite ways.
A class has boys and girls in the ratio 3 : 5. What percentage are boys?
37.5% boys, 62.5% girls
Same class. How many boys are there as a percentage of the girls?
60% as many boys as girls
A portfolio is split 2 : 3 : 5 between cash, bonds and equities. What are the percentages?
20% / 30% / 50%
Convert 1 : 2 to percentages of the whole.
33.33% and 66.67%
Both columns come from the same ratio. The last two are the ones that do not add to 100%.
| Ratio | Total parts | A of whole | B of whole | A as % of B | B as % of A |
|---|---|---|---|---|---|
| 1 : 1 | 2 | 50% | 50% | 100% | 100% |
| 1 : 2 | 3 | 33.33% | 66.67% | 50% | 200% |
| 1 : 3 | 4 | 25% | 75% | 33.33% | 300% |
| 1 : 4 | 5 | 20% | 80% | 25% | 400% |
| 2 : 3 | 5 | 40% | 60% | 66.67% | 150% |
| 3 : 4 | 7 | 42.86% | 57.14% | 75% | 133.33% |
| 3 : 5 | 8 | 37.5% | 62.5% | 60% | 166.67% |
| 4 : 1 | 5 | 80% | 20% | 400% | 25% |
| 5 : 8 | 13 | 38.46% | 61.54% | 62.5% | 160% |
| 16 : 9 | 25 | 64% | 36% | 177.78% | 56.25% |
A ratio and a percentage carry the same information, but percentages are easier to compare
across different situations because they share a fixed denominator of 100. Told that one
class is 3 : 5 boys to girls and another is 4 : 7, working out
which has proportionally more boys takes a moment. Told they are 37.5% and 36.4%, the
comparison is immediate. That common scale is the whole reason percentages exist.
The cost is that a percentage hides the total. 3 : 5 tells you the whole
divides cleanly into eight parts, which is useful if you are physically dividing something
— you know to count out eight units. 37.5% does not suggest that. This is why recipes and
mixing instructions stay in ratio form while survey results and financial breakdowns are
reported as percentages.
Percentages from ratios frequently recur, and rounded percentages frequently fail to sum
to exactly 100. A three-way split of 1 : 1 : 1 is 33.33% three times, which
sums to 99.99%. There is no arithmetic fix — the exact values are 100/3 each
and no finite decimal represents them. Published tables handle this by rounding one figure
up so the column totals correctly, which is why you sometimes see 33.3, 33.3, 33.4.
Share-of-whole percentages can never exceed 100, but A-as-a-percentage-of-B can and often
does. For 16 : 9, A is 177.78% of B — the first quantity is more than three
quarters larger again than the second. A figure over 100% is a signal that you are looking
at a comparison rather than a share, which is a handy way to catch a mislabelled result.
For the decimal and fraction forms of the same conversion, use the ratio to decimal and fraction calculator. To go the other way and turn percentages back into a ratio, the simplify ratio calculator accepts percentage input and reduces it. And if you need actual amounts rather than percentages — dividing £450 in the ratio 2 : 3 : 4 — use the 3-number ratio calculator.
Chiefly about which denominator to use, since that is what decides the answer.
3 : 5 the first part is 3 ÷ 8 × 100 = 37.5%. To express A as a percentage of B, divide A by B instead — 3 ÷ 5 × 100 = 60%. Both are correct answers to different questions.1 ÷ 5 = 20% and the second is 4 ÷ 5 = 80%. Alternatively, A as a percentage of B is 1 ÷ 4 = 25%. The first reading is the one you want for "20% of the mixture is X"; the second for "there is 25% as much X as Y".2 : 3 : 5 the total is 10, giving 20%, 30% and 50%. This calculator handles two to six parts and draws a stacked bar so you can see the split at a glance.37.5 : 62.5, which multiplied by 2 gives 75 : 125, and dividing by the GCD of 25 gives 3 : 5. The simplify ratio calculator will do the reduction if you enter the percentages directly.1 : 2 gives 33.333…% and 66.666…%. The exact answers are 100/3 and 200/3 percent, which this calculator shows as fractions alongside the decimals. When rounding for presentation, round to one or two places and expect the total to come to 99.9% or 100.1% — that is the rounding, not an error.3 : 0 : 5 gives 37.5%, 0% and 62.5%. What does not work is a total of zero — if every term is zero there is no whole to take shares of, and the conversion is undefined.