Ratio to Percentage Calculator

Convert 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.

Try an example
The key distinction

Two percentages, two questions

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

  • Denominator is the sum of all parts
  • For 3 : 5 → total 8 → 37.5% and 62.5%
  • Always adds up to exactly 100%
  • Use for: composition, shares, splits, make-up of a mixture
  • "What percentage of the class are boys?"

A as a percentage of B

A ÷ B × 100

  • Denominator is the other quantity
  • For 3 : 5 → 60% (and B is 166.67% of A)
  • Does not add to 100% — they are separate comparisons
  • Use for: direct comparison, "how much of one relative to the other"
  • "There are 60% as many boys as girls."

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.

Aᵢ / (A₁+A₂+…) × 100

Share of the whole. Works for any number of parts and always totals 100%.

A / B × 100

A as a percentage of B. A two-quantity comparison. Reversing it gives a different number: B/A × 100.

When the percentage recurs

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.

Worked examples

Both readings, side by side

Share of the whole

A class has boys and girls in the ratio 3 : 5. What percentage are boys?

Total parts
3 + 5 = 8
Boys' fraction
3/8
As a decimal
0.375
× 100
37.5%
Girls
5/8 = 62.5% — sums to 100 ✓

37.5% boys, 62.5% girls

Direct comparison

Same class. How many boys are there as a percentage of the girls?

Divide A by B
3 ÷ 5
As a decimal
0.6
× 100
60%
Reversed
5 ÷ 3 = 166.67%
Note
these do not sum to 100

60% as many boys as girls

Three parts

A portfolio is split 2 : 3 : 5 between cash, bonds and equities. What are the percentages?

Total parts
2 + 3 + 5 = 10
Cash
2/10 = 20%
Bonds
3/10 = 30%
Equities
5/10 = 50%
Check
20 + 30 + 50 = 100 ✓

20% / 30% / 50%

Recurring result

Convert 1 : 2 to percentages of the whole.

Total parts
3
First part
1/3 = 0.3333…
Exactly
100/3 %
Second part
2/3 = 200/3 %
Rounded
33.3% and 66.7%

33.33% and 66.67%

Reference

Common ratios as percentages

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 : 1250%50%100%100%
1 : 2333.33%66.67%50%200%
1 : 3425%75%33.33%300%
1 : 4520%80%25%400%
2 : 3540%60%66.67%150%
3 : 4742.86%57.14%75%133.33%
3 : 5837.5%62.5%60%166.67%
4 : 1580%20%400%25%
5 : 81338.46%61.54%62.5%160%
16 : 92564%36%177.78%56.25%
Background

Why percentages read better than ratios

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.

The rounding problem

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.

Percentages above 100

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.

Related tools

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.

Questions

Ratio to percentage — questions

Chiefly about which denominator to use, since that is what decides the answer.

How do you convert a ratio to a percentage?
It depends which question you are asking, and this is the crux of the whole topic. To get each part as a share of the whole, divide that part by the total of all parts and multiply by 100 — for 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.
Why do I get two different percentages from the same ratio?
Because the denominator is different. Share-of-whole uses the total (3 + 5 = 8) as the denominator; A-as-a-percentage-of-B uses B (5). If the question mentions a total, a whole, or the parts summing to 100%, use share-of-whole. If it compares one quantity directly against another — "A is what percent of B?" — use the second. This calculator gives you both so you can pick.
Do the percentages have to add up to 100?
The share-of-whole percentages always do, because they are shares of a single total. The A-as-percentage-of-B figures do not, since they are separate comparisons rather than parts of one thing. If your percentages should sum to 100 and do not, you have used the wrong denominator — or rounded too aggressively.
How do you convert a ratio like 1 : 4 to a percentage?
Total parts = 5, so the first share is 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".
What about a ratio with three or more parts?
The share-of-whole method extends directly: add all the parts to get the total, then divide each part by it. For 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.
Can I convert a percentage back into a ratio?
Yes. Write each percentage over 100 and simplify. 37.5% and 62.5% become 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.
How do I handle a recurring decimal in the percentage?
Some ratios do not convert to a terminating percentage. 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.
What if a ratio term is zero?
A zero part simply gets 0% of the whole, and the remaining parts share the full 100% between them. 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.