Ratio Calculator
Split a total in any ratio — three parts, four, up to twelve — and the shares add back to exactly the total, leftover cents included. The same tool simplifies a ratio to lowest terms and solves A∶B = C∶D for whichever term is missing.
Work with a ratio
Splitting is the one people usually need: divide a bill, a batch, or a profit share into two or more parts.
Two to twelve terms. Colons, commas and spaces all separate, so 3:5:4 and 3, 5, 4 both work — which means a comma cannot also be a thousands separator.
The amount being divided — currency, kilograms, hours, or anything else. The unit comes out the other side unchanged.
How finely each share is reported: 2 for money, 0 for whole units. Whatever does not divide evenly is handed to the shares with the largest leftovers, so the parts always add back to the total.
3∶5∶4 is 12 parts in total, so one part of 1,200 is 100 — and the shares above add back to exactly the total.
- Simplified ratio
- 3∶5∶4
- Parts in the whole
- 12
- Share of the whole
- 25% ∶ 41.67% ∶ 33.33%
- As a decimal
- 0.6
- In 1∶n form
- 1∶1.666667
- Already in lowest terms
- Yes
- Rounding redistributed
- 0
| # | Part | % of whole | Amount | Exact amount | Rounded up |
|---|---|---|---|---|---|
| 1 | 3 | 25% | 300 | 300 | No |
| 2 | 5 | 41.67% | 500 | 500 | No |
| 3 | 4 | 33.33% | 400 | 400 | No |
Three questions, one idea: parts of a whole
A ratio names how many parts each side gets. Add the terms and you have the number of parts the whole divides into — and that single number is what every mode below is built on.
parts = a + b + … • share = total × (term ÷ parts) • A × D = B × C- parts
- The terms added together — 12 for 3∶5∶4, not 3, and not 5
- share
- What one side of the ratio receives from the total
- A × D = B × C
- The cross-multiplication that solves A∶B = C∶D for any one missing term
Why a ratio is not a fraction
3∶5 is three parts to five parts. There are eight parts altogether, so the first side is three eighths — 37.5%. The fraction 3/5 is 60%. They are different numbers, and reading one as the other is the mistake that turns a fair split into an unfair one. Whenever you need the fraction, add the terms first: 3∶5 gives 3/8 and 5/8.
How the leftover is handled
Rounding each share on its own can never be made to add up, because each share rounds independently of the total. So the shares are apportioned instead: every share is first cut down to the chosen precision, the shortfall is counted in whole rounding steps — cents, when you ask for two decimal places — and those steps are handed out one apiece to the shares that lost the most in the cutting. That is the largest-remainder rule. Ties go to the larger part, then to the earlier one, so running the same split twice always gives the same answer.
Decimal terms are scaled up, never rounded off
A ratio is a list of whole numbers, so 2.5∶5 has to become integers before it can be reduced. Rounding would make it 3∶5, which is a different ratio entirely. Multiplying both sides by ten makes it 25∶50, which reduces to 1∶2 — the same ratio, correctly named. The calculator scales by up to a million, which covers six decimal places.
Splitting 1,200 three ways in 3∶5∶4
Three people put unequal work into a 1,200 job and agree to split it 3∶5∶4. First add the terms: 3 + 5 + 4 = 12 parts. Divide the total by that and one part is 1,200 ÷ 12 = 100. Now multiply: 3 × 100 = 300, 5 × 100 = 500, 4 × 100 = 400. Those add to 1,200, which is the check worth doing every time.
Notice what the ratio does not say. The first person does not get three fifths, or three twelfths of anything except the parts — they get 3 of the 12 parts, which is 25% of the money. The middle share is 5/12, or 41.67%. Writing the shares as percentages of the whole is the fastest way to check a split looks like what everybody agreed to.
Now change the total to 100 and keep three equal parts, 1∶1∶1. One part is 33.333…, which at two decimal places is 33.33 — and three of those is 99.99. A cent is unaccounted for. The calculator gives it to the share with the largest discarded fraction, so the split reads 33.34, 33.33, 33.33 and adds to exactly 100. The Rounding redistributed line shows 0.01, so the adjustment is visible rather than buried.
Ratios that turn up in ordinary life
- Splitting money. A shared bill weighted by who ate what, a partnership dividing profit 2∶2∶1∶1, rent split by room size. Set the decimal places to 2 and the shares come back in whole cents that still total the bill.
- Mixing materials. Concrete at 1∶2∶4 cement, sand and aggregate; mortar at 1∶1∶6; a fertiliser blend. Enter the batch size as the total and the ratio as the parts, with 0 decimal places if you are counting whole bags or scoops.
- Scaling a recipe. A dough written as 5∶3∶0.1 flour, water and salt scales to any batch weight, and the decimal term is handled without being rounded away.
- Comparing two ratios. The 1∶n form puts both on the same footing: 3∶5 is 1∶1.667 and 4∶7 is 1∶1.75, so the second is wider.
Resizing an image or a video frame is a different question — it keeps a shape rather than dividing a quantity — and it has its own tool: the aspect ratio calculator.
What this calculator assumes
- Every term is in the same unit. The units cancel in a ratio, so the tool never asks what they are — but 3 kg to 5 lb is not a ratio, it is a conversion waiting to happen.
- Terms are above zero. A term of zero says one side gets nothing, which makes the ratio a statement about the other side alone, and negative parts of a total are not a division.
- Decimal terms are scaled to whole numbers by a power of ten, up to six decimal places. A term with more places than that — or a genuinely irrational one — is named to the nearest millionth.
- Shares are apportioned by the largest-remainder rule, with ties broken by the larger part and then by input order. Other rules exist and give slightly different answers; none of them can give every share its exact fraction, because whole cents do not divide that way.
- Percentages are taken from the ratio itself, not from the rounded shares, so they stay exact even when a share has absorbed a rounding step.
- Figures are shown to six decimal places. The arithmetic underneath runs at full double precision, and the rounding happens once, at the end.
Ratio FAQ
Is the ratio 3∶5 the same as the fraction 3/5?
No, and this is the single biggest source of wrong answers with ratios. 3∶5 means three parts and five parts, eight parts in total — so the first share is three eighths of the whole, or 37.5%. The fraction 3/5 is 60%. The two are only ever equal when the second number happens to be the total, which in a ratio it is not. A ratio compares the parts to each other; a fraction compares one part to the whole. If you want the fraction, add the terms first: 3∶5 becomes 3/8 and 5/8.
How do I split a bill or a payout in a ratio?
Add the terms to get the number of parts, divide the total by that, then multiply by each term. Splitting 1,200 in 3∶5∶4: the parts add to 12, so one part is 100, and the shares are 300, 500 and 400. The calculator above does exactly this, and then fixes up the rounding so the shares still add back to the total — which hand arithmetic usually does not.
Why does one share come out a cent bigger than the others?
Because the split does not divide evenly and something has to absorb the difference. Split 100 three ways to two decimal places and each share is 33.333…, which rounds to 33.33 — and three of those is 99.99. A cent is missing. This calculator gives it to the share with the largest discarded fraction, which is the largest-remainder rule; ties go to the larger part and then to the earlier one, so the answer is the same every time you run it. The Rounding redistributed line tells you how much moved.
Can a ratio have three or more parts?
Yes, and that is where a calculator actually earns its keep. 3∶5∶4, 1∶2∶2∶1, a mortar mix of 1∶1∶6 — the arithmetic is identical, you just add more terms before dividing. Most online ratio calculators only accept two, which is the case people can do in their heads. This one takes up to twelve.
What is the 1∶n form for?
It rescales the ratio so the first term is 1, which makes two ratios instantly comparable. 3∶5 is 1∶1.667 and 4∶7 is 1∶1.75, so the second is the wider of the two — something that is not obvious from the original numbers. Gear ratios, map scales, and mixing instructions are conventionally written this way for exactly that reason.
Is this the same as an aspect ratio calculator?
No — they answer different questions with the same algebra. An aspect ratio calculator keeps the shape of a box while you change its size: give it 1920×1080 and a new width of 1280 and it returns the height. This tool divides a quantity into proportional parts. If you are resizing an image or a video frame, use the aspect ratio calculator; if you are dividing money, material, or time, you are in the right place.
Sources and review notes
- NIST Special Publication 811, Guide for the Use of the International System of Units — §7.10 on quantities expressed as ratios, and why a ratio of two like quantities is dimensionless
- U.S. Census Bureau, Computing Apportionment — the canonical statement of the same problem this calculator solves for money: dividing a fixed whole into integer shares that must sum exactly. Congress uses the method of equal proportions rather than largest remainders, which is a different rule for the same unavoidable leftover
The arithmetic here is definitional and has no data behind it to go stale: an addition, a division, and a greatest common divisor. What can go wrong is the rounding, which is why the engine behind this page is a pure function under unit test — including a case that fails if the shares ever stop adding back to the total.