Why use this calculator
Ratios turn up constantly outside the classroom. Mixing fuel and oil, splitting a bill or a profit share, scaling a recipe, working out aspect ratios, reading a set of accounts. And the arithmetic is simple enough to be embarrassing to get wrong and easy enough to get wrong anyway.
The three operations people need are reducing a ratio to something readable, solving a proportion when one value is unknown, and dividing a total into parts. This calculator does all three, and shows the fraction, decimal and percentage forms alongside, because a ratio is often easier to act on once it is expressed a different way.
How to use it
- Choose the mode first, since it changes what the third field means.
- In simplify mode, enter the two terms and the third field is ignored.
- In solve mode you are completing A : B = C : ?, so enter the known pair as A and B, the third known value as C, and the calculator finds the fourth.
- In split mode, A and B are the ratio parts and C is the total being divided.
- So 3, 2 and 500 splits 500 in a three-to-two ratio.
- Negative numbers are accepted but rarely meaningful outside financial contexts.
What each result means
- Ratio as a decimal
- The second term divided by the first, so a ratio of 2 : 3 reads as 1.5. It is the multiplier that turns the first quantity into the second.
- Simplified ratio
- The ratio reduced to its lowest whole-number terms, which is the readable form used in recipes, plans and reports.
- As a fraction
- The same relationship written as a fraction, since a ratio of A to B is the fraction A over B.
- As a decimal
- The first term divided by the second, useful for comparing two ratios quickly.
- As a percentage
- The first term expressed as a percentage of the second. Note this can exceed 100 per cent.
- Greatest common divisor
- The largest number dividing both terms exactly, which is what the simplification divides by.
- Scaled to 1 : n
- The ratio rewritten with the first term as 1, which is how mixing and gear ratios are usually quoted.
- First term's share of the whole
- What proportion of the combined total the first term represents, which is the figure to use when splitting something in this ratio.
- Missing value
- The fourth term that completes the proportion, found by cross multiplication of the three values you supplied.
- Completed proportion
- The full proportion with the missing value filled in, so you can sanity-check it reads correctly.
- Scale factor
- How many times larger the second pair is than the first. The multiplier connecting them.
- Cross products check
- In a true proportion the two cross products are equal, which is the standard way to verify the answer.
- First share
- The first party's portion of the total, based on their number of parts.
- Second share
- The second party's portion, which together with the first adds back to the total.
- Total parts
- The ratio terms added together. The number of equal shares the total is divided into.
- Value of one part
- The total divided by the number of parts, which is the unit the shares are built from.
- First share as a percentage
- The first party's portion expressed as a percentage of the total, which is often easier to check than the raw amount.
- Second share as a percentage
- The second party's portion as a percentage, which adds to 100 with the first.
The formula
Simplifying divides both terms by their greatest common divisor, found with the Euclidean algorithm.
Solving a proportion uses cross multiplication: if
A : B = C : D then A × D = B × C, so the missing D is (B × C) ÷ A
Splitting a total adds the ratio parts to get the total number of parts, divides the total by that to find the value of one part, then multiplies by each side's parts. The percentage form is the first term divided by the sum of both terms.
How this number is used in practice
The distinction that causes most errors is between a ratio and a fraction of the whole. A 3 : 2 split is not three fifths and two fifths of each side's own money. It means the total is divided into five parts, with three going one way and two the other.
Someone splitting $500 in a 3 : 2 ratio gets $300 and $200, not $300 and $250, and the mistake shows up whenever a ratio is treated as two separate fractions.
Two-stroke fuel mixing is where the arithmetic has physical consequences. A 50 : 1 mix means 50 parts fuel to one part oil, so five litres of fuel takes 100 millilitres of oil, not 50. Getting it wrong in the lean direction seizes an engine; too rich fouls plugs and smokes. Reading the ratio as parts rather than as a fraction is what avoids it.
In financial reporting, ratios are the standard comparison tool precisely because they remove scale. A current ratio of 2 : 1 means the same thing in a small business and a large one, which is why debt-to-equity, price-to-earnings and current ratios are quoted as ratios rather than dollar amounts. The comparison only works once size is divided out.
Worked examples
Simplify 16 : 24
2 : 3, a fraction of 2/3, a decimal of 0.6667, and a first-term share of 40 per cent.
Solve 3 : 5 = 12 : ?
The missing value is 20, with a scale factor of 4 and matching cross products of 60.
Split $500 in a 3 : 2 ratio
$300 and $200. Five parts of $100 each, or 60 per cent and 40 per cent.
When people use it
- Simplifying a ratio to lowest terms for a plan or report
- Scaling a recipe or a mix up or down proportionally
- Splitting a bill, a profit share or an inheritance in agreed parts
- Working out fuel and oil quantities for a two-stroke engine
- Solving a proportion in a maths or science problem
Tips
- A ratio of 3 : 2 divides a total into 5 parts, not into thirds and halves. This is the most common error.
- Simplify by dividing both terms by their greatest common divisor; 16 : 24 both divide by 8 to give 2 : 3.
- Check a proportion with cross multiplication: if A : B = C : D then A x D must equal B x C.
- A 50 : 1 two-stroke mix means 100 ml of oil in 5 litres of fuel, not 50 ml.
- Keep the order consistent. 3 : 2 and 2 : 3 describe opposite splits and are not interchangeable.
- Convert both to decimals when comparing two ratios. It is faster than finding a common denominator.
What it assumes, and where it stops being accurate
- Terms are treated as pure numbers; any units must already be consistent before entry.
- Simplification rounds to whole numbers before finding the greatest common divisor, so decimal inputs are approximated.
- Solve mode requires a non-zero first term, since a proportion cannot be solved against zero.
- Split mode requires the two parts to sum to something other than zero.
- Negative values are accepted but are rarely meaningful outside financial contexts.
Terms used on this page
- Ratio
- A comparison of two quantities, written A : B.
- Proportion
- A statement that two ratios are equal, which allows solving for an unknown term.
- Greatest common divisor
- The largest number that divides two values exactly, used to simplify a ratio.
- Cross multiplication
- Multiplying the outer and inner terms of a proportion to check or solve it.
Questions people ask
- How do I simplify a ratio?
- Divide both terms by their greatest common divisor. For 16 : 24 the largest number dividing both is 8, giving 2 : 3. If the terms share no common factor other than 1, the ratio is already in its simplest form. The same process is exactly how fractions are reduced.
- How do I split an amount in a given ratio?
- Add the ratio parts to find the total number of shares, divide the amount by that, then multiply by each side's parts. Splitting $500 in a 3 : 2 ratio means 5 parts of $100, giving $300 and $200. The common error is treating the ratio as separate fractions of the whole for each party.
- What is the difference between a ratio and a proportion?
- A ratio compares two quantities, such as 3 : 5. A proportion states that two ratios are equal, such as 3 : 5 = 12 : 20. Proportions are what let you solve for an unknown, using cross multiplication: the product of the outer terms equals the product of the inner terms.
- How do I work out a 50:1 fuel mix?
- It means 50 parts fuel to 1 part oil, so divide the fuel volume by 50. Five litres of fuel is 5,000 millilitres, divided by 50 gives 100 millilitres of oil. Getting this wrong in the lean direction can seize a two-stroke engine, so always check the manufacturer's specified ratio rather than assuming.
- Can a ratio have more than two terms?
- Yes. 2 : 3 : 5 is a valid three-part ratio and splits a total into ten parts. This calculator handles two terms, which covers most everyday cases. For three or more, add all the parts to get the total, divide the amount by that, and multiply by each term's parts in turn.
- How do I convert a ratio to a percentage?
- Decide what you are measuring against. To express the first term as a share of the whole, divide it by the sum of both terms: 3 : 2 gives 3 ÷ 5, or 60 per cent. To express the first term as a percentage of the second, divide A by B instead, which can exceed 100 per cent.
Use this with
Ratio Calculator answers one part of the question. These pick up where it stops: Fraction Calculator, Percentage Calculator, Aspect Ratio Calculator and Recipe Scaler.
Where these figures come from
This calculation is jurisdiction-neutral arithmetic. No country-specific rules are applied.
- NRICH: ratio and proportion resources. University of Cambridge teaching material on ratio
- Khan Academy: ratios and proportions. Worked explanations of ratio and proportional reasoning
Ratio Calculator produces an estimate for general information. It is not financial, tax, medical, legal or engineering advice. read the full disclaimer. Spotted a wrong number? Report it and it gets fixed. The form picks up this calculator and the inputs you used.