Simplify to lowest terms
Divides every term by the greatest common factor and shows which number was used, so the answer is checkable rather than magic.
Ratio Calculator – Simplify, Solve and Share Ratios
Simplify a ratio to its lowest terms, solve a proportion for a missing value, scale a ratio up or down, or share a total amount in any ratio. Decimals and three or more terms are handled, and every answer comes with the percentages, the fraction form and the working written out.
Two or more termsDecimals supportedMissing value solverShare a totalPercentages & fractions
Try:
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Leave exactly one box empty and it will be solved by cross multiplication. Here 3 : 8 = 12 : ? gives 32.
Simplified ratio
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Four ratio jobs, one calculator
Almost every ratio question is one of four things: make it smaller, fill in a gap, resize it, or split something with it. Most online tools only do the first two, and only for two terms.
Solve for the missing value
Leave any one of the four boxes empty in A : B = C : D and it is solved by cross multiplication, with the rearranged equation shown.
Scale up or down
Set a new value for any term and every other term follows by the same factor – the calculation behind recipes, mixes and scale drawings.
Share a total
Split money, time or quantities into parts, with each share, its percentage and a note when the split does not land on whole units.
Decimals and long ratios
Enter 2.5 : 4 or a six-term ratio. Decimals are converted to whole numbers first, and the multiplier used is shown in the working.
More than one answer format
Every result also appears as percentages, a 1 : n decimal ratio, a fraction and a proportion bar, because different questions want different forms.
How to use the ratio calculator
Pick the job
Simplify, solve a proportion, scale, or share a total. The input boxes change to match.
Type the ratio
Use a colon, comma or space between terms. Two terms or ten, whole numbers or decimals, all work the same way.
Read the headline answer
The purple panel gives the result, with the percentage split, the decimal form and the total number of parts beside it.
Check the working
The Working tab shows the greatest common factor used, the cross multiplication, or the value of one part, depending on the mode.
Use the equivalent ratios
The second tab lists ratios that mean the same thing, which is handy for finding a version with whole numbers that suits your units.
Copy the answer
One button copies the result and the key figures into your notes, homework or spreadsheet.
Ratios in plain English
What a ratio isA comparison of quantities of the same kind.
2 : 3 means two parts of one thing for every three of the other, five parts in total.Ratio vs fractionThe ratio 2 : 3 is not the fraction 2/3. As a fraction of the whole it is 2/5, or 40%. The fraction 2/3 is the ratio of the first part to the second.
SimplifyingDivide every term by their greatest common factor.
24 : 36 = 2 : 3 because both divide by 12.Equivalent ratiosMultiply or divide every term by the same number and the ratio is unchanged.
2 : 3 = 4 : 6 = 20 : 30ProportionA statement that two ratios are equal. Cross multiply to solve: from
a : b = c : d you get a x d = b x c.Ratio vs rateA ratio compares like with like and has no units; a rate compares different quantities, such as kilometres per hour or price per kilogram.
Where ratios come up
- Scaling a recipe up or down while keeping the proportions right.
- Mixing paint, fuel, concrete, fertiliser or cleaning solution to a specified ratio.
- Splitting a bill, a prize, an inheritance or profits between people in agreed shares.
- Working out map scales, model sizes and scale drawings.
- Comparing financial ratios such as debt to equity or current assets to liabilities.
- Setting gear ratios, aspect ratios and mixing ratios in engineering and design.
- Checking homework where the marks are for the method, not just the answer.
Ratio calculator FAQ
Find the greatest common factor of all the terms and divide every term by it. For 24 : 36 the greatest common factor is 12, giving 2 : 3. The ratio is in its lowest terms when the only number that divides every term exactly is one. If the ratio contains decimals, multiply every term by ten, a hundred or a thousand first so that you are working with whole numbers.
Write it as a : b = c : d and cross multiply, so a times d equals b times c. Rearranging gives you whichever value is missing. For 3 : 8 = 12 : d, multiply 8 by 12 to get 96, then divide by 3 to get 32. Leave any one box empty above and the rearranged equation is shown for you.
Add the terms of the ratio to find the total number of parts, divide the amount by that number to get the value of one part, then multiply by each term. Sharing 1,200 in the ratio 2 : 3 : 7 gives twelve parts of 100, so the shares are 200, 300 and 700. They always add back up to the original total.
They are related but not interchangeable. The ratio 2 : 3 compares one part with the other, while the fraction that describes the first part of the whole is 2/5. Writing 2 : 3 as 2/3 is only correct when you mean the first quantity divided by the second, which is the decimal or 1 : n form rather than a share of the total.
Yes to both. A ratio such as 2.5 : 4 is perfectly valid and is usually rewritten as 5 : 8 by multiplying both sides by two. Ratios with three or more terms, such as 2 : 3 : 7, work the same way: simplify by dividing every term by their common factor, and share a total by counting all the parts together.
It is the ratio rewritten so the first term is exactly one, which makes comparisons easy. The ratio 24 : 36 becomes 1 : 1.5, telling you immediately that the second quantity is one and a half times the first. Mixing instructions and financial ratios are often quoted this way even when n is not a whole number.
Divide the new value by the matching term in the original ratio to get the scale factor, then multiply every other term by that factor. Going from 3 : 5 to a first term of 45 means a factor of fifteen, so the ratio becomes 45 : 75. This is exactly how recipes and scale drawings are resized.
Because the total does not divide exactly by the number of parts. Sharing 100 in the ratio 1 : 2 gives parts of 33.33 and 66.67. For money you would normally round each share to two decimals and give any leftover penny to one share so the total still balances, which the calculator flags when it happens.
Every ratio question, one screen
Simplify, solve, scale or share – with percentages, fractions, equivalent ratios and the full working. Free, unlimited and calculated on your own device.