Use this ratio calculator to simplify ratios, compare equivalent ratios, split an amount by ratio, convert ratios to decimal, fraction, and percentage form.
Last updated
Ratio workflows
Use one ratio calculator for ratio simplification, equivalent ratios, direct ratio comparison, ratio-to-decimal conversion, ratio-to-fraction conversion, ratio-to-percentage conversion, proportion solving, and unit-rate checks. Each workflow keeps the formula, denominator choice, and result interpretation tied to the question you are answering.
Active workflow
Simplify ratios, create equivalent ratios, compare two ratios, scale one side, or divide a total across ratio parts.
Mode
Quick examples
Interpretation notes
Order matters: 2:3 is not the same relationship as 3:2. Ratios work best when all parts are measuring the same kind of quantity or the same unit family.
Simplified ratio
6:8 simplifies to 3:4. The total of all parts is 14, so you can immediately see both the reduced ratio and each part’s share of the whole.
Equivalent ratios
×1
3:4
×2
6:8
×3
9:12
×5
15:20
×10
30:40
Simplification steps
Normalize to one part
Relative to A = 1
1:1.33
Relative to B = 1
0.75:1
Share of total
Where this helps
Use ratios for recipes, screen proportions, map scales, budgeting shares, mixture problems, and any comparison where the relationship matters more than the raw numbers.
Simplify and equivalent ratios
Answers: What is the lowest-term version of a ratio, or are two scaled ratios equivalent?
Use when: Comparing recipes, mixes, class counts, map scales, and part-to-part relationships
Watch for: Keep the order of the parts fixed; 2:3 and 3:2 describe different relationships.
Ratio conversions
Answers: How does a ratio look as a decimal, fraction, or percentage?
Use when: Moving between homework notation, spreadsheet decimals, and percentage summaries
Watch for: Choose whether the percentage means A divided by B or A divided by the total A+B.
Proportion and unit rate
Answers: What missing value makes a:b = c:d true, and what is the per-1 relationship?
Use when: Scaling recipes, maps, prices, speeds, dosage examples, and similar triangles
Watch for: Leave exactly one term blank and avoid zero in denominator positions.
| Workflow | Answers | Use when | Watch for |
|---|---|---|---|
| Simplify and equivalent ratios | What is the lowest-term version of a ratio, or are two scaled ratios equivalent? | Comparing recipes, mixes, class counts, map scales, and part-to-part relationships | Keep the order of the parts fixed; 2:3 and 3:2 describe different relationships. |
| Ratio conversions | How does a ratio look as a decimal, fraction, or percentage? | Moving between homework notation, spreadsheet decimals, and percentage summaries | Choose whether the percentage means A divided by B or A divided by the total A+B. |
| Proportion and unit rate | What missing value makes a:b = c:d true, and what is the per-1 relationship? | Scaling recipes, maps, prices, speeds, dosage examples, and similar triangles | Leave exactly one term blank and avoid zero in denominator positions. |
The former specialist pages still represent valuable search intents: ratio to decimal calculator, ratio to fraction calculator, ratio to percentage calculator, proportion calculator, and unit rate calculator. They now resolve into anchored workflows on this canonical ratio calculator, so users keep the same targeted answer while search engines see one stronger page for overlapping ratio and proportion questions.
Domain-specific ratio tools such as winning percentage calculator and image aspect ratio calculator stay separate because they need context-specific inputs, labels, and interpretation that go beyond general ratio arithmetic.
Arithmetic
A ratio calculator helps you reduce a ratio to lowest terms, generate equivalent ratios, convert a ratio to a decimal, fraction, or percentage, solve a missing-term proportion, split an amount by ratio, and see how each part compares with the whole.
To simplify a ratio, divide every part by the greatest common divisor, or GCD, of the whole-number form. If the ratio is 12:8, the GCD is 4, so 12:8 simplifies to 3:2. The relationship does not change; only the numbers become smaller and easier to read.
The same idea extends to three-part ratios such as 10:20:30. The common divisor is 10, so the lowest-terms form is 1:2:3. That is why ratio simplification is really a question about common factors, not about changing the underlying comparison.
Decimal ratios can still be simplified, but the decimals must be cleared first. For example, 1.5:2.5 can be rewritten as 15:25 by multiplying both parts by 10, and then simplified to 3:5. A good ratio calculator should do that automatically instead of forcing you to convert the decimals by hand.
For four-part ratios, the same GCD method still applies. A ratio such as 2:2:4:12 has a common divisor of 2, so it simplifies to 1:1:2:6. Showing the whole-number form and common divisor makes it easier to verify that the ratio is fully simplified instead of only partly reduced.
GCD(a, b) via Euclidean algorithm: while b ≠ 0, [a, b] = [b, a mod b]; GCD = a
Repeatedly replace the pair with the smaller number and the remainder until the remainder becomes zero. The last non-zero value is the GCD.
simplified ratio = (a / GCD) : (b / GCD)
Divide every active part of the ratio by the same greatest common divisor to reach lowest terms.
part share (%) = part / total × 100
Convert any ratio part into a percentage of the whole by dividing that part by the sum of all parts and multiplying by 100.
Equivalent ratios describe the same relationship using different absolute numbers. If the simplified ratio is 3:2, then 6:4, 9:6, and 15:10 are all equivalent ratios because every part has been multiplied by the same factor.
Scaling a ratio is the practical version of this idea. If a recipe is written in a 3:4 ratio and you know the first ingredient must be 15 units, then the scale factor is 15 ÷ 3 = 5. Multiply the other side by the same factor to get 20. This is why equivalent ratio calculators and scale ratio calculators are really solving the same proportional relationship from different directions.
Many users also want normalized forms such as 1:n or n:1 because those are easier to compare across cases. A 4:5 ratio can be written as 1:1.25 or 0.8:1 depending on which side you normalize to one. That normalized view helps when comparing aspect ratios, ingredient concentration, or one quantity per unit of another quantity.
A compare ratios calculator answers a slightly different question from simplification: do two ratios describe the same relationship? The fastest check is to simplify both ratios and see whether the lowest-terms forms match. For example, 3:4 and 6:8 are equivalent because 6:8 simplifies to 3:4.
Cross multiplication gives the same answer without needing to reduce both sides first. For a:b and c:d, compare a × d with b × c. If the cross products are equal, the ratios are equivalent. If they differ, the two ratios may still look close as decimals, but they are not the same proportion.
This is useful for checking recipe batches, classroom ratio homework, scale drawings, unit prices, and any case where two people wrote the same relationship with different-sized numbers. The comparison workflow now shows simplified forms, decimals, cross products, and the scale factor when the ratios match.
a:b is equivalent to c:d when a × d = b × c
Use cross products to test whether two ratios are proportional.
scale factor = c / a = d / b
When both divisions match, the right ratio is a scaled version of the left ratio.
A ratio to decimal calculator usually answers one direct question: what is a ÷ b? For 3:4, the decimal is 0.75 because 3 divided by 4 equals 0.75. The same relationship can be shown as 75% when the question means “A as a percentage of B.”
A ratio to fraction calculator often means something slightly different. If the ratio is being treated as parts of a combined whole, 3:4 has 7 total parts, so A is 3/7 of the whole and B is 4/7 of the whole. That is not the same denominator as the direct 3 ÷ 4 comparison, so the calculator keeps the conversion workflow explicit.
A ratio to percentage calculator needs the same distinction. A direct comparison turns 3:4 into 75%, while a share-of-total interpretation turns the first part into 3 ÷ (3 + 4) × 100 = 42.86%. Both are useful answers; the right one depends on whether you are comparing A with B or describing A as part of the total.
direct decimal = a / b
Use this when the ratio means A compared directly with B.
direct percentage = a / b × 100
Convert the direct decimal comparison into a percentage.
part-of-total fraction = a / (a + b)
Use this when the ratio splits one whole into parts.
For a basic two-part example, 12:8 simplifies to 3:2 because both numbers divide evenly by 4. As a whole, the total number of parts is 5, so the first part is 3/5 = 60% and the second part is 2/5 = 40%. This is the same reason a ratio calculator can show both lowest terms and percentage split at the same time.
For decimals, 1.5:2.5 becomes 15:25 after clearing the decimal places, and then 3:5 after simplification. The ratio can also be written as 1:1.67 if you want to normalize it relative to the first part, or 0.6:1 if you want the second part to equal one.
Three-part ratios appear when you divide quantities among more than two groups. If the ratio is 2:3:5, there are 10 parts in total. That means the shares are 20%, 30%, and 50%. If a total amount of 50 must be divided in that ratio, one part is 50 ÷ 10 = 5, so the final split is 10, 15, and 25.
To divide an amount by ratio, first add the parts together. If the ratio is 1:6:7, the total number of parts is 14. If the total amount to divide is 140, one part is worth 140 ÷ 14 = 10. Multiply each ratio part by 10 to get the final split: 10, 60, and 70.
This is one of the most practical reasons people search for a ratio calculator online. The same method works for sharing money, dividing ingredients, allocating time, or distributing inventory. The important step is always the same: find the value of one part before multiplying back out.
When the total does not divide evenly, the share values may include decimals. That does not make the ratio wrong. It simply means the real split is fractional, and any rounding choice should be made deliberately rather than hidden by the calculator.
For a four-way allocation such as 1:1:2:6, there are 10 ratio parts. Splitting a total of 100 gives shares of 10, 10, 20, and 60. A useful divide ratio calculator should also show a check sum so you can confirm the individual shares add back to the amount you started with.
total parts = a + b (+ c)
Add the ratio parts first to find how many equal units the whole contains.
one part value = total amount / total parts
Divide the full amount by the number of ratio parts to find the value of a single unit.
share = ratio part x one part value
Multiply each ratio part by the one-part value to recover each final share.
A proportion states that two ratios are equal, such as a:b = c:d. If one term is missing, cross multiplication solves the unknown by keeping the two ratios equivalent. For example, 3:4 = 6:x gives 3x = 24, so x = 8.
The proportion workflow is useful when a ratio has already been established and you need a matching value at a different scale. Recipes, map scales, similar figures, price comparisons, speed examples, and classroom word problems all use this same structure.
Unit-rate checks restate the solved proportion as a per-1 relationship. If 3 items cost 12, the unit rate is 4 per item. If 4 miles takes 2 hours, the unit rate is 2 miles per hour. Showing the unit rate alongside the proportion makes the answer easier to reuse in follow-up calculations.
a:b = c:d
A four-term proportion says the left ratio and right ratio are equivalent.
a × d = b × c
Cross multiplication checks or solves the proportion.
unit rate = quantity / reference quantity
Divide by the reference quantity to express the relationship per 1 unit.
Ratios appear in recipes, mixture problems, map scales, screen formats, classroom proportion problems, probability comparisons, and budgeting shares. A 16:9 display ratio tells you the width is 16 units for every 9 units of height. A 1:25,000 map scale tells you one unit on the map represents 25,000 of the same units in reality.
Ratios are also common in finance and statistics, but the meaning changes with the context. A price-to-earnings ratio compares price with earnings per share, while a response ratio in a survey may compare one subgroup count with another. The arithmetic is similar, but the interpretation depends on what the terms actually measure.
That is why it helps for the page to distinguish ratios from percentages, fractions, and proportions. A ratio describes the relative sizes of quantities. A percentage expresses a share of a whole. A proportion states that two ratios are equal. Closely related ideas, but not interchangeable.
Further reading
Many ratio mistakes happen because the final answer looks plausible even when one part was scaled incorrectly. A step-by-step ratio calculator helps by showing the whole-number form, the greatest common divisor, the lowest-terms result, and the percentage split in the same place.
The whole-number form is especially helpful when the inputs include decimals. If 1.5:2.5 becomes 15:25 before simplification, you can see exactly why the final ratio is 3:5. That visible intermediate step is easier to trust than a bare answer with no explanation.
The check-sum step matters for split-total problems. After dividing money, ingredients, or time by a ratio, the allocated shares should add back to the original total before any intentional rounding. If the check sum is off, the issue is usually a copied input, an omitted ratio part, or a rounding decision that needs to be made explicit.
The most common mistake is ignoring order. A:B and B:A are different ratios unless the two values are the same. The second mistake is trying to compare unlike units directly. A ratio is most meaningful when the parts are measuring the same kind of quantity or when the context explicitly supports the comparison.
Another common confusion is mixing up direct ratio conversion with share-of-total interpretation. If 3:4 is being converted as A divided by B, the answer is 0.75 or 75%. If it is being converted as A out of the combined total, the first share is 3/7 or 42.86%. The calculator separates those workflows so the denominator is visible.
This page can simplify two-, three-, and four-part ratios, split totals across up to four parts, scale a two-part ratio to a chosen target side, convert two-part ratios into decimal, fraction, and percentage form, and solve four-term proportions with one missing value. It does not automatically convert units for you, and it does not replace a full algebra system for symbolic ratio and proportion problems. Always check that the numbers you enter are describing the same relationship you actually want to compare.
Frequently asked questions
Divide every part of the ratio by the greatest common divisor of the whole-number form. For example, 12:8 simplifies to 3:2 because both values divide by 4. If the ratio includes decimals, clear the decimal places first and then reduce the resulting whole-number ratio.
Yes. Decimal ratios are cleared to whole numbers before simplification, so 1.5:2.5 becomes 15:25 and then 3:5. The calculator can also simplify three-part ratios such as 2:3:5, showing normalized views and each part’s share of the total.
Yes. You can enter an optional fourth part when simplifying a ratio or splitting a total. For example, 1:1:2:6 has 10 total parts, so splitting 100 by that ratio gives 10, 10, 20, and 60, with a check sum that confirms the shares return to the original total.
Take the side you want to match, divide the target value by the original value on that side, and use the result as the scale factor for every part. If a ratio is 3:4 and the first part must become 15, the scale factor is 5, so the new ratio is 15:20.
Simplify both ratios or use cross multiplication. For a:b and c:d, compare a × d with b × c. If the two cross products are equal, the ratios are equivalent; if they differ, the ratios do not describe the same relationship.
A ratio compares two or more quantities, while a proportion states that two ratios are equal. For example, 3:2 is a ratio. Writing 3:2 = 15:10 is a proportion because it says the two ratios describe the same relationship. If you need to solve a full missing-term equality, a dedicated proportion calculator may be more direct.
Yes. Divide both parts by the side you want to set to one. For example, 4:5 can be written as 1:1.25 by dividing both terms by 4, or as 0.8:1 by dividing both terms by 5. Normalized forms make it easier to compare one ratio against another.
Add the ratio parts together, divide the total amount by that part count, and then multiply each ratio part by the value of one part. For example, to split 140 in the ratio 1:6:7, add the parts to get 14, divide 140 by 14 to get 10, then multiply to get 10, 60, and 70.
Use the direct comparison a ÷ b. For example, 3:4 becomes 3 ÷ 4 = 0.75. This is the right conversion when you want A compared directly with B, such as asking what decimal 3 is of 4.
If the ratio describes parts of one whole, add the parts first. For 3:4, the total is 7 parts, so A is 3/7 of the whole and B is 4/7 of the whole. If you mean the direct comparison of A to B instead, the fraction is 3/4.
Choose the denominator that matches the question. For A as a percentage of B, calculate a ÷ b × 100. For A as a share of the total, calculate a ÷ (a + b) × 100. A ratio of 3:4 is 75% in the direct comparison and 42.86% as the first part of the total.
Set the two ratios equal, cross multiply, and isolate the blank term. For 3:4 = 6:x, cross multiplication gives 3x = 24, so x = 8. The completed proportion is 3:4 = 6:8.
A unit rate is a ratio normalized to one unit of the reference quantity. For example, 12 dollars for 3 items is a ratio of 12:3, and the unit rate is 4 dollars per item. Unit rates are especially useful for price, speed, density, and recipe scaling comparisons.
Yes. A three-part ratio such as 2:3:5 can be simplified, converted into percentage shares, and used to divide a total amount. The calculator adds the parts, finds the value of one part, and then allocates the final shares.
The result may include decimals. That is normal because a valid ratio split does not need to land on whole numbers. If you need rounded shares, round them intentionally and then confirm the rounded values still fit your practical goal.
An aspect ratio is a specific kind of ratio that compares width to height, such as 16:9. The underlying arithmetic is the same, but an aspect-ratio problem usually focuses on proportional resizing of dimensions rather than on share-of-total interpretation.
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