📚 What's in This Guide
A ratio calculator compares two or more quantities and writes the relationship in its simplest form. This one does the six jobs people usually need it for: simplifying a ratio, finding a missing value in A : B = C : D, building equivalent ratios, comparing two ratios, splitting a total by a ratio, and converting between ratios, fractions, percents and decimals. It suits students checking homework, cooks scaling a recipe, builders mixing materials, and anyone dividing a cost or a quantity fairly. Ratios matter because every proportion, scale and mix depends on them. Enter your numbers in the calculator above, pick the mode you need, and read the answer together with the working.
To simplify a ratio, divide every term by their greatest common divisor. For 24 : 36 the divisor is 12, so the ratio is 2 : 3. To find a missing term in A : B = C : D, cross-multiply, so D = B × C ÷ A.
1. How the Ratio Calculator Works
You choose a mode and enter your numbers. Whole numbers, decimals and fractions such as 3/4 or 1 1/2 are all accepted, and ratios can have two, three or four terms, so it works as a ratio calculator for 2 numbers and for 3 numbers. The calculator turns every entry into an exact fraction, so there is no floating-point rounding while it works. It then converts the terms to whole numbers, finds the greatest common divisor (GCD), and applies the formula for your mode. Only the final display is rounded, to the number of decimal places you pick, and exact fractions are shown beside rounded decimals.
Each mode gives a clear result, a few related figures, a bar showing each term's share of the whole where that makes sense, and the step-by-step working. The calculator assumes positive terms that use the same unit. It does not accept zero or negative terms, because a ratio with a zero term has no useful simplest form, and it does not convert between units for you. It is a general ratio calculator, so it does not apply financial or scientific formulas such as a debt-to-income ratio.
2. How to Use the Ratio Calculator
- Choose a mode: Simplify, Find missing value, Equivalent / scale, Compare, Split a total or Convert.
- Enter your numbers. For simplify, scale, split and ratio conversion, choose 2, 3 or 4 terms first.
- In Find missing value, fill in three of the four boxes and leave one empty. In Equivalent / scale, enter a factor, or choose a term and the value it should reach.
- In Split a total, enter the total and, if you like, a unit such as $ or kg. In Convert, choose whether you are starting from a ratio, fraction, percent or decimal.
- Choose how many decimal places you want in rounded results.
- Read the result, the shares bar and the working, then copy, share or download the result as a PDF, or reset to start again.
If an entry cannot be used, such as a zero term, a negative number or a comma, the calculator tells you which field to fix instead of showing a result.
3. Ratio Calculator Formulas
Here is how to calculate ratio problems by hand: write the quantities as A : B in the same unit, then divide every term by their greatest common divisor. These ratio calculation formulas cover the rest of the modes:
Simplest form: (A ÷ g) : (B ÷ g), where g = GCD(A, B)
Whole numbers: multiply every term by the LCM of the denominators
Proportion: A : B = C : D ⇒ A × D = B × C
Missing value: D = B × C ÷ A (and likewise for A, B or C)
Scaling: new term = term × k, where k = new value ÷ old term
Split a total: share = total × term ÷ (sum of all terms)
Share of the whole: term ÷ (sum of all terms)
Fraction to ratio: a/b = a : b; part to rest = a : (b − a)
Percent to ratio: p% = p : 100; part to rest = p : (100 − p)
Here g is the greatest common divisor, the largest whole number that divides every term exactly, and k is the scale factor. The LCM is the lowest common multiple, used to clear decimals and fractions before the GCD step. Ratios have no unit of their own, but the terms must be measured in the same unit before you compare them.
4. Worked Examples
These ratio calculator examples show how to calculate for each type of ratio problem, so you can check the calculator's answers by hand.
Example 1: What is the ratio of 24 and 36?
Inputs: 24 and 36. The GCD of 24 and 36 is 12. Dividing both terms by 12 gives 24 ÷ 12 : 36 ÷ 12 = 2 : 3. This is how you reduce a ratio to its simplest form, and the same steps simplify any ratio. As shares of the whole, 2 + 3 = 5, so the first term is 2/5 = 40% and the second is 3/5 = 60%.
Example 2: Find the missing value in 5 : 8 = 35 : D
Formula: D = B × C ÷ A. Calculation: D = 8 × 35 ÷ 5 = 280 ÷ 5 = 56. Check: 5 × 56 = 280 and 8 × 35 = 280, so the cross products match. The scale factor is 35 ÷ 5 = 7.
Example 3: Split 480 in the ratio 3 : 2 : 1
The terms add up to 3 + 2 + 1 = 6 parts. One part is 480 ÷ 6 = 80. The shares are 3 × 80 = 240, 2 × 80 = 160 and 1 × 80 = 80, which add up to 480.
Example 4: Ratios with fractions and decimals
As a ratio calculator with fractions, the tool finds the ratio of fractions by clearing the denominators. For 1/2 : 3/4, multiply both terms by 4, the LCM of the denominators, to get 2 : 3, which is already simplest. For 0.5 : 1.25, multiply by 100 to get 50 : 125, then divide by the GCD of 25 to get 2 : 5.
Example 5: Compare 7 : 5 with 9 : 7
Cross-multiply: 7 × 7 = 49 and 5 × 9 = 45. Because 49 is larger than 45, the first ratio is larger. As decimals, 7 ÷ 5 = 1.4 and 9 ÷ 7 ≈ 1.2857.
5. Understanding Your Result
A ratio such as 2 : 3 is a part-to-part ratio: for every 2 of the first quantity there are 3 of the second. It does not tell you the size of either quantity, only their relationship, which is why 24 : 36, 12 : 18 and 2 : 3 are all the same ratio. The shares in the result are part-to-whole, so they show what portion of the combined total each term makes up, and they add up to 100%. Ratios can also be read as a unit rate, such as 2/3 of one unit per unit of the other. The Common Core State Standards describe both ideas in the Grade 6 ratios and proportional relationships standards, including ratio language and the unit rate a/b for a ratio a : b.
Results are exact when the answer is a whole number or a simple fraction. When a decimal repeats, such as 1 ÷ 3, the displayed value is rounded and the exact fraction is shown next to it. Round only at the end: for a split of $100 in three equal shares, each share is $33.33 rounded, but the shares add up to $99.99, so keep the exact value of $100 ÷ 3 until you decide who receives the spare cent. The practical decisions the result supports are how much of each ingredient or cost to use, whether two ratios describe the same mix, and what a scaled-up quantity should be.
6. Ratio to Fraction, Percent and Decimal
Used as a ratio to fraction calculator, the Convert mode shows a ratio as a fraction in two different ways, so you can pick the one that matches your question. The first is part-to-whole: add the terms and divide each term by the total. The ratio 3 : 2 has a total of 5, so the parts are 3/5, which is 60%, and 2/5, which is 40%. The second divides one term by the other: 3 ÷ 2 = 1.5 = 150%, which says the first quantity is 150% of the second. These answers are both correct, but they answer different questions.
Going the other way depends on the same idea. A fraction a/b can be written as the ratio a : b, so 3/4 is 3 : 4. If it is a part of a whole, the part-to-part ratio is a : (b − a), so 3/4 is also 3 : 1. A percent p% is p : 100, so 25% is 25 : 100 = 1 : 4, and as part to rest it is 25 : 75 = 1 : 3. A decimal d is the ratio d : 1, so 0.75 is 0.75 : 1 = 3 : 4. The table below shows common ratios such as 1:2, 2:1, 3:2 and 3:4 in each form.
| Ratio | A ÷ B | Share of A | Share of B |
|---|---|---|---|
| 1 : 2 | 1/2 = 0.5 | 1/3 = 33.33% | 2/3 = 66.67% |
| 2 : 1 | 2 | 2/3 = 66.67% | 1/3 = 33.33% |
| 3 : 2 | 3/2 = 1.5 | 3/5 = 60% | 2/5 = 40% |
| 2 : 3 | 2/3 = 0.667 | 2/5 = 40% | 3/5 = 60% |
| 3 : 4 | 3/4 = 0.75 | 3/7 = 42.86% | 4/7 = 57.14% |
| 4 : 3 | 4/3 = 1.333 | 4/7 = 57.14% | 3/7 = 42.86% |
| 3 : 1 | 3 | 3/4 = 75% | 1/4 = 25% |
| 1 : 3 | 1/3 = 0.333 | 1/4 = 25% | 3/4 = 75% |
For example, a 3 to 1 ratio means 3 parts of one thing for every 1 part of another. It has 4 parts in total, so the first is 3/4 = 75% and the second is 1/4 = 25%.
7. Equivalent Ratios and Proportions
Equivalent ratios are different pairs of numbers that describe the same relationship, such as 2 : 3, 4 : 6 and 6 : 9. You make one by multiplying or dividing every term by the same non-zero number. A proportion is an equation stating that two ratios are equal, such as 2 : 3 = 8 : 12, and you can also use our Proportion Calculator to solve proportions. Use Find missing value, which is a ratio proportion solver, when one term is unknown, and use Equivalent / scale as an equivalent ratio calculator to find equivalent ratios when you know a factor or a target. For example, to scale 2 : 3 so that the first term becomes 7, the factor is 7 ÷ 2 = 3.5, and the ratio becomes 7 : 10.5. The table in the calculator lists the first ten multiples of the simplest form.
8. Ratios of Three or More Numbers
The ratio of 3 numbers works like the ratio of 2, and the calculator handles up to four terms, such as 6 : 9 : 12. Simplify ratios of any length the same way: the GCD of 6, 9 and 12 is 3, so the reduced ratio is 2 : 3 : 4. Three-term ratios are common in mixes and recipes, and splitting a total works the same as with two terms: add the terms, divide the total by that sum, and multiply by each term. When one term of a three-term ratio is known, use Equivalent / scale with the term you know to find the others.
9. Units and Conversions
The terms of a ratio must use the same unit. To compare 30 minutes with 2 hours, convert first: 2 hours is 120 minutes, so the ratio is 30 : 120, which simplifies to 1 : 4. Entering 30 : 2 would give 15 : 1, which is a different and misleading result. The ratio itself has no unit, so 1 : 4 means the same thing whether the quantities are minutes, grams or dollars. If the units differ and you want a rate, such as kilometers per hour, the result is a unit rate with a unit, not a pure ratio.
10. Practical Tips
- Convert both quantities to the same unit before you enter them.
- Keep the order consistent. 2 : 3 and 3 : 2 are different ratios.
- Use fractions like 1/3 instead of 0.33 when you want an exact answer.
- Keep full precision until the last step, then round to the accuracy you need.
- When splitting money, decide in advance who receives any rounding remainder.
- Check the answer by cross-multiplying: equal cross products confirm equivalent ratios.
11. Common Mistakes
- Mixing units: comparing minutes with hours without converting.
- Reversing the order: A : B is not the same as B : A.
- Mixing part-to-part and part-to-whole: 1 : 3 means 1 part in 4, which is 25%, not 33%.
- Adding instead of multiplying: to scale 2 : 3 up, multiply both terms by the same number, do not add the same amount to both.
- Rounding too early: rounding 1 ÷ 3 to 0.33 before multiplying can shift the final answer.
- Forgetting a term: in a three-term ratio, the share of the whole uses the sum of all three terms.
12. Related Calculations and Use Cases
People use a ratio calculator to scale a recipe, mix concentrate with water, divide costs or profit between partners, work out a map or model scale, check a screen's aspect ratio, and compare rates. For instance, a cleaning solution of 1 part concentrate to 9 parts water is a 1 : 9 ratio, which is 10 parts in total, so the concentrate is 1/10 or 10% of the mix. A 1920 × 1080 screen simplifies to 16 : 9, because the GCD is 120. In geometry, the golden ratio is about 1.618, the value where the whole divided by the larger part equals the larger part divided by the smaller. The same simplify, scale and split steps used here apply to all of these. Use the ratio simplifier mode for homework answers, the equivalent ratios calculator mode for proportions, and the percentage to ratio and ratio to percent conversions when a problem switches between forms.
13. Frequently Asked Questions
Write the two quantities in the same unit as A : B, then divide both by their greatest common divisor to reach simplest form. For 24 and 36 the greatest common divisor is 12, so 24 : 36 simplifies to 2 : 3. If either number is a decimal or fraction, multiply both by the same number first to turn them into whole numbers, which the calculator does automatically.
Set up the proportion A : B = C : D and cross-multiply: A × D = B × C. To find D, use D = B × C ÷ A. For 5 : 8 = 35 : D, D = 8 × 35 ÷ 5 = 56. The same steps work for any missing term, and the calculator shows the working.
Add the terms to get the whole, then divide each term by that total. For 3 : 2 the whole is 5, so the parts are 3/5 (60%) and 2/5 (40%). If you divide A by B instead, 3 ÷ 2 = 1.5, which means A is 150% of B. Which one you need depends on whether you are comparing a part with the whole or with the other part.
A fraction a/b can be written as the ratio a : b, so 3/4 is 3 : 4. If the fraction is a part of a whole, the part-to-part ratio is a : (b − a), so 3/4 becomes 3 : 1. A percent p% is p : 100, and as part to rest it is p : (100 − p). For 25%, that is 1 : 4 (part to whole) or 1 : 3 (part to rest).
Yes. Choose 3 or 4 terms to simplify, scale or split a ratio such as 6 : 9 : 12, which reduces to 2 : 3 : 4. You can also type decimals like 0.5 or fractions like 1/2 and 1 1/2, and the calculator converts them to whole numbers first. Terms must be greater than zero and use the same unit.
Conclusion
A ratio calculator takes the guesswork out of comparing quantities. Whether you need to simplify a ratio, find a missing value, scale a mix, compare two proportions, split a total or convert to a fraction or percent, the method is the same: keep the units consistent, work with exact fractions, and round only at the end. Accurate inputs matter because every result depends on the relationship between the terms. Use the ratio calculator above for fast answers with the working shown, and check important results by cross-multiplying.
This calculator is for general mathematics and planning. Check that both quantities use the same unit, and confirm important quantities, such as medicine, chemical or structural mixes, with the supplier's or professional's instructions.