Ratio Calculator
This ratio calculator does three jobs. It simplifies a ratio such as 12:18 to 2:3 and shows it as 1:n, n:1 and percentages of the whole; it solves A:B = C:? for the missing term; and it shares a total in a given ratio. Below the tool you will find the method for each, worked examples, and the mistakes that trip people up.
12:18 or 2:3:5.How to use the ratio calculator
Pick one of the three modes with the buttons at the top. The result updates as you type, and each mode has its own numbered steps underneath.
- Simplify (the default). Type a ratio such as
12:18. The calculator returns2:3, the same ratio as1:1.5and0.667:1, and each part as a share of the whole: 40% and 60%. It takes two or three parts, and decimals too, so1.5:2.5becomes3:5. - Solve A:B = C:? Enter A, B and C. With the defaults 3, 4 and 15, the missing term is 20, found by cross multiplication.
- Share a total. Enter a ratio and a total. Splitting 100 in the ratio
2:3gives 40 and 60.
Separate the parts with a colon. Order matters: 2:3 and 3:2 are different ratios, so keep the parts in the order the question names them.
How to simplify a ratio
A ratio compares sizes, not amounts, so you can divide every part by the same number and the comparison stays the same. Simplifying means dividing by the largest number that goes into every part: the greatest common factor.
For 12:18, the factors of 12 are 1, 2, 3, 4, 6 and 12, and the largest of those that also divides 18 is 6. Dividing both parts by 6 gives 2:3. If finding the GCF is the slow part, the GCF calculator lists the factors and runs Euclid’s method for you.
Example: the default ratio 12:18
Find the GCF, divide, then read the other forms.
All four answers describe the same comparison. Which form you report depends on the reader: recipes and mixes use whole numbers, and gear ratios or odds often use 1:n.
This is the same move as reducing a fraction to lowest terms. The guide to simplifying fractions covers the GCF route and the repeated-division route in more detail, and both carry over to ratios unchanged.
Ratios with three parts
Find the GCF of all three numbers, not just two of them. For 24:36:60 the GCF of the three is 12, so the ratio simplifies to 2:3:5. Checking only 24 and 36 would suggest 12 as well here, but in a ratio like 4:6:9 the first pair shares 2 while 9 does not, so 4:6:9 is already in simplest form. The guide to finding the GCF and LCM shows how to get the GCF of three or more numbers from their prime factors.
Ratios with decimals or fractions
Clear the decimals first by multiplying every part by 10, 100 or whatever power of ten removes them, then simplify as usual.
For fractions, multiply every part by the least common denominator. For 1/2 : 1/3, multiply by 6 to get 3 : 2. If you prefer to type decimals into the calculator, the fraction to decimal calculator converts each part first.
Ratios with different units
Put both parts into the same unit before you simplify. 50 cm to 2 m is not 50:2; it is 50 cm to 200 cm, which simplifies to 1:4. Once the units match, they cancel and the ratio has no unit at all.
Solving A:B = C:? for a missing term
Two ratios are equal when one is a scaled copy of the other. To find the missing fourth term, work out how much the first term was scaled by, then scale the second term by the same amount. Written as one step, that is cross multiplication.
Example: 3:4 = 15:?
The default values in the solve mode.
The missing term is 20. Cross multiplication gives the same answer in one line: 4 × 15 ÷ 3 = 60 ÷ 3 = 20.
If the missing value sits somewhere else, or you have a word problem with fractions and rates, the proportion calculator solves a/b = c/d with the blank in any of the four positions and explains direct and inverse proportion.
How to divide a total in a given ratio
Sharing in a ratio is the question people most often bring to a ratio calculator: split $240 between two people in the ratio 3:5, mix 600 grams of something in the ratio 7:5:3, divide prize money by hours worked. The method is the same every time.
Example: share 100 in the ratio 2:3
The default values in the share mode.
Example: split $240 in the ratio 3:5
Two partners put in money in the ratio 3:5 and share a $240 profit the same way.
The first partner gets $90 and the second $150. A useful check: $150 ÷ $90 ≈ 1.667, and 5 ÷ 3 ≈ 1.667 too.
Example: three parts, 600 g in the ratio 7:5:3
The method does not change with more parts.
When you know the difference, not the total
Some problems give the gap between the shares instead. “Two numbers are in the ratio 3:5 and the second is 24 more than the first.” The gap is 5 − 3 = 2 parts, so one part is 24 ÷ 2 = 12, and the numbers are 3 × 12 = 36 and 5 × 12 = 60. Check: 60 − 36 = 24.
Ratios, fractions and percentages are not the same thing
A ratio of 2:3 compares one part with another part. A fraction compares a part with the whole. Mixing the two up is the most common error in ratio questions.
In a class with boys and girls in the ratio 2:3, the boys are not 2/3 of the class. The whole is 2 + 3 = 5 parts, so boys are 2/5 of the class (40%) and girls are 3/5 (60%). To turn a part into a percentage of any total, the percentage calculator does the division for you. The 2/3 compares boys to girls, which is a different question: there are two boys for every three girls.
| Ratio A:B | A as a fraction of the whole | A as a % of the whole | A ÷ B |
|---|---|---|---|
| 1:1 | 1/2 | 50% | 1 |
| 1:2 | 1/3 | ≈ 33.33% | 0.5 |
| 1:3 | 1/4 | 25% | ≈ 0.333 |
| 2:3 | 2/5 | 40% | ≈ 0.667 |
| 3:5 | 3/8 | 37.5% | 0.6 |
| 3:7 | 3/10 | 30% | ≈ 0.429 |
| 4:1 | 4/5 | 80% | 4 |
| 16:9 | 16/25 | 64% | ≈ 1.778 |
If you need a ratio turned into a percentage both ways, the part-of-whole reading and the A-compared-to-B reading, the ratio to percentage calculator shows them side by side.
Comparing two ratios
To tell which of two ratios is larger, turn each into a single number by dividing, or rewrite both with the same second term. Is 3:5 bigger than 5:8? As decimals, 3 ÷ 5 = 0.6 and 5 ÷ 8 = 0.625, so 5:8 is slightly larger. Rewritten over 40, they become 24:40 and 25:40, which shows the same thing without decimals. It is the same trick used to compare fractions, and the equivalent fractions guide walks through it.
Ratios that describe screens and prices
Ratios turn up wherever one quantity is compared with another. A 1920 × 1080 screen has an aspect ratio of 16:9, because the GCF of 1920 and 1080 is 120. A price per ounce is a ratio of dollars to ounces, which is exactly what the unit price calculator compares across pack sizes.
Common mistakes with ratios
- Reading a ratio as a fraction of the whole. In 2:3, the first part is 2/5 of the total, not 2/3.
- Swapping the order. “Flour to sugar is 3:1” means three flour for each sugar. Writing 1:3 reverses the recipe.
- Simplifying with mixed units. 30 minutes to 2 hours is 30:120, which is 1:4, not 15:1.
- Dividing by a common factor that is not the greatest. Dividing 12:18 by 2 gives 6:9, which is correct but not simplest. Divide again by 3, or use the GCF of 6 from the start.
- Sharing by the ratio terms instead of the parts. Splitting 100 in 2:3 is not 2% and 3%, or 50 and 50. Add the terms first to find how many parts there are.
- Adding the same number to both terms. Adding 1 to each side of 2:3 gives 3:4, a different ratio. Only multiplying or dividing every term keeps the ratio the same.
- Rounding one share and not checking the total. Splitting $100 in 1:2 gives $33.33 and $66.67 (the exact shares are 33 1/3 and 66 2/3). Round so that the shares still add up to the original total.
Frequently asked questions
How do you simplify the ratio 12:18?
Divide both parts by their greatest common factor, which is 6. That gives 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12:18 simplifies to 2:3. In 1:n form it is 1:1.5, and as shares of the whole the first part is 40% and the second 60%, because 2 + 3 = 5 parts in total.
How do you split $240 in the ratio 3:5?
Add the ratio terms to get 8 parts, then divide the total by 8 to find one part: $240 ÷ 8 = $30. Multiply each term by $30, which gives 3 × $30 = $90 and 5 × $30 = $150. The two shares add back to $240, which confirms the split is correct.
How do you find the missing number in a ratio?
Use cross multiplication. For 3:4 = 15:?, multiply the two known terms on the diagonal and divide by the remaining one: 4 × 15 ÷ 3 = 20. You can also see it as scaling: 3 became 15, which is a factor of 5, so 4 becomes 4 × 5 = 20. Both routes always give the same answer.
What is a ratio of 1920 to 1080 in simplest form?
It is 16:9. The greatest common factor of 1920 and 1080 is 120, and 1920 ÷ 120 = 16 while 1080 ÷ 120 = 9. That is why 1920 × 1080 screens are described as 16:9. In decimal form the width is about 1.778 times the height.
How do you simplify a ratio with decimals?
Multiply every part by the power of ten that removes the decimals, then simplify as usual. For 1.5:2.5, multiply by 10 to get 15:25, then divide by the GCF of 5 to get 3:5. For 0.75:2, multiply by 100 to get 75:200, then divide by 25 to get 3:8.
Is a ratio the same as a fraction?
Not quite. A ratio compares one part with another part, while a fraction compares a part with the whole. A ratio of 2:3 means two of one thing for every three of another, so the first thing makes up 2/5 of the total, not 2/3. You can write 2:3 as 2/3 only when you mean “first divided by second.”
How do you write a ratio in the form 1:n?
Divide both parts by the first part. For 4:7, divide by 4 to get 1 : 1.75. For 12:18, divide by 12 to get 1 : 1.5. The second number tells you how many of the second thing there are for each one of the first. To get n:1 instead, divide both parts by the second part.
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