Ratio Calculator
Updated on June 18, 2026
Enter a ratio to simplify it, solve a proportion (A:B = C:D), or scale it up or down — and see the missing value, the simplest form, and a step-by-step breakdown your child (or you) can actually follow. Our ratio calculator handles two-part and three-part ratios, accepts whole numbers, decimals, and fractions, and shows the working so the answer makes sense, not just appears.
Step-by-Step Solution
Quick answer: A ratio compares two or more quantities. To simplify a ratio, divide every term by their greatest common factor; to find a missing value in a proportion, cross-multiply. Our calculator runs both methods for you and shows each step.
How to Use This Ratio Calculator
Step 1: Enter your values. Type your ratio into the boxes — for example, 3:4 to simplify it, or 3:4 = 9:? to solve for a missing value. The calculator reads whole numbers, decimals, and fractions.
Step 2: Choose what you want to do. Pick “Simplify” to reduce a ratio to its smallest whole numbers, “Solve” to find the missing term in a proportion, or “Scale” to enlarge or shrink a ratio by a chosen factor.
Step 3: Read your results. You see the answer instantly, along with the simplest form and an optional step-by-step breakdown so you can check the math yourself.
Answer a few quick questions about your child’s learning, and we’ll recommend next steps. 
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Part-to-Part vs. Part-to-Whole Ratios — Which Do You Need?
A part-to-part ratio compares one group directly to another — for example, 3 boys to 4 girls, written 3:4. A part-to-whole ratio compares one group to the total instead — those same 3 boys out of 7 students, written 3:7 or as the fraction 3/7. Picking the right one is what trips most students up: a question that asks “how many boys for every girl?” wants part-to-part, while “what fraction of the class is boys?” wants part-to-whole. The numbers stay the same, but whether you include the total completely changes the answer, so read each problem for the word “total,” “altogether,” or “out of” before you write the ratio down.
How to Simplify a Ratio
Divide every term by the greatest common factor (GCF) — the largest number that divides all the terms evenly. Once no whole number larger than 1 divides them all, the ratio is in its simplest form. A simplified ratio means exactly the same thing as the original; it just uses the smallest possible numbers, which makes it far easier to read and compare.
How to Solve a Proportion (A:B = C:D)
When two ratios are set equal, the cross-products are always equal too: in A:B = C:D, the value of A × D matches B × C. To find a missing term, write the proportion as two equal fractions, cross-multiply, and divide. This single move — cross-multiplication — solves almost every “find the missing value” ratio problem you will meet through middle and high school.
Step-by-Step Example — How to Simplify and Solve a Ratio
Example 1 — Simplify the ratio 18:24.
Step 1: Find the greatest common factor. The largest number that divides both 18 and 24 is 6.
Step 2: Divide each term by the GCF. 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
Result: 18:24 simplifies to 3:4 — the smallest whole-number ratio that carries the same meaning.
Example 2 — Solve the proportion 3:4 = 9:x.
Step 1: Write it as equal fractions. 3/4 = 9/x.
Step 2: Cross-multiply. 3 × x = 4 × 9, which gives 3x = 36.
Step 3: Solve for x. x = 36 ÷ 3 = 12.
Result: 3:4 = 9:12. You can check it instantly — 9 ÷ 12 = 0.75, exactly the same as 3 ÷ 4.
What Is a Ratio?
A ratio compares two or more quantities, showing how much of one there is relative to another. We write it three ways that all mean the same thing: with a colon (3:4), as a fraction (3/4), or in words (“3 to 4”). A ratio of 1:1 means the quantities are equal, while 2:1 means there is twice as much of the first as the second. In short, a ratio answers the question “for every ___ of this, how much of that?”
Ratio vs. Fraction
A fraction compares a part to the whole, while a ratio can compare a part to another part or a part to the whole. The part-to-part ratio 3:4 describes a group of 7 split into 3 and 4, whereas the fraction 3/4 describes 3 items out of a total of 4 — same digits, different meaning.
Ratio vs. Proportion
A ratio compares quantities; a proportion is an equation stating that two ratios are equal, such as 3:4 = 9:12. You simplify a single ratio, but you solve a proportion to find a value that keeps both sides equal.
Where Are Ratios Used?
Ratios are one of the most practical ideas in math — once your child can read and scale a ratio, they can follow a recipe, read a map, and resize an image. Understanding ratios, not just calculating them, turns a homework skill into an everyday one.
Cooking & Baking
Recipes are ratios in disguise. A rice-to-water ratio of 1:2 means two cups of water for every cup of rice, and that relationship holds whether you cook one cup or six — you just scale both numbers by the same amount.
Maps, Models & Scale Drawings
A map scale of 1:100,000 means one unit on the map stands for 100,000 of the same units in real life. Architects, model builders, and mapmakers all rely on ratios to shrink huge things down to a size that fits on paper.
Aspect Ratios for Screens & Photos
The shape of a screen or photo is a ratio of width to height — a widescreen TV is 16:9, an older monitor is 4:3, and a standard photo print is often 3:2. Knowing the aspect ratio is how you resize an image without stretching or squashing it.
Money, Odds & Everyday Rates
Ratios show up whenever something is split or compared: dividing $50 between two people in a 3:2 ratio, reading betting odds, or comparing prices as a unit rate. They are the quiet math behind a surprising number of daily decisions.
For more practice with these everyday problems, our online math tutoring walks students through ratios, rates, and proportions one example at a time.
Struggling With Ratios and Proportions?
Your child can get the right answer from the calculator above and still freeze when a word problem asks them to set up the ratio themselves — and that is where most marks are lost. Our certified tutors close that gap one problem at a time, so your child learns to spot part-to-part versus part-to-whole, simplify with confidence, and cross-multiply without second-guessing. They can work through ratios, proportions, percentages, and the rest of the curriculum with a certified tutor inside our structured math courses. The first lesson is free, with no card required.
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How to Scale a Ratio Up or Down
To scale a ratio, multiply or divide every term by the same number. The relationship stays identical even though the digits change — this is exactly what happens when you double a recipe or resize a photo. Here’s how each direction works:
- Scale up (enlarge): multiply every term. A 2:3 ratio scaled ×4 becomes 8:12.
- Scale down (shrink): divide every term. A 30:45 ratio scaled ÷15 becomes 2:3.
- Multi-part ratios scale the same way: a paint mix of 2:1:4 scaled ×3 becomes 6:3:12.
One rule to remember: whatever you do to one term, do to all of them. Multiplying or dividing only part of a ratio changes its meaning entirely.
Frequently Asked Questions
What is a ratio?
A ratio is a comparison of two or more quantities that shows how much of one there is relative to another. It can be written with a colon (3:4), as a fraction (3/4), or in words (“3 to 4”).
How do I simplify a ratio?
Divide every term in the ratio by their greatest common factor until no whole number larger than 1 divides them all. For example, 18:24 divides by 6 to become 3:4.
What is the difference between a ratio and a fraction?
A fraction always compares a part to the whole, while a ratio can compare a part to another part or a part to the whole. The ratio 3:4 can describe a group of 7, whereas the fraction 3/4 describes 3 out of 4.
What is a proportion?
A proportion is an equation that states two ratios are equal, such as 3:4 = 9:12. You solve a proportion to find a missing value that keeps both sides equal.
How do I find a missing value in a proportion?
Write the proportion as two equal fractions, cross-multiply the diagonal terms, and divide to isolate the unknown. For 3:4 = 9:x, cross-multiplying gives 3x = 36, so x = 12.
How do I calculate a ratio in Excel?
Divide both numbers by their greatest common factor using the GCD function: =A1/GCD(A1,B1) and =B1/GCD(A1,B1) returns the simplified ratio. You can also enter =A1&”:”&B1 to display two values in ratio form.
What is the difference between a part-to-part and a part-to-whole ratio?
A part-to-part ratio compares one group to another, like 3 boys to 4 girls (3:4). A part-to-whole ratio compares one group to the total, like 3 boys out of 7 students (3:7).
How do I convert a ratio to a percentage?
Treat the ratio as part-to-whole, divide the part by the total, and multiply by 100. In a 1:3 ratio the total is 4 parts, so the first part is 1 ÷ 4 = 25%.
What is an aspect ratio?
An aspect ratio is the ratio of an image or screen’s width to its height, written as width:height. A widescreen display is 16:9, while a standard photo print is often 3:2.
How do I scale a ratio up or down?
Multiply every term by the same number to scale up, or divide every term by the same number to scale down. A 2:3 ratio multiplied by 4 becomes 8:12, and the relationship stays the same.
What does a ratio like 1:2 mean?
A ratio of 1:2 means that for every one of the first quantity there are two of the second. It is the same as saying the second amount is twice the first.
How can a tutor help my child with ratios and proportions?
A tutor helps a student set up the ratio correctly from a word problem — the step most learners struggle with — instead of only crunching numbers. One-to-one sessions let a child practice spotting part-to-part versus part-to-whole and cross-multiplying on problems matched to their grade.
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