Simplify ratios, compare proportions, and solve ratio problems instantly. Find equivalent ratios, check if two ratios are equal, and solve for missing values. Free online ratio calculator with step-by-step solutions and real-world examples.
Please provide any three values below to calculate the fourth in the ratio A:B = C:D.
So you've got a ratio problem, and you're not sure where to start. Maybe you're trying to figure out how to split a pizza fairly between friends, or you're working on a math problem that just won't click. That's where our ratio calculator comes in.
This tool does the heavy lifting for you. You just punch in your numbers, and it gives you the simplified ratio, the equivalent ratios, and even helps you compare two ratios to see if they're the same. No more guessing or staring at a blank page.
But here's the thing - a calculator is only as good as your understanding. So let's break down what ratios actually are, how to use them, and why they matter. By the end of this, you'll be a ratio pro.
A ratio is a quantitative relationship between two numbers that describe how many times one value can contain another. Applications of ratios are fairly ubiquitous, and the concept of ratios is quite intuitive. This could likely be demonstrated by giving a child half as many cookies as his sister — the child intuitively understands receiving 1:2 as many cookies.
Ratios are often expressed as two numbers separated by a colon (e.g., 3:4). They can also be written as "1 to 2" or as a fraction ½. The ratio represents the number that needs to be multiplied by the denominator to yield the numerator.
Ratios are common in many daily applications including: aspect ratios for screens, maps and models as scaled-down versions, baking and cooking recipes, odds of events occurring, and financial rates. For example, making 5 cakes with a 1:2:3 ratio of butter:sugar:flour simply means multiplying by 5 to get a 5:10:15 ratio.
Think of a ratio as a way to compare two or more things. It tells you how much of one thing there is compared to another. Simple, right?
Let's say you have a bowl of fruit with 3 apples and 2 oranges. The ratio of apples to oranges is 3:2. That means for every 3 apples, there are 2 oranges. You could also say the ratio of oranges to apples is 2:3. The order matters!
Ratios are everywhere. Recipes use them (2 cups flour to 1 cup sugar). Maps use them (1 inch on the map equals 10 miles in real life). Even your phone's screen has a ratio (16:9 for most screens).
Using the calculator is super straightforward. Here's what you do:
The calculator will show you:
Example time: Let's say you have 8 boys and 12 girls in a class. The ratio of boys to girls is 8:12. But that's not simplified. Our calculator will tell you it's 2:3. For every 2 boys, there are 3 girls. Makes more sense, right?
The aspect ratio is the ratio of a geometric shape's sizes in different dimensions. For a rectangle, it is width to height. Below are common computer screen/video resolutions.
| Name | Aspect Ratio | Width (px) | Height (px) |
|---|---|---|---|
| Standard Definition (SD) | 4:3 | 640 | 480 |
| HD Ready (720p) | 16:9 | 1280 | 720 |
| Full HD (1080p) | 16:9 | 1920 | 1080 |
| Quad HD (1440p) | 16:9 | 2560 | 1440 |
| Ultra HD (4K) | 16:9 | 3840 | 2160 |
| Ultra HD (8K) | 16:9 | 7680 | 4320 |
| CinemaScope | 2.35:1 | 1920 | 817 |
| Ultrawide | 21:9 | 2560 | 1080 |
| Square | 1:1 | 1080 | 1080 |
| Vertical Video | 9:16 | 1080 | 1920 |
Simplifying a ratio is like simplifying a fraction. You find the biggest number that divides evenly into both parts. That's called the greatest common factor (GCF).
Here's the step-by-step:
Example: Simplify 12:18. The GCF of 12 and 18 is 6. 12 ÷ 6 = 2, 18 ÷ 6 = 3. So 12:18 simplifies to 2:3. See? Not so hard. But if you're dealing with bigger numbers or you just want to double-check your work, our ratio simplifier is here to help.
You and two friends earn $100 for a job. You agree to split it in the ratio 2:3:5 based on how much work each person did. How much does each person get?
Here's the trick: First, add up all the parts of the ratio. 2 + 3 + 5 = 10 parts total. Then divide the total amount by the number of parts: $100 ÷ 10 = $10 per part. Now multiply each part by $10:
Check your work: $20 + $30 + $50 = $100. Perfect!
If the ratio of cats to dogs is 3:5, and there are 15 cats, how many dogs are there?
Set it up as a proportion: 3/5 = 15/x. Cross-multiply: 3 × x = 5 × 15. So 3x = 75. Divide both sides by 3: x = 25. There are 25 dogs.
Our ratio and proportion calculator can do this for you in a second.
Are 4:6 and 6:9 the same ratio? Simplify both: 4:6 becomes 2:3, and 6:9 also becomes 2:3. Yes, they're equivalent! Our calculator checks this instantly.
Compares a part to the whole. 3 apples out of 5 fruits = 3/5.
Compares part to part. Apples to oranges = 3:2. Notice the total isn't 5.
Here's a quick way to remember: Fractions are about "out of." Ratios are about "for every."
Mistake 1: Getting the order wrong. The ratio of boys to girls is not the same as girls to boys. Always read the problem carefully.
Mistake 2: Forgetting to simplify. A ratio of 10:15 is technically correct, but it's much cleaner as 2:3. Always simplify if you can.
Mistake 3: Treating ratios like fractions. Remember, 3:2 is not the same as 3/2. A ratio compares parts, a fraction compares a part to the whole.
Mistake 4: Not checking your work. After you solve a ratio problem, plug your numbers back in to make sure they work.
You've probably heard of the golden ratio. It's about 1.618:1, and it shows up everywhere in nature, art, and architecture. The Parthenon in Greece, the Mona Lisa, and even the spiral of a nautilus shell all follow the golden ratio. Some people think it's the most pleasing ratio to the human eye.
You can have ratios with three, four, or even more numbers. Like a 3:4:5 triangle (a right triangle where the sides are in that ratio). Or a recipe that calls for a 1:2:3 ratio of ingredients. The same rules apply - you just have more numbers to work with.
A unit ratio is when one of the numbers is 1. Like 5:1 or 1:3. These are super useful for comparing things. For example, if a car gets 30 miles per gallon, that's a unit ratio of 30:1 (miles to gallons).
Use whole numbers: The calculator works best with whole numbers. If you have decimals, multiply everything by 10 or 100 first.
Check your inputs: Make sure you're entering the numbers in the right order. The calculator can't read your mind!
Use the "compare" feature: If you're not sure if two ratios are the same, let the calculator check for you.
Bookmark it: You'll use this more than you think. Homework, cooking, DIY projects - ratios pop up everywhere.
Here's the thing about ratios - they're not just some abstract math concept. They're a way of thinking about the world. When you understand ratios, you start seeing them everywhere. You'll notice the proportions in a painting, the mix of ingredients in your favorite dish, or the balance of a budget.
Plus, ratios are the foundation for a ton of other math. Percentages, proportions, scaling, and even algebra all build on ratio concepts. Get good at ratios now, and everything else gets easier.
So go ahead, play around with the calculator. Try different numbers. See what happens. And if you get stuck, just remember: a ratio is just a way of saying "for every X, there are Y." Everything else is just details.
A ratio is a way to compare two or more things. It tells you how much of one thing there is compared to another. For example, if you have 2 cups of flour and 1 cup of sugar, the ratio of flour to sugar is 2:1. That means for every 2 cups of flour, you need 1 cup of sugar.
To calculate a ratio, you divide both numbers by their greatest common factor (GCF). For example, to find the ratio of 8 to 12, find the GCF (which is 4), then divide both numbers by 4. You get 2:3. That's the simplified ratio. Our ratio calculator does this automatically.
A fraction compares a part to the whole. A ratio compares one part to another part. For example, if you have 3 apples and 2 oranges, the fraction of apples is 3/5 (3 out of 5 fruits). But the ratio of apples to oranges is 3:2 (for every 3 apples, there are 2 oranges). They're related but not the same.
Find the greatest common factor (GCF) of both numbers, then divide each number by that GCF. For example, to simplify 48:72, the GCF is 24. 48 ÷ 24 = 2, and 72 ÷ 24 = 3. So 48:72 simplifies to 2:3. If you're not sure about the GCF, our ratio simplifier can do it for you.
Yes! Our ratio calculator works with two or three numbers. Just enter all three numbers, and it will simplify the ratio and show you equivalent ratios. This is super useful for things like splitting money between three people or mixing three ingredients.
Simplify both ratios to their simplest form. If they're the same, the ratios are equal. For example, 4:6 simplifies to 2:3, and 6:9 also simplifies to 2:3. So 4:6 and 6:9 are equal ratios. Our calculator has a compare feature that does this instantly.
The most common mistake is getting the order wrong. The ratio of boys to girls is not the same as girls to boys. Always read the problem carefully to see which order they want. Another common mistake is forgetting to simplify the ratio to its smallest form.
Ratios are everywhere! You use them in cooking (recipe proportions), photography (aspect ratios), construction (mixing concrete), finance (comparing company performance), and even when reading maps (scale ratios). Once you start looking, you'll see ratios all around you.
The golden ratio is about 1.618:1, and it's considered very pleasing to the eye. It shows up in nature (like in the spiral of a nautilus shell), in art (the Mona Lisa), and in architecture (the Parthenon). Some people believe it's the most beautiful ratio in the world.
First, identify what the ratio is comparing. Then set up the ratio with the numbers you know. If you're missing a number, set up a proportion (two equal ratios) and cross-multiply to solve for the unknown. For example, if the ratio of cats to dogs is 3:5 and there are 15 cats, set up 3/5 = 15/x, cross-multiply to get 3x = 75, so x = 25 dogs.