I ended up building a ratio calculator because of a recurring, slightly embarrassing pattern: I kept reaching for the phone calculator to do arithmetic I learned at twelve, getting it half right, and second-guessing myself. Scaling a recipe. Working out whether 1512 by 850 was close enough to 16:9 to matter. Splitting a shared bill in the ratio two people had spent. None of it is hard, but all of it is fiddly enough to get wrong when you are doing it in your head, and the wrong answer looks just as confident as the right one. This guide is the reasoning I baked into the tool: how to reduce a ratio properly, why solving a proportion is not the same as guessing, and where the everyday traps are.
TL;DR: A ratio compares two quantities, written A to B. Simplifying it means dividing both sides by their greatest common divisor until the numbers are as small as they can be, so 1920:1080 becomes 16:9. A proportion says two ratios are equal, and you solve it by cross-multiplying to find the one missing value. The ratio calculator does both, handles decimals, and shows the working, all in your browser.
What is a ratio, and what does simplifying it mean?
A ratio is a way of saying how two quantities relate in size. Two cups of flour to three eggs is a ratio, written 2:3 and read "two to three". A screen that is 1920 pixels wide and 1080 tall has a ratio of 1920:1080. The numbers on their own are less interesting than the relationship between them, and that relationship does not change if you scale both sides by the same amount. 2:3 and 4:6 and 200:300 all express exactly the same thing.
Because so many equivalent forms describe the same relationship, there is a single simplest form, and reaching it is what "simplify" means. You divide both numbers by the largest whole number that divides them both evenly, their greatest common divisor, until nothing divides both any more. 1920 and 1080 share a greatest common divisor of 120, and dividing both by 120 gives 16:9. That is why every monitor and television is described as 16:9 rather than 1920:1080: it is the same ratio in its clearest form, the smallest pair of whole numbers that still carries the meaning.
The greatest common divisor is doing the real work here, and it is the same idea used to reduce a fraction to lowest terms, because a ratio and a fraction are close cousins. The ratio calculator finds it with the classic Euclidean algorithm, which repeatedly divides and takes the remainder until the remainder is zero. It is fast, exact, and older than almost every other piece of mathematics you use daily.
How do I simplify a ratio?
In the tool, you pick the simplify mode, type the two numbers, and read off the reduced form. Behind that, the steps are the ones you could do by hand, and it is worth seeing them once so the answer is not magic.
Take 45:60. List what divides both: 1, 3, 5, 15. The largest is 15. Divide both sides by 15 and you get 3:4, which cannot be reduced further because 3 and 4 share no divisor above 1. That is the answer. The tool also shows you the decimal value, which is 45 divided by 60, or 0.75, and the fraction form 3/4, because sometimes the ratio you are checking is really a proportion in disguise and the decimal is the number you want to compare.
One detail that trips people up: the order matters. 3:4 and 4:3 are different ratios describing opposite relationships, and simplifying never reorders them. The tool keeps your first value first and your second value second, so a reduced ratio always lines up with the quantities you entered.
What about decimal ratios?
Real measurements rarely arrive as clean integers, and this is where a lot of quick mental arithmetic falls apart. Suppose you have a ratio of 2.5 to 5. You cannot take a greatest common divisor of decimals directly, because the algorithm is defined for whole numbers.
The fix is to scale both numbers up until they are integers, reduce, and the ratio is unchanged because you multiplied both sides by the same thing. 2.5:5 becomes 25:50 when you multiply by ten, and 25:50 reduces to 1:2. So 2.5:5 is just 1:2, which is obvious once you see it but easy to miss in your head. The ratio calculator does this scaling automatically. It looks at how many decimal places your inputs have, multiplies both by the right power of ten, reduces the resulting whole numbers, and gives you clean terms rather than leaving something like 2.5:5 or a fractional term in the answer.
This is the same job the fraction calculator does for fractions, and the two tools lean on the same underlying arithmetic. If you find yourself simplifying a lot of decimal ratios, it is often because the real question is a fraction or a percentage, which is why the tool shows all three forms at once.
What is a proportion, and how do I solve one?
A proportion is a statement that two ratios are equal: A:B = C:D. It is the single most useful tool in practical arithmetic, because it is how you scale something up or down while keeping its shape. The whole point is that three of the four numbers are known and you want the fourth.
The recipe case makes it concrete. A recipe uses 2 cups of flour for every 3 eggs, and you have 9 eggs. How much flour? Set up the proportion 2:3 = x:9. Cross-multiply, meaning multiply the two diagonally opposite known numbers and divide by the remaining one: x = (2 times 9) divided by 3, which is 6. Six cups of flour. The tool does exactly this. You put 2 and 3 on the left, 9 in the D position, leave C blank, and it fills in 6 and shows you the multiplication it used so you can check it.
Cross-multiplication works because if A:B equals C:D, then A times D equals B times C. That single fact lets you solve for whichever of the four is missing, just by rearranging. The calculator handles all four cases, so it does not matter which position you leave empty. Fill in any three, blank the one you want, and it solves it.
Why can't I just add or subtract to scale a ratio?
This is the trap that catches people, and it is worth stating plainly. To scale a ratio you multiply, you do not add.
Say a photo is 4:3 and you want to enlarge it. If you add 2 to each side you get 6:5, which is a completely different shape, taller and narrower than the original. To keep the shape you multiply both sides by the same factor: 4:3 doubled is 8:6, which reduces right back to 4:3. Addition changes the ratio; multiplication preserves it. A proportion is just the formal way of asking "multiplied by what factor does one side become this new number", and solving it gives you the matching value on the other side automatically.
The same mistake shows up in mixing and dilution. A cleaning solution mixed 1:8 does not become 2:9 when you want more of it, it becomes 2:16, then 3:24, always scaling both parts together. If you only remember one thing about ratios, make it this: equivalent ratios are related by multiplication, never by adding the same amount to both sides.
How does this relate to aspect ratios?
Aspect ratios are the most common place people meet ratios without calling them that, and they are a good worked example. A 1512 by 850 image: is that 16:9? Simplify it and you get 756:425, which is not 16:9, it is a fraction of a percent off. That kind of near-miss is exactly what causes thin black bars or a slight stretch when an image is placed in a 16:9 frame.
For pure aspect-ratio work, where you want to solve for a missing width or height at a fixed ratio and see presets like 16:9 and 4:3, the dedicated aspect ratio calculator is the sharper tool, because it is built around screen and image dimensions specifically. The general ratio calculator is the one to reach for when the quantities are not pixels: money, ingredients, mixing ratios, map scales, or splitting anything in proportion. The two overlap deliberately and link to each other, so you can start in one and move to the other when the problem gets more specific.
Ratio, fraction, decimal, or percentage: which form do I want?
A ratio is one of four ways to write the same relationship, and part of what confuses people is not knowing which form the situation calls for. They are interchangeable, and the calculator shows several at once for that reason, but each has a job it does best. Here is the same set of relationships in every form:
| Ratio | Fraction | Decimal (A/B) | A as % of whole | Best when |
|---|---|---|---|---|
| 1:1 | 1/1 | 1.0 | 50% | Two things are equal, like a 50/50 split |
| 1:2 | 1/2 | 0.5 | 33.3% | One part is half the other, like a dilution |
| 2:3 | 2/3 | 0.667 | 40% | A recipe or mix with two unequal parts |
| 3:4 | 3/4 | 0.75 | 42.9% | A shape or format, like a 4:3 photo |
| 16:9 | 16/9 | 1.778 | 64% | Widescreen displays and video |
| 1:3 | 1/3 | 0.333 | 25% | One part against three, like odds |
Read the table by column depending on your question. If you are comparing two relationships to see which is larger, the decimal column is the one to look at, because 0.75 is plainly bigger than 0.667 in a way that 3:4 versus 2:3 is not. If you are describing how much of a whole one part takes up, the percentage column is what people expect. If you are stating a mix or a format, the ratio itself is the clearest. And the fraction is the bridge to any further arithmetic, which is why it shares its machinery with the fraction calculator. The ratio calculator gives you the ratio, the decimal, the fraction, and the percentage split together, so you can pick the form the moment you see it rather than converting by hand.
Where do ratios and proportions come up?
The reason I use this tool more than I expected is that proportions are hiding inside a surprising number of everyday calculations. A few that come up for me constantly:
Scaling recipes, as above, in either direction. Splitting a bill or a prize in the ratio people contributed, rather than evenly. Converting between units when you know the conversion as a ratio, such as miles to kilometres at roughly 5:8. Working out map or model scale, where 1:50000 tells you a centimetre on the map is half a kilometre on the ground. Mixing paint, fuel, fertiliser, or cocktails to a stated ratio and needing a larger batch. Comparing two ratios to see which is bigger, which is really just comparing their decimal forms, which the tool shows for you.
Turning a ratio into a percentage is close enough to this that the calculator does it automatically: for a ratio of 1:3, the two parts are 25 percent and 75 percent of the whole. If percentages are the real destination, the percentage calculator handles the increase, decrease, and "what percent of" questions directly, and the average calculator covers the related job of combining several numbers. All three sit in the same corner of toolz.dev, and the broader developer productivity tools guide maps the wider set of everyday calculators alongside the age calculator guide for date math.
Is my data private, and does it work offline?
Yes to both, and it is the same answer for every tool on the site. The ratio calculator runs entirely in your browser. The numbers you type are used to do arithmetic in the memory of the page and are never sent anywhere. There is no account, no tracking of what you calculate, and no server involved in the maths at all.
For a calculator that sounds almost beside the point, since the numbers are rarely secret, but the principle is what keeps the tool fast and available. Because nothing is uploaded, results appear the instant you type, and the tool keeps working if your connection drops after the page has loaded. It is the same design choice, applied everywhere, that I argue for at length in the data privacy and online tools guide: a utility this small has no business phoning home.
Frequently asked questions
How do I simplify a ratio?
Enter the two numbers in simplify mode and the calculator divides both by their greatest common divisor to give the lowest whole-number terms. For example, 1920 and 1080 reduce to 16:9 instantly, and the tool also shows the decimal and fraction forms.
How do I solve a proportion?
Switch to proportion mode, enter three of the four values in A:B = C:D, and leave the unknown one blank. The calculator cross-multiplies to find the missing value and shows the calculation it used so you can check the result.
What does it mean to reduce a ratio to lowest terms?
Reducing a ratio means dividing both sides by the largest number that divides them both evenly, until no whole number divides both. It gives the smallest pair of numbers that express the same relationship, such as 2:3 instead of 8:12.
Can the calculator handle decimal ratios?
Yes. A ratio like 2.5:5 is scaled up to whole numbers before the greatest common divisor is taken, so it reduces to 1:2. Proportions also accept decimal values, which matters for money, measurements, and unit conversions.
How do I scale a ratio up or down?
Use proportion mode. Put your known ratio on the left as A:B, enter one side of the new size, and leave the other blank. Solving 2:3 = x:9, for instance, scales the ratio to 6:9. Scaling always multiplies both sides, it never adds to them.
How do I turn a ratio into a percentage?
The simplify mode shows each part as a percentage of the whole automatically. For a ratio of 1:3, the two parts are 25 percent and 75 percent of the total, which the calculator displays alongside the reduced ratio.
What is the difference between a ratio and a proportion?
A ratio compares two quantities, written A:B. A proportion is a statement that two ratios are equal, A:B = C:D. This calculator reduces ratios in one mode and solves proportions in the other.
Is my data kept private?
Yes. All calculations happen entirely in your browser with JavaScript. Your numbers are never uploaded or stored, and the tool keeps working with no network connection once the page has loaded.
