Ratio Calculator

Reducing 8:12 to 2:3 is the part every ratio tool gets right, and often the part you could do in your head. The reason you actually pulled up a ratio calculator is usually the step after that. You need the percentage split for a budget, or you're missing one number in a proportion and have to solve for it. A lot of the free simplifiers stop at the reduced ratio and leave you to finish by hand. This one carries the ratio all the way to the answer you came for.

Two modes cover it. Simplify takes a two or three part ratio, reduces it to lowest terms, and then does the useful bit: it shows the same relationship as a decimal and as each part's percentage of the whole. Solve takes a proportion like 2:3 = x:9, lets you mark any of the four slots as the unknown, and cross-multiplies to fill it in with the steps written out. Everything runs in your browser, nothing you type gets uploaded, and once the page has loaded it keeps working with no connection.

This is the conversion people actually get stuck on, and it isn't the arithmetic. A ratio compares parts to each other. 3:2 means three of one thing for every two of another. But the number you usually need is the share, what fraction of the total each part takes, and you cannot read that straight off the ratio. 3:2 is not "3% and 2%," and it is not 30% and 20% either.

Say you're splitting $100 between two people at 2:3. That's five parts total. The first person gets 2 of the 5, which is $40, and the second gets 3 of the 5, which is $60. Simplify mode does that step for you. It totals the parts and shows each one as a percentage of the whole, so 2:3 comes back as 40% and 60% without you dividing anything. That single feature bridges the gap that trips most people, the jump from a part-to-part ratio (2:3) to the part-to-whole shares (40 / 60) you were actually after.

It matters anywhere a ratio hides a split. Dividing profit between three partners at 2:3:5, mixing a paint color, working out how much of a batch each ingredient is. You set the ratio, the tool hands you the percentages, and you scale to whatever total you like from there.

Type 2.5:5 into a lot of ratio simplifiers and they either reject it or hand back garbage. This one takes it and reduces to 1:2. It works by scaling every term up to whole numbers first, then reducing, so 1.5:2 comes out as 3:4 and 0.2:0.5 as 2:5. You don't have to clean up your inputs before typing them, messy decimals are fine.

The other gap is three-part ratios. Plenty of basic tools only do a:b and quit. This one takes a third term, so a paint mix at 2:3:5 (red : blue : white) or a triangle's sides stay in one calculation. It finds the largest number that divides evenly into all three and reduces every term by it at once, so 12:18:24 becomes 2:3:4 and 10:20:30 becomes 1:2:3. By hand it's easy to reduce two terms and forget the third, here that's a single keystroke.

Solve mode is the classic proportion problem. Three numbers known, one unknown, cross-multiply to find it. 2:3 = x:9 returns x = 6, nothing special in itself, but two things make it worth using instead of scribbling.

First, x can sit in any of the four positions, not just the last one that most quick calculators assume. Pick the slot from the dropdown and fill the other three. 4:5 = 12:x gives x = 15. Move x to the front and x:6 = 2:3 gives x = 4. The tool rearranges the cross-multiplication to isolate whichever term you left blank, so you're never forced to reshuffle the problem to fit the tool.

Second, it shows the step, not just the number. You get the cross-multiply formula it used and the full proportion with x filled in. A student can copy that working straight onto homework, and anyone else can check the logic instead of trusting a bare result. If solving for x would mean dividing by zero, there's no real answer, and the tool says which value to change rather than printing something broken.

Why cross-multiplication works at all is simpler than it looks. a:b = c:d is really the fraction equation a/b = c/d, and clearing both denominators leaves a times d equal to b times c. It's ordinary algebra, the colon is just how ratios happen to be written.

One thing the calculator can't decide for you: which quantity goes first. 2:3 and 3:2 are different ratios, opposite relationships, and the tool reduces whatever order you type. If the ratio of cats to dogs is 2:3 and you type 3:2, you've now claimed there are more cats than dogs, and every number downstream is wrong. Spend the two seconds to be sure your first term really is the first quantity, that's the one part no tool can cover.

1. Pick a mode. Choose Simplify a ratio to reduce one you already have, or Solve a proportion to find a missing value.
2. To simplify: type your first two terms in the A and B boxes. Add a third in C for a ratio like 2:3:5, or leave C blank for a plain two-part ratio.
3. Read the results. You get the reduced ratio, a decimal form for two-term ratios, and each part as a percentage of the whole.
4. To solve: pick which slot is x from the dropdown (x can be any of the four positions in a:b = c:d), then fill in the other three numbers.
5. Read x. The answer appears with the cross-multiply step, so you can check the working or copy it down.

Decimals are welcome in both modes, and there's no button to press. Results update as you type.