Splitting a bill fairly, scaling a recipe, and solving a textbook proportion problem all reduce to the exact same idea: a ratio is a relationship, not a pair of fixed numbers.
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Ratio & Proportion Calculator
Simplify a ratio, solve a missing value, or split a total by a ratio, with the working shown.
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Three ratio problems, one underlying idea
Simplifying, solving, and splitting all lean on the same fact: a ratio describes a relationship between numbers, not the numbers themselves, 2:3 and 200:300 mean exactly the same thing. Simplifying shrinks that relationship to its smallest whole-number form, solving finds a missing number that keeps the relationship intact, and splitting distributes a real total while preserving it.
Ratio & proportion calculator FAQ
How is a ratio simplified?
The same way a fraction is: divide both numbers by their greatest common factor. 12:18 and 2:3 describe the exact same relationship, 2:3 is just the smallest whole-number version of it.
How do I solve a proportion like "a is to b as c is to x"?
Cross-multiply: a × x = b × c, then divide to isolate x, giving x = (b × c) ÷ a. This works because a proportion is really a statement that two ratios are equal, a/b = c/x, and cross-multiplying is just the standard way to clear both fractions at once.
What does "splitting a total by a ratio" actually calculate?
It divides one total amount into parts that keep a given ratio to each other, splitting €500 in a 2:3 ratio gives €200 and €300, which is 2 parts and 3 parts of €100 each (the total divided by 2+3=5 parts). It's the same math behind splitting a bill, a recipe, or a business partnership by an agreed share.
Is a ratio the same thing as a fraction?
Closely related but not identical. 3:4 as a ratio compares two separate quantities (3 of one thing for every 4 of another), while 3/4 as a fraction usually describes a part out of a whole. A class with a 3:4 ratio of boys to girls has 3 boys for every 4 girls, 7 students total, not "3/4 of the class."
Is my data private?
Yes. Every calculation runs in your browser. Nothing you enter is sent to a server.
Free ratio & proportion calculator by ANUPRESS
A ratio doesn’t care about its own size
2:3, 20:30, and 200:300 all describe the identical relationship, twice as much again for every three of the other thing. Simplifying just finds the smallest whole-number pair that says the same thing, dividing both sides by their greatest common factor. That’s the entire operation, nothing about the underlying relationship changes.
Solving “a is to b as c is to x”
A proportion states that two ratios are equal: a/b = c/x. Cross-multiplying clears both fractions at once, giving a × x = b × c, and dividing by a isolates x. This exact move, taught early and used constantly afterward, is how map scales, unit conversions, and similar-triangle problems all get solved once they’re framed as a proportion.
Splitting a total fairly by ratio
Three business partners agreeing to split profit 2:3:5 doesn’t mean fixed amounts, it means whatever the total profit is, it divides into 2+3+5=10 equal parts, with each partner taking their share of parts. €10,000 split that way gives €2,000, €3,000 and €5,000. The same math handles splitting a recipe’s ingredients when you’re cooking for a different number of people than the original recipe intended.