Three ratio jobs on one page: reduce a ratio to its simplest form, find the missing value in a proportion, and split a total in a given ratio. Switch with the buttons; the share of the whole is shown every time, because that is where the mistakes happen.
Key terms
- Ratio — how two quantities compare to each other, written 3 : 4.
- Proportion — a statement that two ratios are equal, like 3 : 4 = 12 : 16.
- Simplest form — both sides divided by their greatest common divisor, so no whole number divides them both again.
How it works
The three operations
simplify: a ÷ g : b ÷ g, where g = gcd(a, b) · solve: A : B = C : X gives X = B × C ÷ A · share: each part gets total ÷ (a + b) per unit
All three rest on the same idea — a ratio is unchanged when both sides are multiplied or divided by the same number.
A ratio of 3 : 4 is not three quarters
This is the error the page exists to prevent. In 3 : 4 there are seven parts in total, and the first share is three of them — 42.9%, not 75%.
Split 350 in 3 : 4 correctly and you get 150 and 200. Treat the ratio as a fraction and take three quarters, and you get 262.50 — off by 112.50, and the gap grows with the total. The difference is what the denominator means: in a fraction it is the whole, in a ratio it is the other part.
Because it is so easy to slip, the share of the total is shown as a percentage on every calculation here, not just when you ask for a split.
Decimals do not belong in a simplified ratio
2.5 : 5 is a valid ratio but not a simplified one. Multiply both sides by ten to clear the decimal, then divide by the greatest common divisor, and it becomes 1 : 2. A “simplified” ratio that still contains a decimal point has not really been simplified — it has just been divided by something.
Some proportions have no answer
Solving 0 : 4 = 0 : x looks like a normal problem, but any value of x satisfies it. There is no scaling factor to find, because you cannot scale up from nothing. Rather than returning zero — which would look like an answer — this calculator says the value is not determined.
How to use this calculator
- Choose Simplify, Solve for ?, or Share a total.
- Enter the two parts of your ratio.
- For a proportion, add the third number: A : B = C : ?
- For a split, enter the total. Check that the two shares add back to it.
Frequently asked questions
How do I convert a ratio to a percentage?
Add the parts to get the whole, then divide each part by that total. For 3 : 4 the total is 7, so the shares are 42.9% and 57.1%. Both percentages shown here are worked out this way.
How do I simplify a ratio?
Divide both sides by their greatest common divisor. For 18 : 24 that is 6, giving 3 : 4. Dividing by any smaller common factor leaves it partly reduced — 9 : 12 is equivalent but not simplest.
What is a proportion?
Two equal ratios. Because they are equal, the cross products match: in 3 : 4 = 12 : 16, both 3 × 16 and 4 × 12 give 48. That identity is what lets you solve for a missing fourth value.
Can a ratio have three parts?
Yes — 2 : 3 : 5 works the same way, with ten parts in total. This calculator handles two parts; for three, split the total by the sum of all three parts and multiply each out.
Is 3 : 4 the same as 4 : 3?
No. Ratios are ordered, and the order tells you which quantity is which. 3 : 4 gives a first share of 42.9% while 4 : 3 gives 57.1%.
