Ratio calculator
Find the missing term in a proportion, or reduce a ratio to its simplest form.
A : B = C : x — so 3 : 4 = 12 : x
x
16
3 : 4 = 12 : 16
- Simplified A : B
- 3 : 4
- C : x
- 12 : 16
- As a decimal
- 0.75
Two jobs
A ratio calculator answers one of two questions:
- Solve a proportion — three terms are known and the fourth is missing.
- Simplify — reduce a ratio to the smallest whole numbers that keep the same relationship.
They look similar and are used for different things. Solving is what you need for scaling a recipe or a map; simplifying is what you need to compare two ratios fairly.
Solving a proportion
A proportion says two ratios are equal:
A : B = C : xCross-multiplying gives A × x = B × C, so:
x = (B × C) ÷ AWith 3 : 4 = 12 : x, that is x = 4 × 12 ÷ 3 = 16.
The method works because both sides describe the same rate. If it takes 4 units of paint to cover 3 walls, then 12 units cover 16 walls.
Simplifying a ratio
Divide both terms by their greatest common divisor:
18 : 24 → ÷6 → 3 : 4The GCD is the largest number that divides both terms without a remainder. If the ratio contains decimals, multiply both sides by a power of ten first, then reduce:
1.5 : 2.5 → ×10 → 15 : 25 → ÷5 → 3 : 5Screen resolutions simplify neatly this way: 1920 : 1080 ÷ 120 = 16 : 9.
A worked example
A recipe uses flour and sugar in a 3 : 2 ratio. You have 450 g of flour.
- 3 parts = 450 g, so 1 part = 150 g
- 2 parts of sugar = 300 g
- Total mix = 750 g
Solving 3 : 2 = 450 : x gives x = 2 × 450 ÷ 3 = 300, the same answer. Proportions
and “one part equals” reasoning are the same method written differently.
Ratios do not add like fractions
A 3 : 4 mixture has seven parts in total. Three sevenths are the first ingredient and four sevenths the second. If you treat 3 : 4 as “three quarters”, you get a different and wrong mixture — this is the most common ratio mistake in the kitchen and in the paint aisle.
Ratios with units
Ratios are unitless by construction: 3 : 4 could be 3 kg to 4 kg, 3 hours to 4 hours, or 3 apples to 4 apples. Convert both sides to the same unit before simplifying, or the result is meaningless. A map scale of 1 : 50,000 means one centimetre on the map is 50,000 centimetres — 500 metres — on the ground.
When not to use a ratio
If the two quantities are measured in the same unit and one is genuinely a part of the other, you want a fraction or a percentage, not a ratio. A ratio is for comparing separate quantities, and using it for parts of a whole makes the numbers harder to read, not easier.
Frequently asked questions
Does the order of a ratio matter?
Yes, completely. 3 : 4 is not the same as 4 : 3. A ratio compares a first quantity to a second, and swapping them changes the meaning — a 16:9 screen is not a 9:16 screen. Write the ratio in the order the question states.
How do I solve a proportion with an unknown?
Cross-multiply. From A : B = C : x, the two diagonals are equal, so A × x = B × C and x = B × C ÷ A. With 3 : 4 = 12 : x that gives x = 4 × 12 ÷ 3 = 16.
What does simplifying a ratio actually do?
It divides both parts by their greatest common divisor, keeping the relationship identical. 18 : 24 and 3 : 4 describe the same proportion; the second is just the smallest whole-number version. Simplifying is useful for comparing ratios, not for changing them.
Can a ratio contain decimals?
Yes, and it still simplifies. 1.5 : 2.5 is the same as 15 : 25, which reduces to 3 : 5. The calculator scales decimals away first, then divides by the greatest common divisor, so the answer is always a whole-number pair.
How is a ratio different from a fraction?
A fraction is a part of a whole — 3/4 of a pizza. A ratio compares two separate quantities and does not add up to one — a 3:4 mix of paint to thinner has seven parts in total, of which three are paint. The notation is similar; the meaning is not.
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