What a ratio actually compares
A ratio compares two or more quantities of the same kind, showing how much of one you have for a given amount of another. Three parts sand to one part cement, a screen 16 units wide for every 9 tall, two cups of flour to three of milk: each is a ratio, written with a colon between the terms. Unlike a fraction, a ratio does not have to describe parts of a single whole; it just fixes a relationship, so 2:3 stays 2:3 whether you are mixing two teaspoons to three, or two tonnes to three.
This tool covers the three jobs a ratio question usually asks for: reducing an ugly ratio to its simplest whole-number form, filling in a missing term when two ratios are declared equal, and scaling a ratio up or down, either by a multiplier or to hit a target total.
Simplifying a ratio to lowest terms
A ratio is in its lowest terms when its numbers share no common factor bigger than 1. Finding that shared factor is the highest common factor, or HCF (also called the greatest common divisor, GCD), and dividing every term by it shrinks the ratio without changing what it describes.
Take 45:75. The highest common factor of 45 and 75 is 15, so dividing both by 15 gives 3:5, the smallest whole-number pair that describes the same relationship. The same idea extends to decimals: a ratio such as 2.5:1.5 is first scaled up until both terms are whole numbers (multiply by 10 to get 25:15), then reduced by the HCF as normal, landing on 5:3.
Some ratios resist simplifying entirely. A 16:9 widescreen ratio has an HCF of 1, since 16 and 9 share no common factor, so 16:9 is already as simple as it gets; that is exactly why 16:9 is the number printed on television and monitor spec sheets rather than some tidier-looking alternative.
Reading a ratio as 1 : n
Alongside the simplest whole-number form, it often helps to see a ratio with one side pinned at 1, since that turns it into a straightforward multiplier. Dividing both terms of 16:9 by 16 gives 1:0.5625, meaning "for every 1 unit of width, allow 0.5625 units of height." Dividing instead by 9 gives 1.778:1, the more familiar way monitor and film aspect ratios get quoted. Map scales work the same way in reverse: a map marked 1:25,000 means 1 unit on the paper stands for 25,000 of the same unit on the ground, so a centimetre on the map is 250 metres in real life.
Solving the missing value in a proportion
When two ratios are declared equal, A : B = C : D, knowing any three of the four terms is enough to find the last one. The trick is cross-multiplication: multiply the outer pair and the inner pair, and the two results must match.
Rearranging that single equation for whichever letter is missing gives four short formulas, one per position:
Try 4 : 3 = X : 12. Here A=4, B=3, D=12 and C is missing, so C = (A×D)÷B = (4×12)÷3 = 16. Check it the long way round: 4:3 simplifies the same as 16:12 does, both reduce to 4:3, so the two ratios genuinely match.
Scaling a ratio up or down
Scaling keeps a ratio's relationship fixed while changing the size of the quantities it describes. Multiplying every term by the same number is the most direct route: a pancake batter of 3 cups flour to 2 cups milk (3:2), multiplied by 4, becomes 12 cups flour to 8 cups milk (12:8), still exactly the same balance of flour to milk, just enough for a bigger crowd.
The other common version works backwards from a known total. Mixing paint in a 2:3 ratio of white to blue for 40 litres altogether means splitting 40 into 2+3=5 shares, each share worth 40÷5=8 litres, so the mix needs 2×8=16 litres of white and 3×8=24 litres of blue.
Turning a ratio into a fraction or a percentage of the whole
A two-term ratio A:B also describes a split of a single whole, A+B, into two shares. Written as fractions of that whole, A is A÷(A+B) and B is B÷(A+B); multiply each by 100 for the percentage version. A 3:2 mixing ratio, for instance, is 3÷5 = 60% of the first ingredient and 2÷5 = 40% of the second. This is the calculation behind the "share of the whole" row in the results table on the Simplify tab, and it is the same arithmetic a classroom "share £60 in the ratio 3:2" problem is really asking for.
Reading the results panel
Every answer here shows the simplified whole-number ratio, the 1:n and n:1 forms, and each term's share of the whole as both a fraction and a percentage, alongside the exact working. The bars below the answer are drawn to scale, so the bigger term always fills more of the row, which is a quick sanity check that a result looks right before you rely on it.
Questions people ask
How do you simplify a ratio with decimals in it?
Multiply every term by whatever power of ten clears the decimal point, then simplify as normal using the highest common factor. 2.5:1.5 becomes 25:15 once multiplied by 10, and 25:15 reduces to 5:3 once divided by their HCF of 5.
What does the 1:n form of a ratio mean?
It rewrites the ratio so the first term is exactly 1, turning the second term into a straightforward multiplier. 16:9 becomes 1:0.5625, meaning every 1 unit of width pairs with 0.5625 units of height.
How do you find a missing number in a proportion like A:B = C:D?
Cross-multiply: A×D always equals B×C when the two ratios are equal. Rearranging that equation for whichever letter is unknown, then dividing, gives the missing term directly.
Can a ratio include a zero or a negative number?
A zero term is mathematically fine, for instance 4:0 describing all of one thing and none of the other, though it breaks the 1:n form on whichever side the zero sits, since dividing by zero has no answer. Negative numbers work through the arithmetic too, but ratios are conventionally written using positive numbers, so double-check the real-world quantities you started from if a minus sign appears.
How do you scale a ratio to a target total?
Add the terms together to find how many equal shares the total splits into, divide the target total by that number of shares, then multiply each original term by the resulting share size. A 2:3 ratio scaled to a total of 40 splits into 5 shares of 8 each, giving 16:24.
What is the difference between a ratio and a fraction?
A fraction always describes part of a single whole, while a ratio compares separate quantities to each other and does not need to add up to anything in particular. The two connect once you add a ratio's terms together, since each term can then be read as a fraction of that combined total.
Why is 16:9 already in its simplest form?
Because 16 and 9 share no common factor above 1; 16 is 2×2×2×2 and 9 is 3×3, with nothing in common between the two lists. A ratio with no shared factor cannot be reduced any further, no matter how the numbers look.
Ratios here are calculated exactly wherever the terms allow; only the on-screen decimal display rounds a repeating result. For splitting fractions and mixed numbers instead of ratios, try the fraction calculator on this site.