Ratio Calculator
Simplify a ratio, scale it up or down, or solve a proportion for the missing value — with the working shown at each step.
How to use this calculator
- Choose whether you want to simplify, solve a proportion, or split an amount.
- Enter the two parts of your ratio.
- For splitting, add the total amount you want divided.
How the calculation works
Simplify: divide both parts by their GCD.
Proportion: a/b = c/d ⟹ d = bc/a- GCD
- Greatest common divisor of the two parts
- a : b
- A ratio — a parts of one thing to b parts of another
A ratio compares two quantities; a proportion states that two ratios are equal.
Dividing an amount in a ratio works by treating the ratio parts as shares: add them, divide the total by the sum, then multiply by each part.
Worked example
Simplify 16 : 9
- The greatest common divisor of 16 and 9 is 1.
- So 16 : 9 is already in its lowest terms — this is why it is the standard widescreen aspect ratio.
Result: 16 : 9 (unchanged)
Simplify 32 : 18
- Find the greatest common divisor of 32 and 18: it is 2.
- Divide both parts by 2: 32 ÷ 2 = 16 and 18 ÷ 2 = 9.
Result: 32 : 18 simplifies to 16 : 9
"I have 5 pairs of green socks and my friend has 6 pairs of white socks — what is the ratio of my green socks to their white socks?"
- Count each quantity: 5 green pairs, 6 white pairs.
- Write them in the order the question asks — green to white — so 5 : 6.
- Check whether it simplifies: the GCD of 5 and 6 is 1, so 5 : 6 is already in lowest terms.
- Order matters: the ratio of white to green would be 6 : 5, a different answer.
Result: 5 : 6
Split 500 in the ratio 3 : 2
- Add the ratio parts: 3 + 2 = 5 shares in total.
- One share is worth 500 ÷ 5 = 100.
- First share: 3 × 100 = 300. Second share: 2 × 100 = 200.
Result: 300 and 200
Write 10% as a ratio
- 10% means 10 parts out of every 100 — leaving 90 parts that are not.
- As a part-to-rest ratio that is 10 : 90; divide both by their GCD of 10.
- The part-to-WHOLE reading is different: 10 out of 100 total is 1 : 10. Say which one you mean.
Result: 1 : 9 (part to rest) — or 1 : 10 against the whole
What a ratio compares
A ratio compares two or more quantities directly, expressing how many units of one thing correspond to how many units of another. A recipe that calls for a 2:1 ratio of flour to water means exactly that — for every 2 parts of flour, use 1 part of water, whatever "part" happens to be, as long as it is used consistently on both sides.
Ratios only make sense when both quantities are measured in the same units, or when the units are made explicit. "3 cups to 2 cups" is a valid ratio; "3 cups to 2 people" is not a ratio in the mathematical sense, even though people sometimes talk about it that way.
Ratios vs fractions vs percentages
These three are close cousins but answer different questions. A ratio compares one part to another part — 3 boys to 2 girls. A fraction compares a part to the whole — 3/5 of the class is boys. A percentage does the same job as a fraction, just scaled to a base of 100 — 60% of the class is boys. Any ratio can be converted to a fraction or percentage by first turning the ratio parts into a share of the total: 3:2 becomes 3/5 and 2/5, which is 60% and 40%.
Where ratios show up in everyday life
Ratios are one of the more visible pieces of math in ordinary life once you know to look for them.
- Maps and scale models — a map scale of 1:25,000 means one unit of distance on the map equals 25,000 of the same unit in reality.
- Cooking — recipes are frequently given as ratios — a basic vinaigrette is often 3:1, oil to vinegar — so they scale cleanly to any batch size.
- Screens and photography — aspect ratios like 16:9 or 4:3 describe the shape of a screen or image, independent of its actual size in pixels or inches.
- Finance — debt-to-income and price-to-earnings ratios compress two numbers into a single comparison lenders and investors can judge at a glance.
- Mixing materials — concrete, paint and cleaning solutions are often specified by ratio — a 1:2:3 cement, sand and gravel mix, for instance — so the mixture keeps its properties at any quantity.
Simplifying and scaling a ratio
A ratio simplifies exactly the same way a fraction does: divide every part by their greatest common divisor to reach the smallest whole numbers that keep the same proportion. 16:9 is already in its lowest terms — which is exactly why it became the standard for widescreen video, since no smaller pair of whole numbers describes the same shape.
Scaling works the same way in reverse: multiply every part of the ratio by the same factor to get an equivalent ratio at a larger or smaller size. This is the entire basis for resizing a recipe, redrawing a map at a different scale, or enlarging a photograph without distorting it.
A couple of mistakes to avoid
A couple of mistakes come up often enough with ratios to be worth calling out specifically.
- Reading a ratio as if it were a fraction of the total — a ratio of 3:2 does not mean the first quantity is 3/2 of the total — it means it is 3 out of 5 total parts, since the total number of parts is the sum of both sides.
- Ignoring order — a ratio of 3:2 is not the same as 2:3 — order matters, and it should match the order the quantities were named in.
What this assumes, and where it stops
Assumptions
- Both quantities are measured in the same units.
Limitations
- Handles two-part ratios. Three-part ratios (a : b : c) need to be simplified in stages.
- Simplification of non-integer ratios uses a tolerance-based GCD, so very long decimals may not reduce exactly.
Common questions
How do I split money in a ratio?
Add the parts to find the total number of shares, divide the amount by that, then multiply by each part. To split $500 in the ratio 3 : 2, there are 5 shares of $100, so the split is $300 and $200.
What is the difference between a ratio and a fraction?
A ratio compares two parts to each other (3 : 2 means three of one for every two of the other). A fraction compares a part to the whole (3/5 of the total). The same situation gives 3 : 2 as a ratio and 3/5 as a fraction.
How do I turn a word problem into a ratio?
Count each quantity, then write the counts in the order the question names them. "I have 3 pairs of green socks and my friend has 8 pairs of white socks" asks for green to white, so the ratio is 3 : 8 — and it stays 3 : 8 unless both numbers share a common divisor. The single most common mistake is reversing the order: white to green would be 8 : 3, which is a different (and wrong) answer to that question.
How do I write a percentage as a ratio?
Decide first which comparison you mean, because there are two honest readings. 10% as a part-to-rest ratio is 10 : 90, which simplifies to 1 : 9 — one part in, nine parts out. 10% as a part-to-whole comparison is 10 out of 100, or 1 : 10. Maths courses usually intend the first; everyday speech often means the second. State which you are using and either is correct.
How do I simplify a ratio that contains fractions?
Multiply both parts by the same number until both are whole, then simplify as usual — multiplying both sides of a ratio by the same value never changes it. For 16/9 : 3/2, multiply both by 18 (the least common multiple of the denominators): 16/9 × 18 = 32 and 3/2 × 18 = 27, so the ratio is 32 : 27, which is already in lowest terms.
What does a 5 to 1 ratio mean?
Five parts of the first thing for every one part of the second — so out of every 6 parts in total, 5 are the first and 1 is the second. Dilute a cleaner at 5 : 1 and a 600 ml mix uses 500 ml of water to 100 ml of concentrate. The "part" can be any unit, as long as both sides use the same one.
What is the ratio 2 : 1 in real terms?
Twice as much of the first as the second, whatever the quantities are — 2 cups of flour to 1 of water, 2 adults to 1 child, £2 of every £3. Note that 2 : 1 does not mean "2 out of 3" as a ratio, but it does put the first quantity at 2/3 of the combined total, which is how a ratio converts to a fraction of the whole.
Formula and content last reviewed on .
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Results are estimates for information only, not professional advice.
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