⚖️ Ratio & Proportion Calculator
Solve missing proportion values (A : B = C : X) and simplify mathematical ratios.
Ratios and proportions, and how to scale anything
A ratio compares two quantities. A proportion says two ratios are equal. Between them they cover scaling a recipe, mixing concrete, reading a map, converting currency and resizing an image without distorting it: anything where the relationship between two numbers has to stay fixed while the numbers themselves change.
Solving for a missing value
Given A : B = C : X, cross-multiply and divide:
A × X = B × C → X = B × C / A
If 3 kg of flour makes 48 rolls and you want 80, then 3 : 48 = X : 80, so X = 3 × 80 / 48 = 5 kg. The structure is always the same: put matching units in matching positions and the arithmetic takes care of itself.
Part-to-part and part-to-whole
This distinction causes more errors than the arithmetic does. A class with a 3 : 2 ratio of girls to boys is a part-to-part ratio. It does not mean three fifths are girls by accident, it means exactly that, because the parts sum to five. But a statement that girls make up 3 in 5 of the class is part-to-whole, and confusing the two turns a 3 : 2 ratio into a 3 : 5 one.
| Description | Form | Meaning |
|---|---|---|
| 3 : 2 | Part to part | 3 girls for every 2 boys |
| 3/5 | Part to whole | 3 of every 5 students are girls |
| 60% | Percentage | Same as 3/5 |
Simplifying and scaling
Divide every term by the greatest common divisor. A ratio of 18 : 24 : 30 has a GCD of 6, giving 3 : 4 : 5. To scale a ratio up, multiply every term by the same number; to split a total according to a ratio, add the parts and divide.
Splitting $4,800 in the ratio 3 : 5 : 4: the parts sum to 12, so one part is $400, and the shares are $1,200, $2,000 and $1,600. Checking that the shares sum back to the total catches almost every arithmetic slip.
Aspect ratios
An aspect ratio is width : height. A 16 : 9 image at 1,920 pixels wide must be 1,920 × 9 / 16 = 1,080 pixels tall. Resizing to any other height distorts it. Common ratios worth recognising:
| Ratio | Decimal | Typical use |
|---|---|---|
| 16 : 9 | 1.778 | Video, most monitors, YouTube |
| 4 : 3 | 1.333 | Older screens, many cameras |
| 3 : 2 | 1.500 | 35 mm photography, most DSLRs |
| 1 : 1 | 1.000 | Square social media posts |
| 21 : 9 | 2.333 | Ultrawide monitors, cinema |
The golden ratio
Approximately 1 : 1.618, the golden ratio appears when a line is divided so that the whole is to the longer part as the longer part is to the shorter. It shows up in the Fibonacci sequence, where the ratio between consecutive terms converges on it, and in a great deal of design folklore, much of which is retrofitted.
A worked example
A concrete mix is specified as 1 : 2 : 3 cement, sand and gravel by volume, and you need 1.8 cubic metres. The parts total 6, so one part is 0.3 m³. That means 0.3 m³ of cement, 0.6 of sand and 0.9 of gravel. The concrete calculator handles slab volumes and bag counts if you need those too.
Frequently Asked Questions (FAQs)
What is the difference between a ratio and a fraction?
A ratio usually compares parts to each other; a fraction compares a part to the whole. A 2 : 3 ratio means two of one thing for every three of another, five items in total, so as a fraction of the whole it is 2/5, not 2/3.
How do I scale a recipe by a ratio?
Divide the new quantity by the old to get a scaling factor, then multiply every ingredient by it. Scaling from 4 servings to 10 gives a factor of 2.5. Cooking times do not scale the same way and usually need less adjustment than the quantities suggest.
Can a ratio have more than two terms?
Yes. Mixing ratios, class compositions and investment allocations often use three or more, as in 1 : 2 : 3. The same rules apply: simplify by the GCD of all terms, and to split a total, sum the parts and divide.
How do I turn a ratio into a percentage?
Convert it to a part-to-whole fraction first, then multiply by 100. A 3 : 7 ratio means 3 of every 10, so 30% and 70%. Dividing 3 by 7 to get 42.9% answers a different question, namely how big the first part is relative to the second.
What is a unit rate?
A ratio with the second term reduced to 1, which makes comparison easy. $4.50 for 3 litres is a unit rate of $1.50 per litre. Supermarket shelf labels show unit prices for exactly this reason.
How do I keep an image's proportions when resizing?
Divide the original width by the original height to get the ratio, then multiply the new width by that number's reciprocal to find the matching height. For a 1,200 × 800 image resized to 900 wide, the height is 900 × 800 / 1,200 = 600.