What a ratio actually says
A ratio compares two quantities that belong together: 12 : 18 might be 12 boys to 18 girls in a class, 12 cm to 18 cm on a scale drawing, or 12 parts flour to 18 parts water in a recipe. The colon is read as to, and the key idea is proportion — what matters is not the exact counts but the relationship between them. That is why 12 : 18, 2 : 3 and 200 : 300 all describe the same relationship, and why this calculator offers four modes around that one idea: simplify, scale, find a missing value, and split a total.
The four things people do with ratios
Simplify mode divides both parts by their greatest common divisor, so 12 : 18 becomes 2 : 3, and also reports the ratio as a fraction and as a percentage split (40% / 60% here). Scale mode multiplies both parts by the Mode value — doubling a recipe written as a ratio. Missing mode treats the Mode value as a new first value and works out the second value that keeps the proportion, the classic map-scale and mixture question. Split mode treats the Mode value as a total to divide in the given ratio — sharing money, ingredients or screen space fairly.
Why simplifying uses the GCD
The greatest common divisor is the largest number that divides both parts exactly. Dividing by it in one step lands directly on the smallest whole-number version of the ratio; dividing by smaller common factors works too, but takes several rounds (12 : 18 ÷ 2 = 6 : 9 ÷ 3 = 2 : 3). A simplified ratio is the easiest form to talk about, compare and reuse — nobody orders a 12 : 18 screen when the same shape is called 2 : 3. Note that a ratio is not a fraction of a total unless you add the parts: in 2 : 3 the first quantity is 2 of 5 parts, i.e. 40%, not 2/3 of the whole.
Ratios in daily life
Screen aspect ratios (16 : 9), map scales, gear ratios, odds in betting, ingredient proportions, and financial ratios such as debt-to-income all run on the same machinery. In each case the skill is identical: reduce to the simplest form to understand the relationship, then scale or split to apply it to the amounts in front of you. The mode descriptions beside the Mode value field remind you what that field means in the mode you picked — a multiplier for scale, a new first value for missing, and a total for split.
Worked example
Simplify 20 : 30. The GCD of 20 and 30 is 10, so dividing both parts by 10 gives 2 : 3. Splitting $50 in the ratio 2 : 3 gives 5 parts of $10, so the shares are $20 and $30.
How to use this calculator
- Enter the two parts of your ratio as A and B.
- Choose a mode: simplify, scale, find the missing value, or split a total.
- If the mode needs one, enter the Mode value — multiplier, new first value, or total.
- Read the resulting ratio in the green panel.
- Check the step-by-step panel for the GCD, scaling factor or per-part value used.
Ratios with three or more parts
Real recipes and budgets often have three or more parts, such as 2 : 3 : 5. The method does not change: the GCD simplification divides every part by the same divisor, scaling multiplies every part, and splitting adds all the parts (2 + 3 + 5 = 10), finds one part of the total, and multiplies back up. You can handle a three-part split with this two-part tool by splitting in stages, or work the per-part method by hand using the steps shown below the calculator — the arithmetic is identical, just with one extra share. For turning ratios into percentages of a whole, the Percentage Difference Calculator and the percentage split shown in simplify mode cover the most common follow-up question.