Ratio Calculator
Simplify a ratio, find the missing term of a proportion, or scale a ratio up, down or to a total. Every answer shows the GCD or cross-multiplication step by step.
Defaults to your region. Switch to compare any other scale.
Separate the terms with colons, e.g. 12:18 or 1.5 : 2.5 : 4. Decimals and three or more terms are fine.
Result
2 : 3 : 5
Simplified ratio
12 : 18 : 30 = 2 : 3 : 5
- Greatest common divisorGCD(12, 18, 30) = 6
- Divide each term by the GCD12 ÷ 6 : 18 ÷ 6 : 30 ÷ 6 = 2 : 3 : 5
- 1 : n form1 : 1.5 : 2.5
- Total parts10
Each term of the ratio
| Term | Your value | Simplified | Share of the whole |
|---|---|---|---|
| 1 | 12 | 2 | 20% |
| 2 | 18 | 3 | 30% |
| 3 | 30 | 5 | 50% |
About this tool
How simplifying works: a ratio keeps its meaning when every term is multiplied or divided by the same non-zero number. First clear any decimals by multiplying all terms by the same power of ten (1.5 : 2.5 → 15 : 25), then divide every term by their greatest common divisor (GCD 5 → 3 : 5). The same works for three or more terms: 12 : 18 : 30 has GCD 6 and simplifies to 2 : 3 : 5.
Solving proportions: in A : B = C : D the product of the outer terms equals the product of the inner terms, A × D = B × C. Leave one box empty and the calculator isolates it, e.g. 3 : 4 = 6 : D gives D = 4 × 6 ÷ 3 = 8. When the answer does not terminate it is also shown as an exact fraction (3 : 4 = 5 : 20/3).
Scaling and splitting: multiply each term by a factor to scale a recipe or a model, or split a total in a given ratio — 120 in 2 : 3 is 120 ÷ 5 = 24 per part, so 48 and 72. Related tools: the percentage calculator for shares of a whole, the slope calculator for rise over run, and the grade calculator for turning points into a percentage.
Formula
a : b = (a ÷ g) : (b ÷ g), g = GCD(a, b)Decimals: multiply every term by 10ⁿ firstA : B = C : D ⇔ A × D = B × CD = B × C ÷ ASplit T in a : b → part = T × a ÷ (a + b)
How it is calculated
- Pick what you want to do: simplify, solve a proportion, scale by a factor or split a total.
- Type the ratio with colons (12:18, 1.5:2.5, 2:3:5) — or, for a proportion, fill in three of A, B, C, D.
- Decimals are cleared first by multiplying every term by the same power of ten.
- The calculator finds the greatest common divisor and divides every term by it, or cross-multiplies A × D = B × C and isolates the empty term.
- Read the step rows and the table: each term, its simplified or scaled value, and its share of the whole.
Questions
How do you simplify a ratio?
Divide every term by their greatest common divisor. For 12 : 18 the GCD is 6, so 12 ÷ 6 : 18 ÷ 6 = 2 : 3. If there are decimals, multiply all terms by 10, 100… first so they become whole numbers.
How do I solve a proportion like 3 : 4 = 6 : x?
Cross-multiply: the outer terms multiplied equal the inner terms multiplied, 3 × x = 4 × 6. So x = 24 ÷ 3 = 8. Leave the unknown box empty and the calculator does this for any position — A, B, C or D.
Can I simplify a ratio with decimals or three terms?
Yes. 0.75 : 2 : 1.125 is multiplied by 1000 to 750 : 2000 : 1125, whose GCD is 125, giving 6 : 16 : 9. The arithmetic is exact, so 0.1 : 0.3 really becomes 1 : 3 with no rounding.
How do I split an amount in a ratio?
Add the terms to get the number of parts, divide the total by it, then multiply by each term. 120 in 2 : 3: 2 + 3 = 5 parts, 120 ÷ 5 = 24, so 2 × 24 = 48 and 3 × 24 = 72. Choose “Split a total in this ratio”.
What is the difference between a ratio and a fraction?
A ratio compares parts with each other; a fraction compares a part with the whole. 2 : 3 means 2 parts to 3 parts, so the first part is 2/5 of the whole, not 2/3. The table shows each term's share of the whole.