Simplify 12:18
- Input
- Ratio = 12 : 18
- Working
- GCF of 12 and 18 = 6. 12 / 6 = 2 and 18 / 6 = 3. Check: 2/3 = 12/18 = 0.667, so the proportion is unchanged.
- Result
- 12 : 18 simplifies to 2 : 3
Ratio Calculator
Simplify ratios to lowest terms, scale them up or down, and solve for a missing value in a proportion, with the common factor and working shown. Runs entirely in your browser — your numbers never leave this device.
Calculation
Result ratio
2 : 3
12 : 18 simplifies to 2 : 3
| Multiplier | Ratio |
|---|---|
| ×1 | 2 : 3 |
| ×2 | 4 : 6 |
| ×3 | 6 : 9 |
| ×4 | 8 : 12 |
| ×5 | 10 : 15 |
How it works
Simplify: divide every term by the GCF of all terms | Equivalent ratios: a : b = (a×k) : (b×k) for any k ≠ 0 | Missing value: if a : b = c : x then x = (b × c) / a
| Multiply both terms by | Ratio |
|---|---|
| 1 | 2 : 3 |
| 2 | 4 : 6 |
| 3 | 6 : 9 |
| 4 | 8 : 12 |
| 5 | 10 : 15 |
| 10 | 20 : 30 |
A ratio compares quantities in proportion, and simplifying one works exactly like simplifying a fraction: find the greatest common factor of all the terms and divide every term by it. 12:18 has a GCF of 6, so it becomes 2:3 — the same relationship in smaller, easier numbers. The calculator shows the GCF it used, so you can check the simplification rather than take it on trust.
The same engine handles the other two everyday ratio jobs. Scaling multiplies or divides every term by the same factor, which keeps the proportion identical — doubling a 2:3 recipe gives 4:6, still the same mix. Solving a proportion finds a missing term by cross-multiplication: if 3:5 = 12:x, then x = (5 × 12) / 3 = 20, and you can verify it because 12/20 simplifies back to 3/5.
Ratios with three terms (such as splitting money 2:3:5) simplify by the GCF of all three. Sharing a total in a ratio uses parts: for 3:2 there are 5 parts in total, so each part is the total divided by 5. A term of zero is allowed only where it makes sense — a ratio like 0:5 simplifies to 0:1, but a missing-value problem with zero in the wrong place has no solution, and the calculator flags it instead of dividing by zero.
Worked examples
Share $100 in the ratio 3:2
- Input
- Total = 100, Ratio = 3 : 2
- Working
- Total parts = 3 + 2 = 5. One part = 100 / 5 = 20. First share = 3 × 20 = 60. Second share = 2 × 20 = 40. Check: 60 + 40 = 100.
- Result
- $100 in the ratio 3:2 splits as $60 and $40
Solve the proportion 3:5 = 12:x
- Input
- a = 3, b = 5, c = 12, find x
- Working
- x = (b × c) / a = (5 × 12) / 3 = 60 / 3 = 20. Check: 12/20 simplifies to 3/5 (dividing by 4), matching the original ratio.
- Result
- 3 : 5 = 12 : 20, so x = 20
Frequently asked questions
How do you simplify a ratio?
Find the greatest common factor of all the terms and divide every term by it. 12:18 has a GCF of 6, giving 2:3. A ratio is fully simplified when its terms share no common factor except 1 — exactly the same test as a fraction in lowest terms.
What is the difference between a ratio and a fraction?
A fraction compares a part to a whole (3/5 of a pizza), while a ratio compares part to part (3 parts flour to 5 parts water, written 3:5). They convert easily: the ratio 3:5 means the first quantity is 3/(3+5) = 3/8 of the combined total — a common source of mistakes in exam questions.
How do I scale a ratio up for a bigger batch?
Multiply every term by the same number. To grow a 2:3 mix by a factor of 4, multiply both terms by 4 to get 8:12. If you know the new total instead, divide it by the sum of the parts to find one part, then multiply each term by that part value, as in the $100 example above.
Can a ratio have decimal or fractional terms?
Yes. Ratios like 1.5:2.5 are valid — multiply both terms by 2 to clear the decimals and you get the equivalent whole-number ratio 3:5. The calculator performs this clearing step for you and shows the simplified whole-number form alongside the original.
What does an aspect ratio like 16:9 mean?
It is a ratio of width to height: a 16:9 screen is 16 units wide for every 9 units tall, whatever the actual size. 1920 × 1080 is 16:9 because both numbers divide by 120 to give 16 and 9 — simplifying the pixel counts with the GCF is exactly what this calculator does.
Is anything uploaded when I use this ratio calculator?
No. It runs 100% in your browser, so the numbers you enter never leave your device and nothing is uploaded, saved or tracked. The calculation happens locally the moment you type.
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