Ratio Calculator
Simplify ratios like 12:18 to 2:3 (decimals and three-part ratios too), solve A:B = C:D for the missing value, or split a total in a given ratio.
| Part | Share of the whole | Percent | 1 : n form |
|---|---|---|---|
| 2 | 2/10 | 20% | 1 |
| 3 | 3/10 | 30% | 1.5 |
| 5 | 5/10 | 50% | 2.5 |
What Ratio Calculator Does
This ratio calculator does the three things people need ratios for. Simplify reduces any ratio to its smallest whole numbers (12:18:30 becomes 2:3:5, and decimal ratios like 1.5:2.25 are scaled up first so they come out as 2:3) and shows each part as a share, a percentage and in 1:n form. Solve fills the missing value in a proportion A:B = C:D, whichever of the four it is. Split divides a total, such as money, ingredients or hours, in a given ratio.
Ratios compare quantities with each other: two parts sand to one part cement, a 16:9 screen, a 3:1 odds line. The calculator shows the working for each mode so you can check a homework answer or a mix before committing to it.
How to Use Ratio Calculator
- Choose simplify, solve a proportion or split a total
- Enter the ratio with colons, such as 12:18 or 1:2:3
- For proportions, fill three boxes and leave the unknown empty
- For splitting, enter the total and the ratio
- Read the answer with the working and percentages
Formula Used by Ratio Calculator
Simplifying
Divide every part by the greatest common divisor (GCD)
Worked example
12 : 18 : 30
- GCD(12, 18, 30) = 6
- 12 ÷ 6 = 2, 18 ÷ 6 = 3, 30 ÷ 6 = 5
Result: 2 : 3 : 5
Solving a proportion
A : B = C : D ⇔ A × D = B × C
Worked example
3 : 4 = 15 : x
- 3x = 4 × 15 = 60
- x = 60 ÷ 3
Result: x = 20
Splitting a total
Share = total ÷ (sum of parts) × part
Worked example
$1,200 in the ratio 3 : 2 : 1
- 3 + 2 + 1 = 6 shares
- $1,200 ÷ 6 = $200 per share
Result: $600, $400 and $200.
Everyday Ratios
| Ratio | Where it appears |
|---|---|
| 16 : 9 | Widescreen TVs, monitors and video |
| 1 : 2 : 3 | Concrete: cement, sand, gravel (a common general-purpose mix) |
| 1 : 15–1 : 17 | Coffee to water by weight, a common brewing range |
| 3 : 1 | Odds against (one win for every three losses) |
| 1 : 1.618 | The golden ratio |
How to Read Your Result
Order matters
A ratio of 2:3 is not the same as 3:2. Always check which quantity comes first: “sugar to flour 1:3” means three times as much flour. When solving a proportion, keep the same quantity in the same position on both sides.
Ratios, fractions and percentages
In a 2:3 mix, the first part is 2 of 5 total shares: 2/5, or 40%. Comparing the parts directly gives 2/3 ≈ 0.667, so the first is two thirds of the second. Both are correct answers to different questions, which is why the table shows each.
Limitations & Accuracy Notes
- Negative numbers are not accepted in ratios.
- Decimal results are rounded to 12 significant digits.
Frequently Asked Questions
How do you simplify a ratio?
Divide every part by their greatest common divisor. 12:18 has a GCD of 6, so it simplifies to 2:3. With decimals, first multiply all parts by 10, 100… to make whole numbers: 1.5:2.25 becomes 150:225, which simplifies to 2:3.
How do I solve a proportion?
Cross-multiply. In A:B = C:D, A × D = B × C. For 3:4 = 15:x, 3x = 60, so x = 20. Leave the unknown box empty and the calculator solves it.
How do I divide an amount in a ratio?
Add the parts to find the number of shares, divide the total by that, and multiply by each part. $1,200 in the ratio 3:2:1 is 6 shares of $200, so $600, $400 and $200.
How do I convert a ratio to a percentage or fraction?
Each part’s share of the whole is part ÷ sum. In 2:3 the sum is 5, so the first part is 2/5 = 40% and the second 3/5 = 60%. As a single fraction, 2:3 is 2/3 ≈ 0.667.
What is the difference between a ratio and a fraction?
A ratio compares parts with each other (2 cups flour to 3 cups water); a fraction compares a part with the whole (2 of the 5 cups are flour). 2:3 and 2/5 describe the same mix.
Can a ratio have more than two parts?
Yes. Concrete mixes, paint tints and recipes often use three: 1:2:3 cement, sand and gravel. The simplify and split modes both accept as many parts as you need.