Ratio Calculator
Simplify any ratio to its lowest terms and solve proportions. Enter two numbers to reduce A:B, and a third to solve A:B = C:?
16 : 9 = 32 : 18
How to use this calculator
Enter the two numbers of your ratio (A and B) to see it simplified to lowest terms and expressed as a decimal. To solve a proportion, also enter C and the calculator finds the missing fourth value so that A:B = C:D.
How ratios work
A ratio is a comparison of two quantities expressed with a colon — for example, 3:2. It tells you the relative size of one quantity compared to another but does not specify the actual amounts. A ratio of 3:2 flour to sugar could mean 3 cups and 2 cups, or 3 kg and 2 kg — the ratio is the same either way.
Simplifying a ratio means writing it in the smallest whole-number form while preserving the relationship. You do this by dividing both sides by their greatest common divisor. The GCD of 24 and 36 is 12, so 24:36 simplifies to 2:3.
How proportions work
A proportion states that two ratios are equal: A:B = C:D. This is an extremely useful relationship for scaling. If you know three of the four values, you can always find the fourth by cross-multiplying: A × D = B × C, so D = (B × C) ÷ A.
Worked examples
Example 1 — simplifying a ratio
- Ratio: 18:24
- GCD(18, 24) = 6
- Simplified: 18 ÷ 6 = 3, 24 ÷ 6 = 4 → 3:4
- As a decimal: 3 ÷ 4 = 0.75
Example 2 — scaling a recipe
A recipe calls for 2 cups of flour for every 3 cups of water. You want to use 8 cups of flour. How much water do you need?
- Set up the proportion: 2:3 = 8:D
- Cross-multiply: D = (3 × 8) ÷ 2 = 24 ÷ 2 = 12 cups of water
Example 3 — map scale
A map has a scale of 1:50,000 (1 cm on the map = 50,000 cm in reality). If two cities are 4.5 cm apart on the map, what is the real distance?
- Set up: 1:50,000 = 4.5:D
- D = (50,000 × 4.5) ÷ 1 = 225,000 cm = 2.25 km
Example 4 — splitting money in a ratio
Three people invest in a business in the ratio 2:3:5. Total profit is $10,000. How much does each person get?
- Total parts: 2 + 3 + 5 = 10
- One part = $10,000 ÷ 10 = $1,000
- Person A: 2 × $1,000 = $2,000
- Person B: 3 × $1,000 = $3,000
- Person C: 5 × $1,000 = $5,000
Common mistakes to avoid
- Confusing the order of terms. A ratio of 3:1 is not the same as 1:3. Always be clear about which quantity comes first and keep that order consistent when setting up a proportion.
- Not simplifying before comparing. Two ratios may look different but be equivalent. Always reduce to lowest terms before deciding whether two ratios match.
- Cross-multiplying in the wrong order. In A:B = C:D, the cross-multiply rule is A × D = B × C. Mixing up which values are on the same "diagonal" leads to the wrong answer.
- Treating a ratio as a fraction carelessly.3:2 and 3/2 are related but not identical in meaning. A 3:2 ratio (boys to girls in a class) means 3 boys out of 5 students total, not 3 out of 2.
The formulas
Simplify: divide A and B by GCD(A, B) · As decimal: A ÷ B
Proportion — missing D: D = (B × C) ÷ A
How we calculate this
Frequently asked questions
How do you simplify a ratio?
Divide both numbers by their greatest common divisor (GCD). For example, 16:9 is already in lowest terms because GCD(16, 9) = 1, while 20:30 simplifies to 2:3 because GCD(20, 30) = 10.
How do you solve a proportion?
A proportion sets two ratios equal: A:B = C:D. To find a missing value, cross-multiply. Given A, B, and C, the missing D = (B × C) ÷ A.
What is a ratio as a decimal?
Divide the first number by the second. The ratio 16:9 equals 16 ÷ 9 ≈ 1.78, which is how aspect ratios are commonly compared.
Can I use decimals in a ratio?
Yes. The calculator accepts decimal inputs and simplifies correctly by scaling the values to whole numbers internally before finding the GCD.
What is the difference between a ratio and a fraction?
A ratio (like 3:4) compares two quantities, while a fraction (like 3/4) expresses a part of a whole. They use the same numbers but have different meanings — a 3:4 ratio of boys to girls means 3 boys and 4 girls, while 3/4 as a fraction means three-quarters of one whole thing.
How do ratios relate to percentages?
You can convert a ratio to a percentage by dividing the first part by the total parts and multiplying by 100. A ratio of 1:4 means 1 part in every 5, which is 20%.
What does it mean for ratios to be equivalent?
Two ratios are equivalent if they simplify to the same lowest-terms ratio. For example, 2:3, 4:6, and 8:12 are all equivalent because they all simplify to 2:3.
How is a ratio used in real life?
Ratios are used everywhere: in cooking (2 cups flour : 1 cup water), in maps (1:50,000 scale), in finance (debt-to-equity ratio), and in screen displays (16:9 aspect ratio). Proportions let you scale any of these situations up or down.