Ratio Calculator
Simplify ratios and solve proportions
The Ratio Calculator has two modes: Simplify a ratio to its lowest terms, or solve a proportion to find a missing value (A:B = C:?).
A ratio expresses the relative sizes of two quantities. The ratio 6:9 and 2:3 represent the same relationship — one is just scaled up by 3. Ratios appear everywhere: cooking (2 cups flour to 1 cup water), maps (1:50,000), probability, and finance.
Simplifying a ratio works exactly like simplifying a fraction: divide both parts by their Greatest Common Factor (GCF). For 6:9, GCF(6,9) = 3, so 6:9 simplifies to 2:3.
Solving a proportion (A:B = C:D) uses cross-multiplication: D = (B × C) / A. This is essential for scaling recipes, converting units, reading maps, or solving similar-triangle problems in geometry.
Example
Simplify 24:36.
GCF(24, 36) = 12. So 24:36 = 2:3.
Proportion: If 2:3 = 8:?, find the missing value.
Using D = B × C / A: D = 3 × 8 / 2 = 12.
So 2:3 = 8:12. Both ratios simplify to 2:3, confirming the answer is correct.
Real-world use: if a recipe calls for 2 cups of flour for every 3 cups of liquid, and you're scaling up to 8 cups of flour — you need 12 cups of liquid.
Frequently Asked Questions
How do you simplify a ratio?
Divide both parts of the ratio by their Greatest Common Factor (GCF). For example, to simplify 12:8, GCF(12,8) = 4, so 12:8 = 3:2.
How do you solve a proportion?
Use cross-multiplication. If A:B = C:D, then D = (B × C) / A. For example, if 2:3 = 8:D, then D = (3×8)/2 = 12.
What is the difference between a ratio and a proportion?
A ratio compares two quantities (e.g. 2:3). A proportion is an equation stating that two ratios are equal (e.g. 2:3 = 4:6). Solving a proportion means finding an unknown value.
Are 3:4 and 9:12 equivalent ratios?
Yes. Dividing 9:12 by GCF(9,12) = 3 gives 3:4. Equivalent ratios have the same simplified form.
How do I simplify the ratio 15:25?
GCF(15, 25) = 5. So 15:25 = 3:5. Both parts divide evenly by 5, giving the simplest form 3:5.
How do ratios apply to cooking and recipes?
Recipes use ratios to scale ingredients. If a recipe uses a 2:1 ratio of flour to sugar and you want to scale to 300g flour, the proportion is 2:1 = 300:D, so D = 150g sugar. Use the Proportion mode: enter A=2, B=1, C=300 to find D=150 instantly.
What is a 1:2 ratio in everyday terms?
A 1:2 ratio means for every 1 unit of the first quantity, there are 2 units of the second. Examples: 1 part bleach to 2 parts water in a cleaning solution; 1 egg to 2 cups of flour in a recipe; 1 hour of exercise for every 2 hours of sitting. The total is split 1/3 and 2/3.
How do I convert a ratio to a percentage?
Divide the first number by the sum of both numbers, then multiply by 100. For ratio 3:7: total parts = 10. First part = 3/10 = 30%. Second part = 7/10 = 70%.
What is the golden ratio and why is it famous?
The golden ratio is approximately 1.618:1 (often written as φ). It appears naturally in spirals, plants, and has been used in art and architecture for centuries. Its unique property is that φ:1 = (φ+1):φ — a proportion where the whole-to-larger-part equals the larger-to-smaller-part. It's found in the Fibonacci sequence as ratios of consecutive terms.