Ratio Calculator
Simplify ratios, scale them by any factor, or solve proportions to find a missing value. See your ratio as a fraction, decimal, and percentage split.
Last updated: March 2026
How to Use the Ratio Calculator
- Select a mode — "Simplify Ratio" reduces A:B to lowest terms. "Scale Ratio" multiplies both parts by a factor. "Solve Proportion" finds the missing value in A:B = C:D.
- Enter the ratio values — type A and B (and C or D for proportion mode). You can use decimals.
- Optional: enter a Total — in Simplify mode, entering a total shows how much of that total belongs to Part A and Part B based on the ratio.
- View results instantly — see the simplified ratio, percentage breakdown, fraction form, and decimal equivalent.
What This Calculator Shows You
For any ratio A:B, the calculator returns: the fully simplified ratio (dividing both parts by their GCF), the percentage each part represents of the total (A/(A+B) × 100 and B/(A+B) × 100), the ratio expressed as a fraction A/B, the decimal value of that fraction, and if a total is provided, the actual amount each part represents. In proportion mode, it solves for the missing value using cross-multiplication.
What Is a Ratio? Definition, Types, and Uses
A ratio is a comparison of two quantities that shows their relative sizes. Written as A:B (or A to B, or A/B), a ratio tells you how many times one quantity fits into another. For example, a ratio of 3:1 means the first quantity is three times as large as the second.
Ratios are dimensionless — the units cancel. You can compare apples to apples, meters to meters, or grams to grams. What matters is the relationship: 60g flour to 40g sugar is the same ratio as 3:2 regardless of the actual weight.
Types of Ratios
- Part-to-Part ratio: Compares one group to another (e.g., 3 boys to 5 girls is 3:5).
- Part-to-Whole ratio: Compares one group to the total (e.g., 3 boys out of 8 students is 3:8, which equals 37.5%).
- Rate: A ratio with different units in numerator and denominator (e.g., 60 km per hour, $5 per item).
Simplifying Ratios
A ratio is in simplest form when the GCF of its parts is 1. To simplify 24:36: GCF(24,36) = 12. Divide both by 12: 2:3. To simplify a ratio with decimals: multiply both parts by a power of 10 to make them integers first. For 0.5:1.5 → multiply by 2 → 1:3.
Real-World Applications
- Cooking and baking: Scale recipes up or down using ratios while maintaining flavor balance.
- Maps and scale models: A map scale of 1:50,000 means 1 cm on the map = 50,000 cm (500 m) in reality.
- Finance: Price-to-earnings (P/E) ratio, debt-to-equity ratio, and return on investment all use ratio comparisons.
- Photography and screens: Aspect ratios (16:9, 4:3, 3:2) define image proportions.
- Pharmacy and chemistry: Drug concentrations and dilution ratios follow proportion math.
Proportions and Cross-Multiplication
A proportion states that two ratios are equal: A:B = C:D, equivalently A/B = C/D. Proportions allow you to find an unknown quantity when three of the four values are known. The key tool is cross-multiplication: if A/B = C/D, then A×D = B×C.
Example: A recipe for 4 serves uses 300g flour. How much flour for 10 servings? Set up the proportion: 4:300 = 10:x. Cross multiply: 4x = 3000. Solve: x = 750g.
Proportions are everywhere: calculating drug dosages (dose per kg × patient weight), converting currencies (exchange rate × amount), map reading (map distance × scale = real distance), and geometric similarity (side A of triangle 1 : side A of triangle 2 = side B of triangle 1 : side B of triangle 2).
The Golden Ratio
The golden ratio φ ≈ 1.618 is the proportion A:B where the ratio of the whole (A+B) to the larger part (A) equals the ratio of the larger part (A) to the smaller part (B): (A+B)/A = A/B = φ. It appears in the Parthenon's dimensions, Leonardo da Vinci's works, and spiral patterns in nature. Enter 1.618:1 in the simplify tool to explore it — it cannot be further simplified since φ is irrational.
Ratio Examples and Lookups
What is 15:25 simplified?
15:25 simplifies to 3:5. GCF(15,25) = 5. Divide both by 5.
What is 2:3 as a percentage?
In a 2:3 ratio, Part A = 40% and Part B = 60%. Total parts = 5. A = 2/5 = 40%, B = 3/5 = 60%.
What is a 1:2:3 ratio as percentages?
Total parts = 6. Part A = 16.67%, Part B = 33.33%, Part C = 50%. (This tool handles two-part ratios; for three-part, divide the total by 6 and multiply each part.)
How do I scale a 1:3 ratio to a total of 200?
Each part = 200 ÷ 4 = 50. Part A = 50, Part B = 150. Enter 1:3 in Simplify mode and 200 as the total to get these amounts automatically.
What is a 16:9 ratio as a decimal?
16 ÷ 9 ≈ 1.7778. The 16:9 widescreen ratio means for every 1.78 units of width, there is 1 unit of height.
If A:B = 5:8 and A = 35, what is B?
B = 56. Use proportion: 5/8 = 35/B → 5B = 280 → B = 56.
What is the ratio of 1 hour to 45 minutes?
1 hour : 45 minutes = 60:45 = 4:3. Always convert to the same unit before forming a ratio.
What is 3:4 as a fraction and percentage?
3:4 = 3/4 = 0.75. As percentages: A = 42.86%, B = 57.14% (since 3+4=7, A = 3/7 ≈ 42.86% and B = 4/7 ≈ 57.14%).
How do I mix paint in a 2:1 ratio?
For every 2 parts of Color A, use 1 part of Color B. For 600ml total: A = 400ml, B = 200ml. Entering 2:1 with a total of 600 in the calculator gives these exact amounts.
What is the aspect ratio of a 1920×1080 screen?
1920:1080 simplifies to 16:9. GCF(1920,1080) = 120. 1920÷120 = 16, 1080÷120 = 9.
People Also Search For
How to simplify a ratio with decimals
Multiply both parts by the same power of 10 to eliminate decimals, then simplify. For 0.4:0.6 → multiply by 10 → 4:6 → divide by GCF 2 → 2:3. For 1.5:2.5 → multiply by 2 → 3:5 (already in lowest terms).
How to divide a quantity in a given ratio
Add the ratio parts to get the total share count. Divide the quantity by this total, then multiply by each part. To divide $120 in the ratio 3:5: total shares = 8. Each share = $120/8 = $15. First portion = 3×$15 = $45, second = 5×$15 = $75.
What is the difference between a ratio and a rate?
A ratio compares quantities of the same type; a rate compares quantities of different types. 3:2 cups of flour to sugar is a ratio. 60 miles per hour (distance per time) is a rate. Rates always carry units; ratios are dimensionless.
How to check if two ratios are equivalent
Two ratios are equivalent if they simplify to the same ratio, or if their cross-products are equal. Are 4:6 and 10:15 equivalent? Simplify: 4:6 = 2:3, 10:15 = 2:3. Yes. Or cross-multiply: 4×15 = 60, 6×10 = 60. Equal, so equivalent.
What is the ratio formula for mixing two solutions?
For mixing solutions: the ratio of volumes determines the final concentration by weighted average. Mix 1L of 40% solution with 2L of 10% solution in a 1:2 ratio: final concentration = (1×40 + 2×10) / (1+2) = 60/3 = 20%.
Frequently Asked Questions
How do you simplify a ratio?
Divide both parts of the ratio by their Greatest Common Factor (GCF). For 20:30: GCF = 10. 20÷10 = 2, 30÷10 = 3. Simplified: 2:3. The simplified ratio has the same meaning — the relationship between the quantities is identical.
What is 3:2 as a percentage?
In a 3:2 ratio, the total parts = 5. Part A = 3/5 = 60%, Part B = 2/5 = 40%. This means if you have a total of 500, you'd allocate 300 to A and 200 to B.
How do proportions work?
A proportion states A:B = C:D. Cross-multiply to solve: A×D = B×C. Rearrange to find the unknown. For A:B = C:D with D unknown: D = (B×C)/A. This calculator solves all four variants automatically.
What is the golden ratio?
The golden ratio φ ≈ 1.618:1 is the proportion where (A+B)/A = A/B. It's found in classical art, architecture, and natural growth patterns. It equals (1+√5)/2 ≈ 1.61803... and is irrational, so it cannot be expressed as a simple ratio of whole numbers.
Can I enter decimals in the ratio fields?
Yes. The calculator accepts decimal values. It will simplify using the GCF approach internally. For best results with irrational or very small decimals, round to a reasonable precision (e.g., 3 decimal places).
What is the difference between ratio and proportion?
A ratio compares two quantities (e.g., 3:4). A proportion is an equation stating two ratios are equal (e.g., 3:4 = 6:8). Ratios describe a relationship; proportions use that relationship to find unknown values.
What is a 1:1 ratio?
A 1:1 ratio means equal quantities — 50% each. Examples include a square image (equal width and height), splitting a bill evenly, or mixing equal parts of two ingredients.
How do I scale a recipe with ratios?
First, express the recipe as a ratio. Then enter a scale factor in Scale mode to multiply both parts. Alternatively, enter your desired total in Simplify mode to see how much of each ingredient you need proportionally.
What aspect ratios are most common?
Common screen and image aspect ratios: 16:9 (HD/4K video), 4:3 (standard definition TV), 1:1 (square social posts), 3:2 (35mm photography), 21:9 (ultrawide cinema), 9:16 (vertical/portrait video for mobile).
Is a ratio the same as a fraction?
They are related but not identical. A ratio A:B can be written as the fraction A/B, but the fraction represents one quantity as a part of another, while the ratio compares two separate quantities. 3:4 means "3 for every 4"; the fraction 3/4 means "3 out of every 7 total" in a part-to-whole context.
Is this calculator free?
Yes, completely free. No account needed, no ads blocking the results, and no data sent to any server. All calculations run in your browser.