Simplify ratios, solve proportions, find missing values, convert ratios to percentages, and scale ratios. Instant results for USA and UK.
A ratio expresses the quantitative relationship between two or more values. Ratios appear in everyday life constantly: recipes call for ingredients in a 2:1 ratio, maps use scale ratios like 1:25,000, paint is mixed in specific ratios, financial analysts compare earnings ratios, and sports statistics track win-loss records as ratios. This free ratio calculator handles simplification, proportion solving, percentage conversion, and ratio scaling β all with live results.
A ratio compares two quantities and is written as A:B (read as "A to B"). It tells you how much of one quantity there is relative to another. Unlike fractions, ratios don't necessarily represent parts of a whole β they can compare any two related quantities. The ratio 3:2 means for every 3 of the first quantity there are 2 of the second.
Simplifying a ratio means reducing it to its smallest whole-number form while maintaining the same relationship. The method is identical to simplifying fractions: divide both numbers by their Greatest Common Factor (GCF).
Example: Simplify 12:8. GCF(12,8) = 4. 12Γ·4 = 3, 8Γ·4 = 2. Simplified ratio: 3:2
For non-integer ratios (like 1.5:2.5), multiply both numbers by a power of 10 to make them integers, then simplify. For 1.5:2.5, multiply by 2 to get 3:5.
A proportion states that two ratios are equal: A/B = C/X. To find the missing value X, use cross-multiplication:
X = (B Γ C) / A
Example: If 3 apples cost Β£4, how much do 9 apples cost? 3/4 = 9/X β X = (4 Γ 9) / 3 = Β£12
Proportions appear in recipe scaling, map reading, unit conversion, speed/distance problems, and financial calculations.
To convert a ratio A:B to percentages: A% = A/(A+B) Γ 100, B% = B/(A+B) Γ 100.
Example: A class has a 3:2 male-to-female ratio. Total parts = 5. Males = 3/5 = 60%, Females = 2/5 = 40%.
To scale a ratio by a factor, multiply both parts by the scale factor.
Example: Scale 3:4 by 2.5 β 7.5:10
Scaling ratios is essential in cooking (doubling or halving recipes), architecture (building to scale), and engineering (model to full-size conversions).
Ordnance Survey maps in the UK use a scale of 1:25,000 for Explorer series maps and 1:50,000 for Landranger series. This means 1cm on the map represents 25,000cm (250m) or 50,000cm (500m) in reality. US USGS topographic maps typically use 1:24,000 (7.5-minute series) or 1:100,000. When reading a map or planning a hiking route, you use proportions to convert map distances to real distances.
A bread recipe calls for flour and water in a 5:3 ratio by weight. If you want to make a loaf using 500g of flour, the water needed is: X = (3 Γ 500) / 5 = 300g. Use the proportion mode of this calculator for all recipe scaling calculations.
Paint is often mixed in ratios: a primer might require a 3:1 base-to-hardener ratio. Concrete is commonly mixed in a 1:2:3 cement-sand-aggregate ratio by volume. Antifreeze is typically mixed 50:50 with water. Getting these ratios wrong can ruin a batch of paint or compromise structural integrity in construction.
In finance, ratios are fundamental analytical tools. The debt-to-equity ratio compares total liabilities to shareholders' equity. A current ratio of 2:1 means a company has twice as many current assets as current liabilities. Price-to-earnings (P/E) ratios express how much investors pay per dollar or pound of earnings. These ratios are simplified and compared using exactly the same mathematical methods as any other ratio.
| Ratio | Simplified | A% | B% |
|---|---|---|---|
| 1:1 | 1:1 | 50% | 50% |
| 2:1 | 2:1 | 66.7% | 33.3% |
| 3:1 | 3:1 | 75% | 25% |
| 3:2 | 3:2 | 60% | 40% |
| 4:1 | 4:1 | 80% | 20% |
| 16:9 | 16:9 | 64% | 36% |
Divide both numbers by their Greatest Common Factor (GCF). For 12:8, GCF = 4, so 12Γ·4:8Γ·4 = 3:2.
A proportion states that two ratios are equal: A/B = C/D. If three values are known, cross-multiplication finds the fourth: X = (BΓC)/A.
For ratio A:B, calculate A/(A+B)Γ100 for A's percentage and B/(A+B)Γ100 for B's percentage. Example: 3:2 β 60% and 40%.
Ordnance Survey Explorer maps use 1:25,000 (4cm = 1km) and Landranger maps use 1:50,000 (2cm = 1km). Use the proportion mode to convert map distances to real distances.
Set up a proportion: original amount / original servings = new amount / new servings, then solve for the new amount. Or use the scale mode: multiply all ingredient amounts by your scale factor.
The golden ratio is approximately 1:1.618 (or Ο = 1.61803...). It appears in art, architecture, and nature. A rectangle with sides in the golden ratio is considered aesthetically pleasing. The Parthenon, many Renaissance paintings, and the Fibonacci spiral all approximate this ratio.
A fraction represents a part of a whole (3/4 means 3 out of 4 equal parts). A ratio compares two quantities (3:4 means 3 of one thing for every 4 of another). Ratios can compare independent quantities, while fractions always relate to a whole.
A 1:1 ratio means equal quantities of both parts β 50% each. Common examples: equal parts vinegar and water in a cleaning solution, a coin toss probability, or a perfectly square image (1:1 aspect ratio).
Results are for educational and planning purposes. Verify critical calculations independently, especially for construction, engineering, or food safety applications.