To convert a percentage to a ratio, first express it as a fraction over 100, then simplify using the greatest common divisor. For example, 75% becomes 75/100, which simplifies to 3/4, giving a final ratio of 3:4. This conversion is essential for mathematical analysis and data interpretation.

To convert a ratio to percentage, divide the first part by the sum of both parts and multiply by 100. For ratio a:b, the formula is: Percentage = (a ÷ (a + b)) × 100. For example, a 3:4 ratio converts to (3 ÷ 7) × 100 = 42.86%.

Ratios are simplified by dividing both parts by their greatest common divisor (GCD). Our calculator automatically calculates the GCD using the Euclidean algorithm and divides both numbers to produce the simplest form. For example, 15:20 simplifies to 3:4 by dividing both by 5.

Percentage-ratio conversions are widely used in: financial analysis (profit margins, debt-to-equity ratios), statistics (probability distributions), chemistry (solution concentrations), business (market share analysis), and everyday decisions (recipe scaling, budget allocations). These conversions help standardize comparisons across different data formats.

Yes, our calculator fully supports decimal values. You can input percentages like 33.33% or ratios like 2.5:4.75. The tool maintains your specified decimal precision (up to 10 places) and provides accurate conversions with detailed step-by-step explanations for both integer and decimal inputs.