Ratio Calculator

Understanding Ratios and Proportions

A ratio compares two quantities and shows their relative sizes. Written as A:B, it expresses how many units of A correspond to units of B. Ratios appear everywhere: recipes (flour to sugar), maps (scale ratios), financial metrics (debt-to-income), and mixing solutions (concentrate to water). Understanding ratios helps you scale quantities up or down while maintaining the same proportions.

Simplifying a ratio means dividing both parts by their greatest common divisor (GCD). For example, 12:8 simplifies to 3:2 because the GCD of 12 and 8 is 4. The simplified ratio is mathematically equivalent but easier to interpret. The proportion solver uses cross-multiplication: if A:B = C:D, then A × D = B × C. Given any three values, you can find the fourth.

Two ratios are proportional when their cross products are equal. This is the foundation of proportional reasoning used in geometry (similar triangles), chemistry (dilution calculations), cooking (scaling recipes), and finance (unit pricing comparisons). For example, if 3 workers complete a job in 10 hours, proportional reasoning tells you 6 workers would take 5 hours, assuming equal productivity. This calculator handles all three ratio operations with instant results as you type.