Ratio Calculator

A ratio compares two quantities. The ratio 6:9 says there are 6 of one thing for every 9 of another. Simplifying that ratio to 2:3 makes it easier to work with, since both forms represent the same relationship. Proportions extend ratios to four numbers: if a:b = c:x, cross-multiplication gives x = (b × c) / a. This is the foundation of unit conversion, recipe scaling, and map reading. This calculator handles all three common ratio tasks: simplification, proportion solving, and scaling. Each shows the result as a ratio, fraction, decimal, and percentage for a complete picture.

• Recipe scaling: A recipe calls for ingredients in a 2:3 ratio (e.g., 2 cups flour to 3 cups liquid). Use the scale mode to find quantities for any batch size.
• Map reading: A map uses a 1:50,000 scale. Use proportion mode to find that 3 cm on the map equals 150,000 cm (1.5 km) in reality.
• Paint and mixing ratios: Two-part epoxy mixes at a 2:1 ratio. Simplify any amount to confirm you are using the right proportions before mixing.
• Finance and business: Debt-to-equity ratios, price-to-earnings ratios, and financial risk metrics are all ratios. Simplify or compare them to benchmark values.

1. 1Select the mode: Simplify, Proportion, or Scale.
2. 2For Simplify: enter a and b. The GCD is found and both parts are divided by it.
3. 3For Proportion: enter a, b, and c. The missing value x is found by cross-multiplication.
4. 4For Scale: enter a, b, and the scale factor. Both parts are multiplied by the factor.
5. 5The result is shown as a ratio, along with fraction, decimal, and percentage equivalents.

• Simplifying non-integer ratios with the integer GCD: GCD is defined for integers. For decimal or fractional ratios like 1.5:2, multiply both parts to clear decimals first (3:4), then simplify.
• Swapping a and b in proportion mode: The proportion is a:b = c:x, so x = (b × c) / a. Swapping a and b gives the wrong answer. Make sure the ratio parts are in the correct positions.
• Confusing ratio and fraction: The ratio 3:4 means 3 parts to 4 parts, a total of 7 parts. The fraction 3/4 means 3 out of 4. They look similar but represent different things depending on context.
• Thinking scaling changes the ratio: Multiplying both parts of a ratio by the same factor does not change the ratio. 2:3 and 6:9 are the same ratio. The scale mode just produces a larger equivalent ratio.

• Check simplification with decimals: After simplifying, both the original and simplified ratios should produce the same decimal. 6:9 and 2:3 both equal 0.6667. If the decimals differ, you made an error.
• Use proportion mode for unit conversion: Unit conversion is just a proportion: if 1 mile = 1.60934 km, then 5 miles = x km. Set a=1, b=1.60934, c=5 and solve for x.
• Convert to a 1:n form for easy comparison: To compare two ratios, convert each to the form 1:n by dividing both parts by the first. 3:5 becomes 1:1.667, and 2:4 becomes 1:2. Now comparison is direct.
• Use scale mode for recipe doubling or halving: To double a recipe in 2:3 ratio, set scale factor to 2. To halve it, set scale factor to 0.5. The ratio stays the same, but the actual quantities change.