Ratio Calculator – Solve Proportions
Solve ratio proportions and find missing values. If A:B = C:X, find X.
Understanding Ratios and Proportions
A ratio compares two or more quantities. The ratio 3:2 means for every 3 of the first quantity, there are 2 of the second. Ratios can be written as 3:2, 3/2, or "3 to 2."
A proportion states that two ratios are equal: a/b = c/d. To solve for an unknown: cross-multiply. If 3/4 = x/12, then 3×12 = 4×x, so x = 36/4 = 9.
Simplifying and Scaling Ratios
To simplify a ratio, divide all parts by their greatest common divisor (GCD). 12:8 simplifies to 3:2 (divide by 4). 15:25:10 simplifies to 3:5:2 (divide by 5).
To scale a ratio to a specific total: if you need to mix concrete in a 1:2:4 ratio (cement:sand:gravel) for 700 kg total: parts = 1+2+4 = 7. Each part = 100 kg. So 100 kg cement, 200 kg sand, 400 kg gravel.
Real-World Ratio Applications
Cooking: Scaling recipes up or down while maintaining proportions. Maps: Scale ratios like 1:50,000 mean 1 cm on the map = 50,000 cm (500 m) in reality. Finance: Price-to-earnings ratio, debt-to-income ratio. Construction: Concrete mix ratios, slope ratios. Photography: Aspect ratios (16:9, 4:3, 3:2).
Frequently Asked Questions
How do I convert a ratio to a percentage?
Divide the part by the total of all parts, then multiply by 100. In a 3:2 ratio: 3/(3+2) = 60% and 2/(3+2) = 40%.
What is the golden ratio?
The golden ratio (phi) is approximately 1.618:1. It appears throughout nature, art, and architecture. A rectangle with sides in the golden ratio is considered aesthetically pleasing. It is defined as (1 + sqrt(5)) / 2.
How do I compare ratios?
Convert them to the same form. Either express both as decimals (3:4 = 0.75, 5:6 = 0.833) or find equivalent ratios with a common denominator. The larger decimal or fraction represents the larger ratio.