Ratio Calculator
Simplify ratios and solve proportions.
Simplify a Ratio
Enter two numbers to simplify to the lowest terms.
Proportion Solver
Fill in 3 values and leave one blank to solve. Or fill all 4 to verify.
Common Ratios Reference
| Name | Ratio | Decimal | Use |
|---|---|---|---|
| Golden Ratio | 1 : 1.618 | 0.618 | Design, art, architecture |
| Silver Ratio | 1 : 2.414 | 0.414 | Geometry, paper sizes |
| Rule of Thirds | 1 : 2 | 0.333 | Photography |
| 16:9 | 16 : 9 | 1.778 | Widescreen display |
| 4:3 | 4 : 3 | 1.333 | Classic display |
| 3:2 | 3 : 2 | 1.500 | 35mm photography |
| A-series Paper | 1 : 1.414 | 0.707 | A4, A3 paper sizes |
| Pi ratio | 1 : 3.142 | 0.318 | Circle diameter to circumference |
Frequently Asked Questions
How do I simplify a ratio?
Divide both parts by their greatest common divisor (GCD). For 24:36: GCD = 12, so 24/12 : 36/12 = 2:3. The calculator automatically finds the GCD and simplifies to the lowest terms. It handles two-part ratios (a:b), three-part ratios (a:b:c), and any number of parts.
How do I solve a proportion with a missing value?
A proportion is two equal ratios: a/b = c/d. Cross-multiply to find the missing value. If 3/4 = x/20, then 3 x 20 = 4 x x, so x = 60/4 = 15. Enter three known values and the calculator solves for the fourth. This is useful for scaling recipes, maps, models, and unit conversions.
How do I convert a ratio to a fraction or percentage?
A ratio a:b means a/(a+b) of the first part and b/(a+b) of the second. A 3:2 ratio means 3/5 (60%) first and 2/5 (40%) second. The calculator shows both fractions and percentages for each part of the ratio, making it easy to understand proportional distributions.
How do I scale a ratio?
Multiply both parts by the same number. To scale 2:3 to have a total of 50: each unit = 50/(2+3) = 10, so the scaled values are 20:30. The calculator lets you specify a target total or a target value for one part and scales the entire ratio proportionally.
What are ratios used for in real life?
Ratios appear everywhere: cooking recipes (2:1 flour to sugar), screen aspect ratios (16:9), financial ratios (debt-to-equity), map scales (1:50,000), mixing solutions (3:1 water to concentrate), gear ratios in engineering, and odds in probability. Understanding ratios is fundamental to proportional reasoning.