Ratio Calculator
Simplify ratios, solve proportions, and scale ratios up or down.
What Is a Ratio?
A ratio compares two or more quantities. The ratio 3:4 means "for every 3 of one thing, there are 4 of another." Ratios can be simplified (like fractions) by dividing by the GCF, scaled up or down, and converted to fractions, decimals, or percentages.
Proportions
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 = 4x, so x = 9.
Frequently Asked Questions
How do I simplify a ratio?
Find the GCF (Greatest Common Factor) of all numbers in the ratio and divide each by it. The ratio 12:8 has GCF of 4, so 12/4 : 8/4 = 3:2. The ratio 15:25:10 has GCF of 5, giving 3:5:2. A simplified ratio has no common factor other than 1 among all its parts.
How do I solve a proportion?
Use cross multiplication: if a/b = c/d, then a × d = b × c. Rearrange to solve for the unknown. For example: x/15 = 4/12. Cross multiply: 12x = 15 × 4 = 60. Divide: x = 5. Always check your answer by substituting back: 5/15 = 1/3 and 4/12 = 1/3. They match.
What is the golden ratio?
The golden ratio (φ ≈ 1.618) is a special proportion where a/b = (a+b)/a. It has been celebrated in art, architecture, and nature for centuries — claimed to appear in the Parthenon, Leonardo da Vinci's work, and spiral patterns in shells and sunflowers. Whether its prevalence is as widespread as commonly claimed is debated, but it is mathematically fascinating and genuinely appears in Fibonacci sequences and certain geometric constructions.
How do ratios relate to fractions and percentages?
A ratio a:b is equivalent to the fraction a/b. The ratio 3:4 means 3/4, or 0.75, or 75%. All three forms represent the same relationship. Ratios are often preferred when comparing multiple quantities (3:4:5 is cleaner than listing three fractions), while fractions and percentages are preferred for single comparisons against a whole.
How do I divide a quantity in a given ratio?
Add the ratio parts to find the total number of shares. Divide the total quantity by this sum to find the value of one share. Multiply each ratio part by the share value. Example: divide $200 in the ratio 3:2. Total parts: 3+2=5. One share: $200/5=$40. Parts: 3×$40=$120 and 2×$40=$80. Check: $120+$80=$200.