Ratio Calculator
Simplify ratios, find missing values, and scale ratios up or down.
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How to use this calculator
Divide both parts by their greatest common divisor to simplify. Use cross-multiplication to find missing values.
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Enter the two values that form your ratio.
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The simplified ratio appears automatically.
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Optionally enter a scale factor to multiply the simplified ratio.
Frequently asked questions
What is a ratio?
A ratio compares two quantities. A ratio of 3:2 means for every 3 of one thing, there are 2 of another. Ratios are equivalent to fractions: 3:2 = 3/2 = 1.5.
How do you simplify a ratio?
Divide both numbers by their Greatest Common Divisor (GCD). Example: 12:8 — GCD is 4 — simplified to 3:2.
What are ratios used for?
Ratios appear in recipes (flour:sugar), map scales (1:50,000), financial analysis (debt:equity), photography (aspect ratio 16:9), chemistry (mixing concentrations), and sports statistics.
How do I find the missing value in a proportion?
If a:b = c:d, then a×d = b×c (cross-multiplication). To find d: d = b×c/a. Example: 3:4 = 9:? → ? = 4×9/3 = 12.
Ratio and proportion explained
Ratios in everyday life
Ratios are everywhere: mixing concrete (1:2:3 cement:sand:gravel), cooking recipes, screen aspect ratios (16:9), map scales, financial leverage, and drug concentrations in medicine. Understanding ratios is essential for scaling any recipe or plan up or down.
Ratios vs fractions vs percentages
All three represent relationships between numbers. 3:4 ratio = 3/4 fraction = 75% of 4. They are interchangeable representations. Ratios are preferred when comparing two independent quantities; fractions and percentages when expressing a part of a whole.
Proportional reasoning
If two ratios are equal (a:b = c:d), they form a proportion. Cross-multiplication solves for unknowns: if 2:5 = x:15, then x = 2×15/5 = 6. This is the basis for scaling recipes, technical drawings, and financial models.
Ratio: how it works
Built on well-established mathematical principles, this tool delivers accurate results for students, researchers, and professionals. Enter your values and get instant clarity without specialist software or manual arithmetic.
Who uses this tool?
Teachers, students, engineers, and data analysts use it to verify calculations, check homework, and solve problems faster. It is intuitive enough for beginners while comprehensive enough for professional use.
Learn more from an authoritative source:
WikipediaScientific Calculator
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →