Calculators
Ratio & Proportion Calculator
Simplify ratios and solve proportions with a missing value.
Simplify a ratio
Reduce two non-negative values to their smallest whole-number ratio.
Simplified ratio
2:3
Solve a proportion
For a:b = c:x, solve the missing fourth value x.
Missing value x
12
2:3 = 8:12
About This Tool
Use this calculator for two closely related ratio tasks without splitting them into thin separate pages. Simplify a pair of non-negative quantities to an equivalent smallest whole-number ratio, or solve the missing fourth value in a proportion written a:b = c:x. The calculations run locally in your browser and are useful for recipes, scale drawings, mixtures, classroom math, rates, and comparisons when the quantities are expressed on a compatible basis.
How To Use It
- To simplify a ratio, enter the left and right quantities. Decimal inputs are scaled before reduction so values such as 1.5:2.25 become 2:3.
- To solve a proportion, enter a, b, and c for a:b = c:x. The calculator uses cross multiplication to find x.
- Keep compared quantities on compatible units. Convert units first when necessary, then interpret the simplified ratio or missing value in the context of your problem.
Examples
Simplify 12:18
The greatest common divisor of 12 and 18 is 6. Dividing both sides by 6 gives the equivalent ratio 2:3.
Simplify a decimal ratio
For 1.5:2.25, multiply both values by 100 to work with 150:225, then reduce by 75 to get 2:3.
Solve 2:3 = 8:x
Cross multiplication gives 2x = 3 × 8 = 24, so x = 12. Both ratios therefore describe the same proportion.
Recipe scaling
If 2 cups of one ingredient correspond to 3 cups of another, using 8 cups of the first ingredient requires 12 cups of the second to preserve the 2:3 proportion.
Useful Notes
How ratio simplification works
For whole numbers, divide both sides by their greatest common divisor. Decimal values are first converted to scaled integers, up to eight decimal places, so the calculator can reduce them without pretending an arbitrary rounded decimal is exact.
How proportions are solved
For a:b = c:x, interpret the ratios as a/b = c/x. Cross multiplication gives ax = bc, so x = bc/a when a is nonzero. This preserves the same multiplicative relationship between the two pairs.
Units and interpretation
A numeric ratio is only meaningful when you understand what each side measures. If one length is in meters and another is in centimeters, convert them to the same unit before simplifying. A ratio such as 2:3 means that for every 2 parts of the first quantity there are 3 comparable parts of the second.
Zero and precision limits
A one-sided zero ratio such as 0:15 simplifies to 0:1, while 0:0 is indeterminate and is rejected. Ratio simplification accepts up to eight decimal places and rejects values that cannot be safely scaled to integers.
FAQ
Are 2:3 and 4:6 the same ratio?
Yes. Dividing both values in 4:6 by 2 gives 2:3, so they are equivalent ratios.
Can I simplify ratios with decimals?
Yes. The calculator scales decimal inputs to whole numbers and then reduces them. It supports up to eight decimal places for exact simplification within normal JavaScript safe-integer limits.
Why should units match before simplifying?
Ratios compare quantities. Converting compatible measurements to the same unit prevents the unit scale itself from distorting the numeric comparison.
Why combine ratio simplification and proportion solving?
They are closely related tasks based on equivalent ratios. Keeping them together lets one substantial page serve the complete intent instead of creating near-duplicate single-operation pages.
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