How to use this ratio calculator
Choose Simplify ratio, Scale ratio, or Solve proportion. For simplification, enter the two terms you want to reduce. Scaling also requires a positive whole-number factor. To solve a proportion, enter a, b, and c in a:b = c:x; the calculator finds x using cross-multiplication. Keep all quantities in compatible units before comparing them.
How the calculation works
A ratio compares two quantities in a stated order. Dividing both terms by their greatest common divisor creates the simplest equivalent ratio. Multiplying both terms by the same positive factor creates another equivalent ratio because the relative comparison does not change.
A proportion states that two ratios are equal. In a:b = c:x, cross-multiplication gives a × x = b × c, so x = (b × c) / a. The result may be a whole number or an exact fraction depending on the inputs.
Formulas
Simplest form
Scale a ratio
Solve a proportion
Worked examples
Simplify 12:18
The greatest common divisor of 12 and 18 is 6. Dividing both terms by 6 gives the simplest ratio 2:3.
Solve 2:3 = 10:x
Cross-multiply to get 2x = 30. Dividing by 2 gives x = 15, so 2:3 and 10:15 are equivalent ratios.
Common uses
Recipes, mixtures, and scale models
Preserve relative quantities when enlarging a recipe, preparing an informal mixture, or translating a drawing scale. Multiply every term by the same factor to keep the relationship equivalent.
Rates and comparisons
Express counts such as wins to losses, students to teachers, or parts of different types in a compact form. State the term order and units so readers know exactly what is being compared.
Missing-value problems
Solve an equivalent proportion when three positive terms are known, such as map distance, unit price, or a classroom similarity problem. Cross-multiplication preserves an exact fractional answer when needed.
Accuracy and limitations
Simplification and scaling use positive whole-number terms and exact greatest-common-divisor arithmetic. The proportion solver returns a reduced exact fraction rather than silently rounding a non-integer result.
Ratios are meaningful only when the quantities and order are defined. Convert unlike measurement units before simplification, and use authoritative formulas for regulated concentrations, dosing, or safety-critical mixtures.
Frequently asked questions
What does the order of a ratio mean?
Order identifies which quantity is compared with which. A ratio of 2 red items to 3 blue items is 2:3; reversing it gives the different comparison 3:2.
How do I simplify a ratio?
Find the greatest common divisor of both terms, then divide each term by it. The resulting whole-number ratio has the same relationship in lowest terms.
Can I simplify a ratio with different units?
Convert both quantities to compatible units first. For example, compare 1 meter with 50 centimeters as 100:50, which simplifies to 2:1.
Is a ratio the same as a fraction?
They are closely related but used differently. A fraction often describes part of a whole, while a ratio can compare any two quantities. The ratio a:b corresponds to the quotient a/b.
Can the missing proportion term be a fraction?
Yes. Not every valid proportion has a whole-number fourth term. The calculator preserves an exact reduced fraction instead of rounding it.
Is the ratio calculator free to use?
Yes. NumUtility is free, requires no account, and places no limit on ordinary calculations.
Are my entries stored?
No. The calculation runs in your browser. Values entered into the tool are not sent to NumUtility or saved by us.