A proportion states that two ratios are equal. One missing term can be found because both ratios represent the same scale relationship.
Use proportions for resizing, recipes, maps, unit conversions, similar shapes, and constant-rate relationships.
The relationship
The defining equation
a/b = c/d ⇔ ad = bc
a, b, c, and d form two equal ratios; nonzero denominator positions must remain nonzero.
See the structure
Equal ratios have equal cross-products
2 : 3=4 : 6equal scale, equal cross-products
Worked example
Scale 3 out of 4 to a denominator of 20
3/4 = x/20, so 3×20 = 4x and x = 15
Interpret with care
What the result does—and does not—mean
Cross-multiplication is a consequence of equal ratios, not a substitute for deciding whether the real situation is proportional.
Quick guide
How to use this calculator
Enter the known values using ordinary signed decimals.
Choose an interpretation or relationship when the calculator provides one.
Read the exact result, decimal preview, and any domain explanation.
Calculation method
Use the stated percentage or ratio relationship
a/b = c/d
The calculator keeps finite-decimal inputs as exact reduced fractions and rejects a zero reference or denominator whenever the requested relative quantity would be undefined.
Worked example
Worked interpretation
3/4 = x/20 gives x = 15.
a/b = c/d
Supported inputs
Precision and limits
Input precision
Each value may contain up to 30 digits and 15 decimal places. Scientific notation, fractions typed with a slash, and thousands separators are not accepted.
Exactness
Finite decimals are converted to reduced rational numbers. Detected repeating digits appear in parentheses, while previews that exceed the display limit end with an ellipsis; the exact fraction remains available.
Lists and ratios
List-based tools accept 2–12 entries separated by commas, colons, semicolons, or new lines. Ratio parts must satisfy the positivity rules shown by the calculator.
