Worked example
Recipe scale
- Input
- 2 ÷ 3 = x ÷ 12
- Output
- x = 8
Multiplying 2 × 12 and dividing by 3 preserves the ratio.
Proportion Calculator
Choose A, B, C, or D as the unknown in A/B = C/D, then enter the other three terms. The calculator isolates the selected position and validates both denominators.
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How to use this calculator
Enter the term to solve and the other three known values in A ÷ B = C ÷ D.
Review term order, units, nonzero denominators, sign, and whether direct proportionality is appropriate.
Read the solved missing value and completed proportion.
Formula
For a ÷ b = c ÷ d, cross multiplication gives a × d = b × c. Solve the missing term by isolating it, such as d = b × c ÷ a when a is nonzero.
Worked example
For 3/5 = 12/x, 3x = 60, so x = 20 and both ratios equal 0.6.
Reference guide
Formula details and result guidance
Follow the variables, derivation, precision rule, and worked cases below to reproduce the calculation independently.
Variables
| Symbol | Meaning | Unit | Role |
|---|---|---|---|
| a, b, c, d | Four proportion terms | compatible units | Input |
| x | Unknown term | unit implied by its position | Output |
Derivation
- Write the equality of ratios as a ÷ b = c ÷ d.
- Cross-multiplication gives a × d = b × c; isolate the one unknown by dividing by its nonzero coefficient.
Rounding and precision
The solver retains the full numeric result and shows up to 6 decimal places. It rejects any arrangement that requires division by 0 instead of assigning an infinite value.
Worked and boundary examples
Worked example
Map ratio
- Input
- 5 ÷ x = 15 ÷ 18
- Output
- x = 6
Both cross-multiplication products equal 90 after solving.
Boundary case
Zero numerator
- Input
- 0 ÷ 4 = x ÷ 20
- Output
- x = 0
The proportion is defined because both denominators remain nonzero.
Common mistakes
- Pairing values in a different order on the two sides so unlike quantities occupy matching positions.
- Cross-multiplying correctly but dividing by the wrong coefficient when isolating the unknown.
- Accepting a proportion with a zero denominator, which is undefined.
How to interpret the result
The solution is the value that makes both entered ratios equal. Its practical meaning depends on keeping the same quantity and unit in corresponding numerator or denominator positions.
Scope
Appropriate for
- Scaling a recipe, drawing, or rate with consistent units.
- Solving one missing value in two equal ratios.
Do not use for
- Fitting a nonlinear relationship between variables.
- Comparing ratios whose corresponding terms represent different quantities.
Tools for the same task
Next tools in the workflow
Evidence and sources
- Equal ratios can be solved by equating their cross-products.OpenStax: College Algebra 2e — Preface and ScopeSupports: Slope, equations, radicals, proportions, and inverse algebraic operations. Reviewed 2026-08-22.
- Division by zero is undefined.OpenStax: Prealgebra 2e — Preface and ScopeSupports: Percent, proportion, radical, ratio, and elementary geometry procedures. Reviewed 2026-08-22.
Assumptions and limits
- The two ratios are asserted to be directly equivalent; uncertainty, nonlinear relationships, and sampling error are outside the model.
- Proportion Calculator treats the entered values as estimates and does not infer missing project, account, or personal details.
- Calculations retain working precision except where the cited method requires an intermediate rounding step; displayed values are then formatted separately. Source rules and dated rates must be rechecked when they change.
Sources
- OpenStax: College Algebra 2eAlgebraic, ratio, radical, equation, and function formulas. Reviewed 2026-08-14.
- OpenStax: Elementary Algebra 2eOfficial formula or method source used by this calculator. Reviewed 2026-08-14.
Related calculators
Verification
How this calculator is checked
Trust comes from reproducible evidence, not model confidence. You can inspect the formula, assumptions, worked example, and cited sources on this page.
- Versioned calculationFormula logic is kept separate from the interface and covered by automated registry and behavior checks.
- Cited evidenceSources linked for independent checking: 2.
- Transparent AI useAI may assist drafting or adversarial review. Agreement between models is not proof, and no human expert review is claimed unless a named reviewer is shown.
Frequently asked questions
How does the Proportion Calculator work?
For a ÷ b = c ÷ d, cross multiplication gives a × d = b × c. Solve the missing term by isolating it, such as d = b × c ÷ a when a is nonzero.
What information should I enter in the Proportion Calculator?
Enter the term to solve and the other three known values in A ÷ B = C ÷ D, then verify term order, units, nonzero denominators, sign, and whether direct proportionality is appropriate.
What should I verify before using this Proportion Calculator result?
The two ratios are asserted to be directly equivalent; uncertainty, nonlinear relationships, and sampling error are outside the model.
Last updated 2026-08-25 · any-missing-term-v2 · content-2026-08-14 · Published by YunFanLabs