Proportion Calculator Online
Solve proportions (A/B = C/D) and find missing values with step-by-step cross-multiplication.
Input Parameters
Live Result
Details
Steps
Direct Proportion: 4 / 8 = 12 / x
Cross-Multiply: 4 · x = 8 · 12 = 96
Solve for x: x = (8 · 12) / 4 = 24
Quick Answer & Understanding Your Result
A proportion is a mathematical statement establishing that two ratios or fractions are equal: A / B = C / D, where cross-multiplication yields A · D = B · C.
Core Properties of Proportions
- Direct Proportion: As one quantity scales up by factor k, the other scales up proportionally: y = k · x.
- Inverse Proportion: The product of two variables remains strictly constant: x · y = k or A · B = C · D.
- Cross-Multiplication Rule: For any true proportion A/B = C/D, the extremes product equals the means product: A · D = B · C.
- Scale Multiplier: The ratio between corresponding numerators (C / A) or denominators (D / B).
Practical Applications & Uses
- Culinary Recipe Scaling: Multiplying or dividing ingredients accurately for varying guest serving sizes.
- Cartography & Scale Models: Translating map measurements into real-world geographic distances (e.g. 1:50,000 scale).
- Financial Currencies & Conversions: Calculating exchange rates and unit prices across diverse purchasing quantities.
Input any three known terms into the calculator above to solve for the missing fourth value with detailed step-by-step proofs.
Formula & Calculation Logic
Mathematical FormulaA and B represent the first ratio, while C and D represent the second ratio. In direct proportions, cross-multiplying solves for any unknown variable x. In inverse proportions, the products of corresponding variables are equated.
Step-by-Step Guide
Select Unknown
Choose which variable (A, B, C, or D) represents your target unknown.
Enter Known Values
Input the 3 known numerical quantities into their respective fields.
Choose Proportion Mode
Select Direct Proportion (constant ratio) or Inverse Proportion (constant product).
Review Solution
Analyze the computed unknown value, cross-product verification, and step-by-step algebraic reduction.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Direct Proportion: Recipe Scaling | 2 / 6 = 5 / x => 2x = 30 => x = 15. | ||
| Inverse Proportion: Worker Hours | 4 workers take 6 hours (product = 24). 8 workers take 24 / 8 = 3 hours. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
Euclid's Elements - Book V (Theory of Proportions)
NIST Digital Library of Mathematical Functions
Standard: Direct & Inverse Proportions
Formula: Direct: A / B = C / D ⇒ A · D = B · C
Last Reviewed: August 21, 2026
Primary Source: Euclid's Elements - Book V (Theory of Proportions)
Reference Document: NIST Digital Library of Mathematical Functions
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.