Ratio Calculator Online
Solve proportions A:B = C:D for missing variable X, simplify ratios, scale recipes, and identify aspect ratios.
Input Parameters
Live Result
Details
Steps
Proportion Statement: A : B = C : D
Apply Cross-Multiplication Property: A × D = B × C
D = (B × C) / A = (4 × 15) / 3 = 60 / 3 = 20
Resulting Complete Proportion: 3 : 4 = 15 : 20
Quick Answer & Understanding Your Result
A Ratio Calculator solves missing terms in equivalent proportions A : B = C : D using cross-multiplication: A × D = B × C. It also simplifies arbitrary ratios to their irreducible lowest terms by dividing by the Greatest Common Divisor (GCD).
The 4 Proportion Solving Formulas
- Solve for A: A = (B × C) / D (when A is unknown).
- Solve for B: B = (A × D) / C (when B is unknown).
- Solve for C: C = (A × D) / B (when C is unknown).
- Solve for D: D = (B × C) / A (when D is unknown).
Common Standard Aspect Ratios
- 16 : 9: Widescreen high-definition video displays (1920×1080, 2560×1440, 3840×2160 4K).
- 4 : 3: Classic television and standard photographic formats.
- 1 : 1: Square profile pictures and social media carousel posts.
- 21 : 9: Ultra-wide cinematic cinema displays.
Input your known numbers into the proportion fields above to solve for missing term X with complete cross-multiplication steps.
Formula & Calculation Logic
Mathematical FormulaIn any true proportion, the product of the extremes (A × D) equals the product of the means (B × C). Dividing both terms by their greatest common divisor yields the simplified ratio.
Step-by-Step Guide
Select Calculation Mode
Choose Solve Proportion (solve for X) or Simplify Ratio mode.
Enter Numbers
Input terms A, B, and C (leaving missing term X to solve).
Compute Solution
Click calculate to solve cross-multiplication or extract GCD factor.
Review Output & Aspect
View exact solved value, simplified ratio fraction, and standard aspect ratio matches.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Solve Proportion 3:4 = 15:X | Cross-multiply: 3 × X = 4 × 15 = 60. X = 60 / 3 = 20. | ||
| Simplify Resolution 1920:1080 | GCD(1920, 1080) = 120. 1920/120 = 16, 1080/120 = 9, yielding 16:9. | ||
| Scale Recipe 2:5 for 10 servings | 2/5 = 4/X -> X = (5 × 4)/2 = 10. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
Wolfram MathWorld - Proportion
National Council of Teachers of Mathematics (NCTM)
Standard: ISO / W3C / IETF Authoritative Domain Standard
Formula: A / B = C / D
Last Reviewed: August 21, 2026
Primary Source: Wolfram MathWorld - Proportion
Reference Document: National Council of Teachers of Mathematics (NCTM)
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.