Ratio Calculator
Simplify mathematical ratios to lowest terms, solve missing proportion values (A:B = C:D), and find scaling factors.
Last verified: September 2026Inputs & Parameters
Calculation Results
Simplification divides antecedent and consequent by their Greatest Common Divisor (GCD = 6).
Understanding Ratios, Scaling, and Proportions
A ratio expresses the quantitative relationship between two numbers, indicating how many times one value contains another. Ratios are used in culinary scaling, concrete and chemical mix formulation, aspect ratios, model construction, and financial analysis.
Core Mathematical Principles
- Simplification to Lowest Terms: Divide both terms by their Greatest Common Divisor:
A / GCD(A, B) : B / GCD(A, B) - Proportional Solving (A : B = C : X):
X = (B × C) / A - Scaling Ratios:
Scaled Term = Term × Scale Factor - Part-to-Whole Percentage:
Term A% = [A / (A + B)] × 100
Worked Example
Simplifying the ratio 48 : 36 and solving for an equivalent recipe term where 48 : 36 = 12 : X:
1. Greatest Common Divisor (GCD of 48 and 36) = 12
2. Simplified Lowest Terms Ratio = (48 / 12) : (36 / 12) = 4 : 3
3. Solving for Missing Term: X = (36 × 12) / 48 = 9 (12 : 9)
4. Proportional Breakdown: Part A = 57.14%, Part B = 42.86%
Assumptions & Limitations
Ratio terms must be positive numbers. When scaling physical recipes or chemical solutions, ensure all quantities share identical units of measurement (e.g. all grams or all milliliters) prior to calculating proportional shares.