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Math Calculators / Ratio & Proportion Calculator

Ratio & Proportion Calculator

Simplify ratios, solve for missing proportion terms (A : B = C : X), and scale quantities proportionally.

Proportion & Scale Solver
:
Result
2 : 3

12 : 18 simplifies to 2 : 3 (Divided by GCD 6)

Step-by-Step Method:
Find the Greatest Common Divisor (GCD) of 12 and 18: GCD = 6
Divide both terms by 6: 12 ÷ 6 = 2, and 18 ÷ 6 = 3
Simplified Ratio = 2 : 3

About the Ratio & Proportion Calculator

The CalcNest Ratio & Proportion Calculator simplifies complex ratios, solves for unknown variables in proportions ($A:B = C:X$), scales recipes, and calculates profit-sharing splits for business partners.

Mathematical Formula

Simplification: A/GCD(A,B) : B/GCD(A,B) Proportion: A/B = C/X => X = (B × C) / A Share Division: Total Sum × (A / Total Parts)

Solves ratio reductions, cross-multiplication proportions, scaling factors, and multi-party partnership profit splits.

Variables & Components

A : B Original Ratio: Two comparative quantities expressed in colon notation.
X Missing Proportion Term: The fourth unknown term solved via cross-multiplication (A:B = C:X).
Scale Multiplier Scaling Factor: Factor used to uniformly increase or decrease ratio quantities.
Distributed Share Proportional Share: The absolute monetary or quantity division allotted to each ratio term.

Worked Example: Solving Proportion: If 4 items cost ₹80, how much do 10 items cost?

Express the relationship as a proportion: 4 : 80 = 10 : X.

Step-by-Step Calculation

  1. Set up equation: 4 / 80 = 10 / X
  2. Cross-multiply: 4 × X = 80 × 10 = 800
  3. Solve for X: X = 800 / 4 = 200
  4. Conclusion: 10 items cost ₹200.
Final Result: Proportion: 4 : 80 = 10 : 200 | Solved Value X = 200

How to Use This Calculator

1

Select your ratio operation: Simplify, Solve X (Proportion), Scale, or Divide Sum.

2

Enter your ratio terms (A, B, C) and target quantities.

3

Instantly view simplified ratios, solved missing terms, and distributed shares.

Frequently Asked Questions

A ratio is a comparison of two or more numbers showing their relative sizes. A ratio is simplified to lowest terms by dividing all terms by their Greatest Common Divisor (GCD), just like simplifying a fraction.

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