Ratio Calculator

Discrete Mathematics & Proportional Reasoning

A Ratio is a quantitative comparison expressing the relative size of two or more values (A : B). A Proportion is a mathematical equation stating that two ratios are equivalent.

Core Ratio & Proportion Equations

• Cross-Multiplication Rule: A · D = B · C

• Solving Missing Terms:

• D = (B · C) / (A), C = (A · D) / (B), B = (A · D) / (C), A = (B · C) / (D)

• Ratio Simplification: a = (A) / (GCD)(A, B), b = (B) / (GCD)(A, B)

• Part-to-Whole Percentage: P_A = (A) / (A + B) × 100\%, P_B = (B) / (A + B) × 100\%

• Dividing Total Quantity (Q): Share_A = Q × (A) / (A + B), Share_B = Q × (B) / (A + B)

Real-World Applications

• Aspect Ratios: High-definition video displays operate on a 16:9 width-to-height ratio (1.778 decimal), while standard displays use 4:3 (1.333).

• Culinary Scaling: Multiplying base ingredient ratios (e.g. 3:2:1 flour, fat, liquid pie crust) by volume factors maintains identical dough texture at any batch scale.

How to Use This Calculator

Enter your Ratio Calculation Mode — choose from Solve Equivalent Proportion (A : B = C : D), Simplify / Reduce Ratio (A : B to lowest terms), Scale Ratio by Multiplier (A:B × factor), Variable to Solve for (in A:B = C:D) — choose from Solve for D (D = B · C ÷ A), Solve for C (C = A · D ÷ B), Solve for B (B = A · D ÷ C), Ratio Term A (e.g. 4), Ratio Term B (e.g. 12), Ratio Term C (for Proportion) (e.g. 8), Ratio Term D (for Proportion) (e.g. 24), Scaling Factor (k) (e.g. 2.5), and Total Quantity to Split (Q) (e.g. 1200). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Formula Reference: Ratio Calculator

Input variables:

calculatorMode — Ratio Calculation Mode

missingVariable — Variable to Solve for (in A:B = C:D)

valA — Ratio Term A

valB — Ratio Term B

valC — Ratio Term C (for Proportion)

Computed outputs:

solvedValue — Calculated Result

simplifiedRatio — Simplified Ratio in Lowest Terms

percentageEquivalents — Percentage Breakdown

decimalValue — Decimal Quotient (A ÷ B)

stepByStepWork — Mathematical Solution Steps

Mathematical relationships extracted from calculation logic:

sumAB = A + B

pctA = safeDiv(A, sumAB) * 100

pctB = safeDiv(B, sumAB) * 100

solved = safeDiv(B * C, A)

scaledA = A * factor

scaledB = B * factor

shareA = safeDiv(A, sumAB) * totalQ

shareB = safeDiv(B, sumAB) * totalQ

Standard: NIST / ISO mathematical definitions

Worked Example

Solving 4:12 = 8:D: Cross multiply 4D = 128 -> 4D = 96 -> D =

• Reducing 4:12 by GCD(4) gives 1:3, representing 25% and 75% proportional parts.

Understanding Your Result

Percentages are relative values — context determines what is "good" or "bad." A 50% discount is significant; a 50% failure rate is alarming. Percentage change and percentage points are different: moving from 4% to 5% is a 1 percentage point increase, but a 25% relative increase. When comparing percentages across different base values, always check whether absolute differences are meaningful — a 10% improvement on a large base creates more absolute value than 10% on a small base.