Ratio Calculator
Simplify ratios to their lowest terms or solve proportions to find missing values in A:B = C:D relationships. Use this calculator to allocate products, distribute resources, and scale operations while maintaining consistent ratios.
Simplify ratios to their lowest terms or solve proportions to find missing values in A:B = C:D relationships. Essential for product allocation, resource distribution, and scaling operations.
Numerator of the ratio
Denominator of the ratio
Formula
Simplify: GCD(A, B) determines the simplified form | Proportion: A:B = C:D → D = (C × B) ÷ A
A ratio compares two quantities. To simplify, divide both numbers by their greatest common divisor (GCD). A proportion states that two ratios are equal; use cross-multiplication to solve for missing values.
Worked Example
Warehouse manager needs to allocate 450 units of Product A and 300 units of Product B:
Ratio = 450:300
GCD(450, 300) = 150
Simplified ratio = 3:2
Decimal = 450 ÷ 300 = 1.5 (1.5× more of Product A than B)
If the warehouse receives 600 units next shipment and must maintain the 3:2 ratio, allocate 360 units to A and 240 to B. Using the proportion: 3:2 = 360:240 confirms the ratio holds.
Common Mistakes
❌ Mistake 1: Not simplifying to lowest terms
A ratio of 12:8 stays as 12:8 instead of simplifying to 3:2. Always reduce to the simplest form for clarity and accuracy.
❌ Mistake 2: Cross-multiplying incorrectly for proportions
For A:B = C:D, the correct formula is D = (C × B) ÷ A. Don't multiply A × B or C × D; use cross-multiplication: A × D = B × C.
❌ Mistake 3: Forgetting the order matters
The ratio 3:2 is not the same as 2:3. Always keep the values in the correct sequence when solving proportions.
Frequently Asked Questions
Use this in your workflow
After simplifying or solving a ratio, use the Percentage Calculator to convert ratio allocations to percentages. Use the Margin Calculator to calculate margins from cost-to-revenue ratios. Browse all Free Business Calculators.
Worked examples: ratios in practice
Three common ratio and proportion scenarios in business.
| Scenario | Input | Result |
|---|---|---|
| Simplify product stock ratio | 450 units A : 300 units B | Simplifies to 3:2 (decimal 1.5) |
| Scale allocation to new inventory | 3:2 ratio, new total 600 units | 360 units A, 240 units B |
| Find cost-revenue proportion | Cost $1,200 : Revenue $4,000 | 3:10 ratio (cost is 30% of revenue) |
Ratios simplify comparisons and help maintain consistency when scaling. Proportions let you solve for unknowns while preserving the relationship.
Limitations
This calculator simplifies ratios to their integer lowest terms when possible. It solves simple proportion equations (A:B = C:D). It does not handle complex multi-part ratios, weighted ratios, or proportions with more than four variables. For advanced scenarios (e.g., recipe scaling with ingredient ratios or financial leverage ratios with multiple factors), calculate each step separately. These results are for planning and estimation purposes only — not financial, legal, or operational advice.
When to use this calculator
- →Simplifying product or resource allocation ratios to understand the relationship at a glance
- →Scaling inventory or production quantities while maintaining a consistent ratio between products
- →Solving for unknown quantities in proportion equations (A:B = C:?)
- →Verifying that ratios remain consistent across different scales or time periods
- →Converting cost-to-revenue or cost-to-benefit relationships into simple, comparable ratios
Frequently asked questions
What is the difference between a ratio and a proportion?
A ratio compares two quantities (e.g., 3:2 means 3 parts to 2 parts). A proportion states that two ratios are equal (e.g., 3:2 = 6:4). Ratios show relationships; proportions solve for unknowns.
When should I simplify a ratio?
Always simplify to the lowest terms for clarity. A 12:8 ratio is harder to interpret than 3:2. Simplified ratios make communication easier and help catch errors.
How does cross-multiplication work in proportions?
In A:B = C:D, cross-multiply: A × D = B × C. To solve for D: D = (B × C) ÷ A. This ensures both sides of the proportion are equal.
Can I use this calculator for recipes or mixing ratios?
Yes. If a recipe calls for a 3:2 ratio of ingredient A to B and you want to scale it, use the proportion solver to find new quantities while maintaining the ratio.
What if I need to allocate across three or more products?
This calculator solves two-part ratios. For multi-part allocations (A:B:C), simplify each pair separately or calculate allocation percentages and apply them to the total quantity.
How do I verify my ratio is correct?
Divide the simplified ratio back to check: if 3:2 represents 450:300, then 450 ÷ 300 = 1.5 and 3 ÷ 2 = 1.5. They should match.