Proportion Calculator
Solve proportions using cross-multiplication, find missing values, and verify if ratios are proportional
Solve Mode: Enter 3 values and leave one empty. The calculator will find the missing value.
Verify Mode: Enter all 4 values to check if the proportion is valid.
Quick Examples
Missing Value ()
Step-by-Step Solution
Cross-Multiplication Check
Common Proportions Reference
| Proportion | Decimal | Common Use |
|---|---|---|
| 1/2 = 2/4 = 3/6 | 0.5 | Half portions |
| 1/3 = 2/6 = 3/9 | 0.333 | Third portions |
| 1/4 = 2/8 = 3/12 | 0.25 | Quarter portions |
| 2/3 = 4/6 = 6/9 | 0.667 | Two-thirds |
| 3/4 = 6/8 = 9/12 | 0.75 | Three-quarters |
| 1/5 = 2/10 = 20/100 | 0.2 | 20% or fifth |
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About Proportion Calculator
What is a Proportion Calculator?
A proportion calculator is a mathematical tool that helps you solve for unknown values in proportions. A proportion is an equation stating that two ratios are equal, written as a:b = c:d or a/b = c/d.
How to Use This Calculator
Mode 1: Solve for X
- Enter three known values in the proportion a:b = c:x
- The calculator finds the missing value using cross-multiplication
- View step-by-step solution
Mode 2: Verify Proportion
- Enter all four values (a, b, c, d)
- Check if a:b = c:d is true
- See the cross-multiplication verification
Understanding Proportions
What is a Proportion?
A proportion is an equation that shows two ratios are equal. For example:
- 1/2 = 2/4 (one-half equals two-quarters)
- 3:4 = 6:8 (three is to four as six is to eight)
Cross-Multiplication Method
To solve for an unknown in a proportion a/b = c/d:
- Cross-multiply: a × d = b × c
- Solve for the unknown variable
Example: Solve for x in 2/3 = 4/x
- Cross-multiply: 2 × x = 3 × 4
- Simplify: 2x = 12
- Divide: x = 6
Key Proportion Properties
| Property | Formula | Example |
|---|---|---|
| Cross Product | a × d = b × c | 2/3 = 4/6 → 2×6 = 3×4 |
| Reciprocal | b/a = d/c | If 2/3 = 4/6, then 3/2 = 6/4 |
| Alternation | a/c = b/d | If 2/3 = 4/6, then 2/4 = 3/6 |
Common Applications
Recipes & Cooking
- Scaling recipe ingredients
- Converting measurements
Maps & Scale Drawings
- Calculating actual distances
- Creating scale models
Finance & Business
- Unit pricing
- Cost comparisons
- Exchange rates
Science & Medicine
- Dilution calculations
- Dosage calculations
- Chemical concentrations
Frequently Asked Questions
How do I know if two ratios form a proportion?
Cross-multiply and compare: if a × d = b × c, then a/b = c/d is a valid proportion.
What is the difference between a ratio and a proportion?
A ratio compares two quantities (like 3:4). A proportion states that two ratios are equal (like 3:4 = 6:8).
Can I use decimals in proportions?
Yes! This calculator works with whole numbers, decimals, and fractions converted to decimals.
How accurate is this calculator?
Results are calculated using standard mathematical formulas and displayed to 4 decimal places for precision.
Tip: When solving real-world problems, always check that your answer makes sense in context. If calculating a recipe, the scaled amount should increase when you're making more servings.