Proportion Calculator
Proportion Calculator
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What is a Proportion Calculator?
A proportion calculator is a mathematical tool that helps you work with proportions - equations that state two ratios are equal. Proportions are written as A/B = C/D, meaning the ratio of A to B equals the ratio of C to D. This tool uses cross multiplication to solve for unknown values.
Proportions are fundamental in mathematics and have countless real-world applications. They're used in cooking to scale recipes, in photography for aspect ratios, in medicine for dosage calculations, in construction for blueprints, and in finance for currency conversions.
This calculator provides four key functions: solving for unknown values in proportions, verifying if four values form a valid proportion, working with direct and inverse proportions, and solving percentage-based proportion problems.
Understanding Proportions
What is a Proportion?
A proportion is an equation stating that two ratios are equal: A/B = C/D
Example: 2/4 = 3/6 (both equal 0.5)
Cross Multiplication
If A/B = C/D, then A × D = B × C
2/4 = 3/6 → 2 × 6 = 4 × 3 = 12
This property is used to solve for unknown values and verify proportions.
Direct Proportion
When one quantity increases, the other increases proportionally.
Example: If 3 apples cost $6, then 6 apples cost $12 (price doubles when quantity doubles)
Inverse Proportion
When one quantity increases, the other decreases proportionally.
Example: If 4 workers complete a job in 6 hours, 8 workers complete it in 3 hours
Calculator Features
Solve Proportions
- Solve for A, B, C, or D in A/B = C/D
- Uses cross multiplication formula
- Shows step-by-step solution
- Handles decimal and whole numbers
Other Functions
- Verify if values form a proportion
- Calculate direct proportions
- Calculate inverse proportions
- Solve percentage problems
Frequently Asked Questions
How do I solve for an unknown in a proportion?
Use cross multiplication. In A/B = C/D, if you need to find D, multiply A × D = B × C, then solve for D = (B × C) / A. Enter your known values, select which variable to solve for, and click Solve to see the step-by-step solution.
What is the difference between direct and inverse proportion?
In direct proportion, both quantities increase or decrease together (y = kx). In inverse proportion, when one increases, the other decreases (xy = k). For example, speed and time are inversely proportional - drive faster, arrive sooner.
How do I verify if values form a proportion?
Enter all four values and use the Verify tab. The calculator checks if A × D equals B × C using cross multiplication. If the products are equal, the values form a valid proportion.
How are percentages related to proportions?
Percentages are proportions with 100 as the base. "25% of 80" means Part/80 = 25/100. The Percentage tab solves these problems, finding any missing value (part, whole, or percentage) given the other two.
Common Applications of Proportions
Scale & Measurement
- Blueprint and map scales
- Model building ratios
- Unit conversions
Cooking & Recipes
- Scaling recipe quantities
- Ingredient substitutions
- Serving size adjustments
Finance & Business
- Currency exchange rates
- Profit margin calculations
- Investment returns
Science & Medicine
- Drug dosage calculations
- Solution concentrations
- Chemical mixing ratios