Proportion Calculator
Solve A/B = C/X for the unknown value
If A/B = C/X, enter A, B, and C to find X
X = (B x C) / AWhat is a Proportion Calculator?
A Proportion Calculator is a math tool that helps you solve problems where two ratios are equal. A proportion is written like a:b = c:d or a/b = c/d.
Proportions are used when you want to scale values up or down while keeping the same relationship. This comes up in everyday situations like resizing recipes, converting map scales, mixing solutions, comparing prices, and solving "missing value" problems such as "If 3 items cost $12, how much do 5 items cost?"
This calculator makes it easy to find the unknown value in a proportion (often represented as x) and reduces mistakes from manual cross-multiplication.
How to Use This Proportion Calculator
- Enter the known values -- in the proportion (for example: a, b, and c)
- Leave the unknown value blank -- (or enter x) if your calculator supports it
- Confirm the proportion format -- common formats include a/b = c/d or a:b = c:d
- Click "Calculate" -- to solve for the missing value
- Review the result -- and make sure it makes sense for the problem (especially units)
Tips:
- Keep units consistent (don't mix inches and feet without converting first)
- Proportions assume the relationship is constant—if the relationship changes (discounts, fees, non-linear growth), a simple proportion won't apply
- Double-check that you placed numbers on the correct side (swapping values can change the result)
Proportion Formulas
Basic Proportion
a / b = c / d
Two ratios are equal
Cross-Multiplication Rule
Multiply diagonally across the equals sign:
a × d = b × c
Both fractions represent the same value, so their cross-products must match
Solving for a Missing Value
Solve for d
a/b = c/d
d = (b × c) / a
Solve for c
a/b = c/d
c = (a × d) / b
Solve for b
a/b = c/d
b = (a × d) / c
Solve for a
a/b = c/d
a = (b × c) / d
Example Calculations
Example 1: Solve for x in a Simple Proportion
Proportion: 2/5 = x/20
Cross-multiply: 2 × 20 = 5 × x → 40 = 5x
Solve: x = 40 ÷ 5 = 8
Result: x = 8
Example 2: Price Scaling
Problem: If 3 notebooks cost $12, how much do 5 notebooks cost?
Proportion: 3/12 = 5/x
Cross-multiply: 3x = 12 × 5 = 60
Solve: x = 60 ÷ 3 = 20
Result: $20
Example 3: Recipe Scaling
Problem: A recipe uses 4 cups of flour for 10 servings. How much flour for 25 servings?
Proportion: 4/10 = x/25
Cross-multiply: 4 × 25 = 10x → 100 = 10x
Solve: x = 10
Result: 10 cups of flour
Example 4: Map Scale Conversion
Problem: A map scale says 1 inch = 8 miles. If two towns are 3.5 inches apart, what is the real distance?
Proportion: 1/8 = 3.5/x
Cross-multiply: 1 × x = 8 × 3.5
Solve: x = 28
Result: 28 miles
Frequently Asked Questions
What is a proportion in simple terms?
A proportion states that two ratios are equal. It's a way to say "these two relationships match," like 2/3 = 4/6.
What is cross-multiplication, and why does it work?
Cross-multiplication means multiplying diagonally across the proportion: a/b = c/d becomes a×d = b×c. It works because both fractions represent the same value, so their cross-products must match.
When should I use a proportion calculator?
Use it when a relationship is constant—common cases include scaling recipes, unit conversions, mixture ratios, map scales, and "cost per item" problems.
What mistakes cause wrong answers in proportions?
Common mistakes include mixing units, placing numbers in the wrong positions, forgetting that the relationship must be constant, or including extra factors like fixed fees or discounts that break proportionality.
What's the difference between ratio and proportion?
A ratio compares quantities (like 3:2). A proportion states that two ratios are equal (like 3:2 = 12:8). Proportions are often used to solve for unknown values.
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