Proportion Calculator
Proportion Calculator is a free online tool that helps you quickly and effortlessly solve proportion problems. With step-by-step calculations, it’s perfect for students, teachers, and professionals alike. Simply enter any three of the four values in a proportion, and the tool will instantly find the missing one.
Just input any two ratios with one unknown, and the Proportion Calculator will solve for the missing value using cross-multiplication and equation simplification.
For example, entering $\frac{2}{3} = \frac{c}{6}$ will solve for c = 4.
In addition to results, the calculator provides a clear, step-by-step explanation of how the Proportion process works. You can also toggle the visibility of steps for deeper understanding and flexibility while solving proportions and equations.
How to Use the Online Proportion Calculator?
1. Enter the Values
Fill in the known values for A, B, C, and D in the ratio equation $\frac{A}{B} = \frac{C}{D}$ or solve for the missing value if one is unknown.
2. Click “Calculate”
Press the Calculate button to solve for the unknown variable using the cross multiplication method.
3. View the Results
The calculator will instantly show the solution. For example, entering $A=2$, $B=3$, $C=c$, and $D=6$ will solve for $x=4$.
4. Show or Hide Steps
Click Show Steps to view a detailed, step-by-step breakdown of the calculation process. Select Hide Steps for a cleaner view.
5. Reset for a New Calculation
Click Reset to clear all fields and start a new Proportion problem.
Proportion Calculator
What is a Proportion Calculator?
A ProportionCalculator is a fast, easy-to-use online tool that helps you solve proportion problems where two fractions are set equal to each other. Whether you’re solving for a missing value in $\frac{A}{B} = \frac{C}{D}$ or checking if two ratios are equivalent, this calculator provides instant answers along with clear, step-by-step explanations.
What is Proportion?
A proportion is an equation that states that two ratios or fractions are equal.
In simple terms: If two fractions represent the same value, they form a proportion. This relationship is used to compare quantities or solve for unknowns using the equality of two ratios.
Example:
If: $\frac{A}{B} = \frac{C}{D}$
Then: A×D=B×C
Example 1: Given:
$\frac{2}{3} = \frac{c}{6} $
Step 1: Cross multiply:
$2 \times 6 = 3 \times c$
Step 2: Simplify:
$12 = 3c$
Step 3: Solve for x:
$c = 4$
How to Manually Solve a Problem of Proportion
To manually solve a proportion and find the missing value, use cross multiplication.
Example 1:
Given:
$\frac{5}{3} = \frac{c}{6}$
Step 1: Cross multiply
$5 \times 6 = 3 \times c$
Step 2: Simplify
$30 = 3c$
Step 3: Solve for $c$
$c = \frac{30}{3} = 10$
Example 2:
Given:
$\frac{15}{b} = \frac{7}{6}$
Step 1: Cross multiply
$15 \times 6 = b \times 7$
Step 2: Simplify
$90 = 7b$
Step 3: Solve for $b$
$b = \frac{90}{7}$
Example 3:
Given:
$\frac{8}{x} = \frac{4}{10}$
Step 1: Cross multiply
$8 \times 10 = x \times 4$
Step 2: Simplify
$80 = 4x$
Step 3: Solve for $x$
$x = \frac{80}{4} = 20$
Example 4:
Given:
$\frac{a}{12} = \frac{9}{16}$
Step 1: Cross multiply
$a \times 16 = 12 \times 9$
Step 2: Simplify
$16a = 108$
Step 3: Solve for $a$
$a = \frac{108}{16} = 6.75$
Example 5:
Given:
$\frac{11}{7} = \frac{y}{14}$
Step 1: Cross multiply
$11 \times 14 = 7 \times y$
Step 2: Simplify
$154 = 7y$
Step 3: Solve for $y$
$y = \frac{154}{7} = 22$
FAQs on Proportion Calculator
1. What is a Proportion Calculator?
A Proportion Calculator is a tool that helps you find a missing value in a ratio or proportion equation using the concept of cross multiplication.
2. How does the Proportion Calculator work?
It uses the rule: if $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$. You enter any three values, and the calculator solves for the missing one.
3. What types of problems can it solve?
It can solve for missing numerators or denominators in fractions, scale models, and real-life proportional relationships like speed, distance, and time.
4. Can I solve proportions manually?
Yes! Simply cross multiply and solve the resulting equation. For example, if $\frac{5}{x} = \frac{10}{2}$, then $5 \times 2 = x \times 10$, so $x = 1$.
5. Is the calculator suitable for students?
Absolutely. It’s a great learning aid for school students, helping them check answers and understand the steps in solving proportion problems.
6. Does it support decimals and fractions?
Yes. You can input integers, decimals, or proper/improper fractions, and the calculator will handle them accurately.
7. What is cross multiplication in proportions?
Cross multiplication means multiplying diagonally across the equal sign: numerator of one fraction × denominator of the other. It’s the core method for solving proportions.
8. Do I need to simplify the fractions before using the calculator?
No. The calculator handles all simplifications internally. However, understanding the simplification process is good practice for learning.
9. Is there a formula used by the calculator?
Yes. It uses the formula:
If $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$.
Solve for the unknown using algebra.
10. Can I use it on mobile devices?
Yes, most Proportion Calculators are fully responsive and work on smartphones, tablets, and desktops.
Conclusion: Just input any two ratios with one unknown, and the Proportion Calculator will solve for the missing value using cross-multiplication and equation simplification.
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