Proportion Calculator
Proportion Calculator
Solve for the missing value in a direct proportion using three known terms.
Enter your values
Enter values and select Calculate.
How to Use the Proportion Calculator
Use this Proportion Calculator to solve a direct proportion when three terms are known and one term is missing. Enter A, B and C in the form A : B = C : x. The calculator works out the value of x using the relationship between the two ratios.
- Enter the first term in the A field.
- Enter the second term in the B field.
- Enter the third term in the C field.
- Select Calculate to find the missing fourth term.
- Review the result and select Clear to perform another calculation.
Use values that belong to the same proportional relationship. The first term A cannot be zero because it is used as the divisor in the formula.
What Is a Proportion?
A proportion is an equation that states that two ratios are equal. For example, 2 : 4 and 3 : 6 are equivalent ratios because both simplify to 1 : 2. Proportions are useful for comparing quantities that change at a consistent rate.
Proportion Formula
A : B = C : x
A / B = C / x
Cross-multiply: A × x = B × C
Missing value: x = (B × C) ÷ A
This formula assumes a direct proportion in the order shown. Check that the values and their units are placed in the correct positions before calculating.
Worked Examples
Example 1: Find the missing value
2 : 4 = 3 : x
x = (4 × 3) ÷ 2
Result: x = 6.
Example 2: Recipe quantities
A recipe uses 2 cups of flour for 4 servings. How much flour is needed for 6 servings?
x = (4 × 6) ÷ 2
Result: 12 cups, using the stated ratio arrangement.
Example 3: Map scale
If 1 cm represents 5 km, what distance does 3 cm represent?
x = (5 × 3) ÷ 1
Result: 15 km.
Direct Proportion and Inverse Proportion
In a direct proportion, two quantities increase or decrease together at a constant ratio. In an inverse proportion, one quantity increases as the other decreases so that their product remains constant. This calculator solves a direct proportion only; use an inverse-proportion method when the relationship is inverse.
Practical Uses of Proportions
- Cooking: scale ingredient quantities when changing the number of servings.
- Maps: convert map distances into real-world distances using a scale.
- Shopping: compare quantities and unit prices.
- Construction: scale measurements and material quantities.
- Education: solve ratio, rate and equivalent-fraction problems.
Frequently Asked Questions
1. What does a proportion mean?
A proportion is a statement that two ratios are equal, such as 2/4 = 3/6.
2. How do I solve a proportion with one missing value?
Write the two ratios as an equation, cross-multiply, and divide by the coefficient of the missing value.
3. What formula does this calculator use?
For A : B = C : x, it uses x = (B × C) ÷ A.
4. What is direct proportion?
Direct proportion describes two quantities that change in the same direction while their ratio remains constant.
5. Is direct proportion the same as inverse proportion?
No. In direct proportion, quantities change together at a constant ratio. In inverse proportion, one quantity increases as the other decreases while their product remains constant.
6. Can the first value A be zero?
No. A must not be zero because the formula divides B × C by A.
7. Do all three values need the same unit?
Not necessarily, but the units must be arranged consistently so that the ratios compare like quantities correctly.
8. Where are proportions used in everyday life?
Proportions are used in recipes, map scales, construction measurements, price comparisons and other situations involving equivalent ratios.
9. Can proportions include decimal values?
Yes. Proportions can include whole numbers, decimals or fractions, provided the values represent a valid relationship.
10. Is this Proportion Calculator free?
Yes. You can use this online calculator to solve direct proportion problems without a fee.
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