A proportion is an equation showing that two ratios are equal. For example, 2:3 = 4:6 is a proportion because both ratios represent the same value. Use the calculator above to find a missing term or to check whether two complete ratios are proportional.
This tool is part of our Basic Math Calculators collection.
How to Solve a Proportion
To solve a proportion, write the ratios as equal fractions and use cross multiplication. For A/B = C/D, the cross products must be equal:
- Write the two ratios in the same order.
- Identify the missing value.
- Cross multiply the opposite terms.
- Rearrange the equation to isolate the unknown.
- Divide to find the missing value.
- Check the answer by comparing the two ratios.
Proportion Formula
The standard proportion can be written as:
or
A/B = C/D
In a proportion, A and D are often called the extremes, while B and C are called the means. The cross-product property says that the product of the extremes equals the product of the means.
Formulas for Any Missing Value
Worked Examples
Example 1: Find the Missing Value
Problem: 3 : 5 = 12 : x
Cross multiply: 3x = 5 × 12
Simplify: 3x = 60
Divide by 3: x = 20
Check: 3/5 = 0.6 and 12/20 = 0.6
Answer: x = 20
Example 2: Decimal Proportion
Problem: 2.5 : 7.5 = 4 : x
Cross multiply: 2.5x = 7.5 × 4
Simplify: 2.5x = 30
Divide: x = 12
Check: 2.5/7.5 = 1/3 and 4/12 = 1/3
Example 3: Map Scale
A map uses a scale of 1 cm : 50,000 cm. If two points are 4.5 cm apart on the map:
Set up: 1 : 50,000 = 4.5 : x
Cross multiply: x = 50,000 × 4.5 = 225,000 cm
Convert: 225,000 cm = 2.25 km
Ratio vs. Proportion
| Aspect | Ratio | Proportion |
|---|---|---|
| Meaning | Compares two quantities | Shows that two ratios are equal |
| Example | 3:4 | 3:4 = 6:8 |
| Typical Use | Simplify or compare quantities | Find a missing value in equivalent ratios |
| Related Tool | Ratio Calculator | Proportion Calculator |
Common Uses of Proportions
| Use | Example |
|---|---|
| Price and quantity | If 5 items cost $10, find the cost of 12 items at the same rate. |
| Recipe scaling | Adjust ingredient quantities while keeping the same relative amounts. |
| Maps and scale drawings | Convert a measured map distance into an actual distance. |
| Image dimensions | Maintain the same width-to-height relationship when resizing. |
Using Fractions, Decimals, Negative Numbers, and Scientific Notation
The calculator accepts whole numbers and decimals directly. It also accepts fraction input such as 1/2 or -3/4, and scientific notation such as 2.5e3. Negative values are allowed where the resulting ratio is mathematically valid.
A denominator in a completed ratio cannot be zero. If a value would create an undefined ratio or an impossible division step, the calculator displays an inline error message.
For fraction conversion, you can also use our Fraction to Decimal Converter .
Common Mistakes When Solving Proportions
- Changing the order: Corresponding quantities must stay in the same positions.
- Cross-multiplying the wrong terms: Use A × D and B × C.
- Using inconsistent units: Convert measurements to compatible units first.
- Dividing by the wrong value: Isolate the unknown after cross multiplication.
- Ignoring zero denominators: A completed ratio cannot have a denominator of zero.
How to Check Your Answer
Substitute the calculated value back into the original proportion and compare the two ratios. For example, if the result is 3:5 = 12:20:
3/5 = 0.6
12/20 = 0.6
Because both ratios have the same value, the proportion is verified.
Last reviewed: July 21, 2026 — Formula, calculator logic, and worked examples checked for mathematical consistency.
Frequently Asked Questions
A proportion calculator finds a missing value when two ratios are equal. Enter three known values in A:B = C:D and leave one value blank. You can also enter all four values to check whether the two ratios are proportional.
For A/B = C/D, the cross-product formula is A × D = B × C. The equation is then rearranged to isolate whichever value is missing.
Yes. Leave A, B, C, or D blank and enter the other three values. The calculator automatically detects the missing position and uses the correct rearranged formula.
Yes. You can enter decimals such as 2.5 and fractions such as 1/2 or -3/4. The calculator also accepts scientific notation such as 2.5e3.
Enter all four values. The calculator compares the cross products A × D and B × C. If the cross products are equal within normal numeric precision, the two ratios form a proportion.
A ratio compares two quantities, such as 2:3. A proportion states that two ratios are equal, such as 2:3 = 4:6.
