Divide the first numerator by the first denominator.
Use the proportion calculator to solve an equation in the forma/b = c/d. Leave exactly one value blank and the calculator will find it using cross multiplication.
Proportion solver
Enter three values and leave one blank
The calculator can solve for A, B, C, or D and show each calculation step.
a ÷ b = c ÷ d
ResultEnter three values and leave one field blank.
Completed proportion2/3 = 8/x
Cross productsA × D = B × C
Ratio statusWaiting for calculation
Calculation steps
- Enter three known values.
- Leave the value you want to calculate blank.
- Select Solve Proportion.
How to Use the Proportion Calculator
Enter values for three parts of the proportion and leave the unknown part blank. A proportion compares two equal ratios:
Standard proportiona/b = c/d
Select Solve Proportion. The calculator detects the missing position, applies cross multiplication, and displays the completed equation.
What Is a Proportion?
A proportion is an equation showing that two ratios are equal. For example, 2/3 and 8/12 are proportional because both ratios have the same decimal value.
Both ratios have the same value, so they form a proportion.
Proportion Formula
When a/b equals c/d, the cross products are equal:
Cross-multiplication rulea × d = b × c
This equation can be rearranged to solve for any missing value.
Solve for Aa = (b × c) ÷ d
Solve for Bb = (a × d) ÷ c
Solve for Cc = (a × d) ÷ b
Solve for Dd = (b × c) ÷ a
Example: Solve 2/3 = 8/x
Cross multiply three and eight, then divide by two:
Step 12 × x = 3 × 8
Step 22x = 24
Step 3x = 24 ÷ 2 = 12
The completed proportion is 2/3 = 8/12.
How to Check Whether Two Ratios Are Proportional
Enter all four values instead of leaving a blank. The calculator compares the cross products.
If a × d equals b × c, the ratios are proportional. If the cross products differ, the ratios are not proportional.
| Ratios | Cross products | Result |
|---|---|---|
| 2/3 and 8/12 | 2 × 12 = 3 × 8 | Proportional |
| 4/10 and 6/15 | 4 × 15 = 10 × 6 | Proportional |
| 3/5 and 8/10 | 3 × 10 ≠ 5 × 8 | Not proportional |
Proportions in Everyday Problems
Keep ingredient ratios consistent when changing the number of servings.
Compare a distance on a map with the corresponding real-world distance.
Calculate the cost of a different quantity using a fixed price relationship.
Increase or decrease dimensions while preserving the same shape and scale.
Direct and Inverse Proportion
In a direct proportion, both quantities change by the same scale factor. When one quantity doubles, the other also doubles.
In an inverse proportion, one quantity increases while the other decreases so that their product remains constant.
The ratio y/x remains constant.
The product x × y remains constant.
Common Proportion Mistakes
- Leaving more than one field blank when solving for an unknown.
- Reversing one ratio without reversing the other.
- Cross multiplying the wrong pairs of values.
- Using zero as a denominator.
- Rounding too early before the final answer is calculated.
Related Calculators
Frequently Asked Questions
How do I solve a proportion?
Cross multiply the two ratios and divide by the coefficient attached to the unknown value.
Can the calculator solve for any position?
Yes. Leave A, B, C, or D blank and enter the other three values.
What does cross multiplication mean?
Multiply the numerator of each ratio by the denominator of the opposite ratio.
Can a denominator be zero?
No. A ratio with a zero denominator is undefined.
How do I know whether two ratios are proportional?
Their cross products must be equal.