Proportion Calculator with Exact Steps
Solve one missing value in A/B = C/D or check whether four known values form an exact proportion. Use whole numbers, decimals, fractions, mixed numbers or scientific notation.
Last Updated: July 26, 2026
Online Proportion Calculator
Leave one field empty or type x to solve it. Fill all four fields to test whether the two ratios are equivalent.
Your answer and exact verification will appear here.
Calculation steps
- Enter three known values and leave one field empty.
Equivalent ratio examples
| Scale | Equivalent to the first ratio | Exact check |
|---|---|---|
| Calculate a valid proportion to see scaled equivalents. | ||
Recent calculations
- Your last six results will appear here.
How to Use This Proportion Calculator
- Place the two ratios in the form A/B = C/D. A and C are numerators. B and D are denominators.
- Enter three known values. Leave the value you need empty, or type x or a question mark in its field.
- Select Calculate Proportion. The tool solves the unknown with exact rational arithmetic and checks the answer by cross multiplication.
- Review the exact fraction, rounded decimal, completed equation, scale factor and calculation steps.
- To verify a completed equation, enter all four values. The result will state whether the ratios are exactly equivalent.
You may enter integers, signed decimals, simple fractions, mixed numbers and scientific notation. Examples include 18, -2.5, 3/4, -1 1/2 and 2.5e3. Do not use commas as thousands separators. Enter 1500 instead of 1,500.
What Is a Proportion?
A proportion is an equation stating that two ratios have the same value. The equation 2/3 = 10/15 is a proportion because both sides simplify to 2/3. A proportion compares relationships rather than isolated totals. The numbers may change while the relative relationship stays constant.
The standard form is A/B = C/D, where B and D cannot be zero. A and D are called the extremes. B and C are called the means. For every valid proportion, the product of the extremes equals the product of the means:
A × D = B × C
This cross-product identity is the foundation of the solver. It finds one unknown without estimating either ratio first. The calculator stores valid finite inputs as reduced fractions, so common decimal and fraction examples remain exact until the decimal display is created.
Proportion Formulas for Any Missing Value
| Unknown | Formula | Required condition |
|---|---|---|
| A | A = (B × C) ÷ D | D must not be zero. |
| B | B = (A × D) ÷ C | C must permit one nonzero denominator solution. |
| C | C = (A × D) ÷ B | B must not be zero. |
| D | D = (B × C) ÷ A | A must permit one nonzero denominator solution. |
| Verification | Compare A × D with B × C | B and D must not be zero. |
Worked Example: Solve x/12 = 5/20
Here A is unknown, B = 12, C = 5 and D = 20. Cross multiply first, then divide by the value attached to the unknown.
20x = 12 × 5
20x = 60
x = 60 ÷ 20
x = 3
Substitute 3 into the original equation to verify the result. The left side is 3/12 = 1/4. The right side is 5/20 = 1/4. The cross-products are also equal because 3 × 20 = 12 × 5 = 60.
Example with a Fraction Answer
Consider 7/9 = x/12. The missing value is C, so use C = A × D ÷ B.
x = 84/9
x = 28/3
x = 9 1/3
The exact answer is 28/3. Its mixed-number form is 9 1/3, and its decimal form is approximately 9.333333333333. Keeping the exact fraction prevents a repeating decimal from being mistaken for a terminating value. The calculator shows both forms when useful.
How Cross Multiplication Works
Start with A/B = C/D. Multiply both sides by B and D. Because B and D are nonzero, the operations preserve equality. The denominators cancel, leaving A × D = B × C. You can then isolate the unknown by dividing both sides by its known coefficient.
Cross multiplication is reliable when the original expressions are ratios with nonzero denominators. It should not be applied blindly to an undefined ratio. If B or D is zero, the displayed fraction has no real-number value. The calculator blocks those cases and explains which denominator needs attention.
Checking Whether Two Ratios Are Proportional
Fill all four fields to use the tool as an equivalence checker. For 4/6 = 10/15, the cross-products are 4 × 15 = 60 and 6 × 10 = 60. Equal products prove that the ratios form a proportion.
For 4/6 and 9/15, the products are 60 and 54. The equation is not a proportion, even though the displayed decimal values may look close when rounded. Exact cross-products provide a clearer check than comparing short decimal approximations.
Decimals, Fractions and Mixed Numbers
Decimal inputs are converted to fractions based on their written place value. For example, 2.5 becomes 5/2 and 0.125 becomes 1/8. A scientific-notation input such as 2.5e3 becomes 2500. This conversion lets the calculator solve with integer-based rational arithmetic instead of relying on binary floating-point equality.
Simple fractions may use signed numerators or denominators, such as -3/4 or 3/-4. Mixed numbers may also be signed, such as -1 1/2. A negative sign applies to the complete mixed number. Final fractions are reduced, and their denominators are normalized to positive values.
Long repeating decimals are rounded only for display. The exact fraction remains the primary result. If a practical task needs a fixed number of decimal places, apply the rounding rule required by that task after solving the proportion.
Zero, No-Solution and Multiple-Solution Cases
Zero is valid in a numerator, but never in a denominator. For example, 0/5 = 0/8 is a valid proportion. In contrast, 3/0 is undefined. The same restriction applies when the calculated unknown would become denominator B or D.
Some equations do not have one unique answer. If 0/B = 0/5 and B is unknown, every nonzero B satisfies the equation. That is an infinite family of solutions, so one value cannot be selected without another condition. If 2/B = 0/5, no finite nonzero B works. The calculator identifies these cases instead of returning a misleading zero or division error.
Direct and Inverse Proportion
Direct proportion
Two quantities are directly proportional when their quotient stays constant. If y = kx, then y/x = k. Doubling x doubles y. A price at a fixed unit rate is a common example. If 3 notebooks cost 12 units of currency, 5 notebooks cost x where 3/5 = 12/x, giving x = 20.
Inverse proportion
Two quantities are inversely proportional when their product stays constant. If y = k/x, then xy = k. Doubling one quantity halves the other. For a fixed job, workers and completion time may follow this model only when productivity and conditions stay constant.
The calculator uses the standard equal-ratios form. To solve an inverse problem, reverse one pair before entering it. If x1 × y1 = x2 × y2, rewrite it as x1/x2 = y2/y1. Check that an inverse model fits the real situation before using this rearrangement.
Ratio, Rate, Fraction and Proportion
| Concept | Meaning | Example |
|---|---|---|
| Ratio | Compares the relative size of quantities. | 3:5 |
| Rate | Compares quantities with different units. | 180 km in 3 hours |
| Fraction | Represents division or part of a whole. | 3/5 |
| Proportion | States that two ratios are equal. | 3/5 = 12/20 |
| Percentage | Expresses a ratio per 100. | 3/5 = 60% |
A ratio is one comparison. A proportion is an equality between two comparisons. A rate includes units, while a fraction is a number that may represent a ratio. Keeping the labels and units attached to the values helps you choose the correct arrangement.
Practical Uses of Proportions
- Recipes: scale every ingredient by the same factor while preserving taste and texture.
- Maps and drawings: convert a measured length using the stated scale.
- Unit prices: compare packages after expressing cost for the same quantity.
- Percent problems: solve part/whole = percent/100.
- Similar figures: find a corresponding side when the geometric similarity conditions are met.
- Dosage and mixtures: perform a mathematical check, then follow the qualified professional or product instructions that govern the real decision.
Units must be consistent within corresponding positions. Convert centimetres to metres, minutes to hours or grams to kilograms before solving when the equation mixes units. A correct calculation cannot repair an incorrectly arranged or physically unsuitable model.
Common Proportion Mistakes
- Changing the order of only one ratio. Corresponding quantities must occupy matching positions.
- Using zero as B or D. Division by zero is undefined.
- Rounding a repeating decimal before cross multiplication. Keep exact fractions as long as possible.
- Treating every relationship as directly proportional. Some relationships are inverse, nonlinear or affected by fixed costs.
- Omitting units. A numerical answer needs the unit belonging to its position in the equation.
- Entering more than one unknown. One proportion equation usually does not determine two independent missing values.
Accuracy and Calculator Limits
The solver accepts up to 50 written digits per value and scientific exponents from -100 through 100. It reduces rational values with integer arithmetic and compares cross-products exactly. Decimal outputs are rounded to 12 places for readability, so the decimal line may be approximate even when the fraction line is exact.
Calculations run locally in your browser. Inputs are not needed by a server to produce the result. This tool solves one equation in the form A/B = C/D. It does not determine whether your real-world assumptions, measurement accuracy or chosen units are appropriate.
Method and Review Basis
The calculator follows the standard definition of a proportion and the cross-product property described in OpenStax Prealgebra 2e. The direct and inverse relationship notes follow the constant-quotient and constant-product models in OpenStax Elementary Algebra 2e. Examples and edge cases were independently checked with exact substitution and cross-products.
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Frequently Asked Questions
What is a proportion calculator?
A proportion calculator solves one missing value in A/B = C/D or checks whether two completed ratios are equal. It uses the identity A × D = B × C.
How do I solve a proportion with x?
Enter the three known values and leave the x position empty, or type x there. The calculator cross multiplies, isolates x and verifies the completed equation.
Can the unknown appear in any position?
Yes. A, B, C or D may be unknown. Exactly one field must be empty or marked x when you want a unique solved value.
Does the calculator accept fractions?
Yes. Enter values such as 3/4, -5/8 or 1 1/2. The calculator keeps an exact reduced fraction and also shows a decimal result.
Does it accept decimals and scientific notation?
Yes. Inputs such as 2.5, 0.125 and 2.5e3 are accepted. Written decimals are converted to exact fractions before solving.
How do I check if two ratios form a proportion?
Fill all four fields. If A × D equals B × C and both denominators are nonzero, the ratios form an exact proportion.
Why are zero denominators rejected?
A fraction with denominator zero is undefined. Therefore B and D must be nonzero in the equation A/B = C/D.
Can a numerator equal zero?
Yes. Zero is valid in A or C. For example, 0/5 = 0/8 is a valid proportion because both ratios equal zero.
Why does a problem have no unique solution?
Some zero cases produce no solution or infinitely many nonzero denominator values. More than one unknown also needs another independent condition.
What is the difference between a ratio and a proportion?
A ratio compares quantities, such as 2:3. A proportion states that two ratios are equal, such as 2/3 = 10/15.
How do I enter an inverse proportion?
Rewrite x1 × y1 = x2 × y2 as x1/x2 = y2/y1, then place those four values in the matching fields.
Is the decimal or fraction answer more accurate?
The reduced fraction is exact. The decimal display is rounded to 12 places when the value does not terminate within that limit.
Disclaimer: This calculator provides general mathematical estimates for education and planning. Verify inputs, units and rounding before using a result for financial, medical, engineering or other important decisions.