How to Use
- 1.
For a missing value, enter any three values in A/B = C/D and leave exactly one blank.
- 2.
Use a fraction such as 3/4, a decimal, an integer, or a negative value.
- 3.
Review the cross-multiplication steps, decimal answer, simplified fraction, and verification.
- 4.
Open Ratios to simplify or compare ratios, split a quantity, scale terms, or calculate a percentage.
- 5.
Use Direct / inverse or Continued / compound for those proportion models, or Practice to try a generated question.
- 6.
Copy the answer or LaTeX, create a share link, download a text summary, or print/save as PDF.
Features
Solve A/B = C/D with any one value left blank
Cross-multiplication steps and substitution check
Integer, decimal, fraction, and negative-value support
Simplify two-term and three-term ratios
Compare equivalent ratios and identify the larger ratio
Split a quantity proportionally and scale a ratio
Direct, inverse, continued, and compound proportion calculators
Part-to-whole percentage, practice mode, copy, share, print, and LaTeX
Frequently Asked Questions
How do I solve a proportion with a missing value?+
Write the values in matching order as A/B = C/D, leave the unknown field blank, and enter the other three values. The calculator cross-multiplies and solves for the missing value.
What is the cross-multiplication formula?+
If A/B = C/D and the denominators are nonzero, then A × D = B × C. This equation can be rearranged to find any one missing term.
Can I enter fractions and negative values?+
Yes. Enter fractions such as 3/4, decimals, integers, or negative values. The result is reduced to a simplified fraction and also shown as a decimal.
How do I simplify a ratio such as 12:18?+
Divide both terms by their greatest common factor. For 12:18, dividing each term by 6 gives the simplified ratio 2:3.
Can I split an amount using a ratio?+
Yes. Enter the amount and ratio terms. The calculator allocates the amount according to each term's share of the total parts; for example, 2:3 divides 500 into 200 and 300.
What is the difference between direct and inverse proportion?+
In direct proportion, y/x is constant and y = kx. In inverse proportion, x × y is constant and y = k/x. Choose a model only when it fits the relationship being described.
How do I find the middle term in a continued proportion?+
If a:b = b:c, then b² = a × c, so the real middle term is b = √(a × c). The calculator gives an exact fraction or integer when possible, otherwise it labels the decimal as an approximation.
How does the compound proportion calculator work?+
It applies the explicit model y₂ = y₁ × (new direct factor 1 / old factor 1) × (new direct factor 2 / old factor 2) × (old inverse factor / new inverse factor). Check that your situation follows this direct/inverse relationship before relying on the result.
Why can't a proportion have a zero denominator?+
Division by zero is undefined, so a ratio with a zero denominator does not have a defined value. The calculator flags this instead of treating it as an ordinary ratio.
Are my calculations uploaded or saved?+
Calculations run in your browser. Recent solved proportions may be saved in local browser storage on this device; they are not uploaded to WebToolsEdge.
About this tool
Free Proportion Calculator
Use this proportion calculator to solve for a missing value in A/B = C/D. Enter any three values and leave one field blank to calculate the fourth. The calculator accepts integers, decimals, fractions, and negative values, then displays the result as a simplified fraction and decimal with a cross-multiplication check.
## Solve proportions with cross-multiplication
For a proportion A/B = C/D, cross-multiplication gives A × D = B × C. The calculator uses this relationship to isolate the blank value, then checks the completed ratios. A denominator of zero makes a ratio undefined, so the tool reports an error instead of returning a misleading result.
## Simplify, compare, and scale ratios
Enter a two-term ratio such as 12:18 to simplify it to 2:3, or add a third term for ratios such as 2:3:5. Compare two ratios to check whether they are equal and see which is larger. You can also scale a ratio or divide a quantity into shares based on its terms. For example, a 2:3 split of 500 allocates 200 and 300.
## Direct and inverse proportion
Direct proportion follows y = kx, where the ratio y/x stays constant. Inverse proportion follows y = k/x, where x × y stays constant. Choose the relationship, enter a known pair and a new x-value, and the calculator estimates the corresponding y-value. Use this only when the variables genuinely follow that relationship.
## Continued and compound proportions
For a continued proportion a:b = b:c, the middle term is the geometric mean b = √(a × c). The calculator shows an exact fraction or integer when possible and an approximation when the square root is irrational. A compound proportion can model a result that varies directly with two factors and inversely with another: y₂ = y₁ × (new₁ / old₁) × (new₂ / old₂) × (old inverse / new inverse). Confirm that this relationship matches the quantities in your problem before using the result.
## Fractions, percentages, and practice
The ratio workspace also converts a part-to-whole ratio into a percentage. Practice problems provide instant feedback, and the step summary can be copied, shared as a link, or printed to PDF. Calculations run in your browser; recent solved proportions are stored locally on this device.
Proportions are useful in recipe scaling, maps, scale drawings, unit-price comparisons, similar triangles, and other everyday math. Check that units and term order match before applying a proportion. This tool is a general math aid and does not verify measurements, exchange rates, recipes, or real-world assumptions.
For percentage increase, decrease, or part-of-whole calculations, use the Percentage Calculator. For sale-price changes, try the Discount Calculator.