Proportion Calculator

The Proportion Calculator solves an equation stating that two ratios are equal. In a/b=c/d, any one missing term can be found when the other three are known and the required denominators are nonzero.

Recognizing a constant of proportionality

Cross multiplication converts the proportion into ad=bc. The missing value is then isolated with ordinary algebra. This method works because both sides are multiplied by the same nonzero denominators; it is not a rule for unrelated fractions.

For a/b = c/d with nonzero denominators, the cross products satisfy ad = bc.

Enter the values in their mathematical roles

Place corresponding quantities in the same positions, enter three known values, and leave only the requested term unknown. Include units in your written setup even if the input fields accept numbers only. Reversing both ratios is valid; reversing only one is not.

The governing relationship

For a/b = c/d with nonzero denominators, the cross products satisfy ad = bc.

A compact example

If 3/5 = x/20, then 5x = 60 and x = 12.

Valid inputs and boundary cases

Denominators cannot be zero, and the compared pairs must represent the same relationship. Unit rates, scale drawings, recipes, and percent problems often form proportions, while fixed fees or curved relationships may not.

Read the answer in context

A proportion states that two ratios are equal; it does not prove unrelated quantities are proportional.

An independent check

Substitute the result and compare the two decimal ratios or their cross-products. Both sides should agree within rounding. Then ask whether increasing one quantity should increase or decrease the other; inverse variation requires a different setup.

Errors that change the answer

• Mismatching corresponding quantities
• Cross-multiplying unrelated expressions
• Allowing a zero denominator
• Rounding before isolating the unknown
• Assuming every two-variable problem is proportional

Continue with a related calculator

Continue with the Ratio Calculator or GCF Calculator. For everyday arithmetic and order-of-operations checks, use the Basic Calculator.

What this numerical result cannot decide

A correct proportion can still model the wrong situation. Check for a constant rate and a meaningful zero point before applying direct proportionality. Taxes, tariffs, discounts, and measurement conversions may contain additional terms.

A second way to understand the method

In a direct proportion y=kx, the ratio y/x remains constant. Several observed pairs can be checked by calculating that ratio for each one. If it changes beyond expected rounding or measurement error, a single proportion does not describe the data.

Unit rates offer a second solution path

For 5 notebooks costing $12, the unit price is $12÷5=$2.40. Seven notebooks at the same rate cost 7×$2.40=$16.80. Setting 5/12=7/x and cross-multiplying gives the same answer. Agreement between the unit-rate and proportion methods is a useful check.

Direct and inverse variation look different

At constant speed, distance is directly proportional to time. For a fixed job, however, the time may decrease as the number of equally productive workers increases; that is an inverse relationship. Before solving, describe in words what should happen to one quantity when the other increases. This prevents a neatly solved but backward proportion.

Percent problems are proportions with a base of 100

The question “18 is what percent of 60?” can be written 18/60=p/100. Cross multiplication gives 60p=1,800, so p=30. Keeping the part over the whole in both ratios prevents the common mistake of reversing the percentage relationship. For increases and decreases, distinguish the original base from the final value before forming the proportion.

Proportion Calculator FAQ

How do I solve x/8=3/4?

Cross-multiply to get 4x=24, then divide by 4: x=6.

Can a proportion contain decimals?

Yes. Keep enough precision or convert the decimals to fractions before solving.

What if both ratios have unknown values?

One equation with two unknowns usually needs another independent relationship.

For additional worked mathematics, see the free OpenStax Prealgebra 2e reference.