How To Solve A Proportion Calculator

A proportion says two ratios are equal, which means one unknown journey holds all the information you need. The entire skill is deciding which quantity sits above which in the division.

First quantity (known pair)Units, servings, workers — whatever you have a complete pair for.Its matching valueCost, grams, hours — the other half of the known pair.The quantity you are scaling to

Value for the new quantity

Value per single unit: 2.3333
Scale factor applied: 7
Cross-product check (should match both ways): 147

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

a / b = c / d, so d = c x b / a

a, b: The complete pair you already know both parts of
c: The quantity you are scaling to
d: The unknown value being solved for
b / a: The unit rate — the step that makes the reasoning explicit

How to check the result by hand

1
Write the known pair as a fraction
Three units costing seven dollars becomes 3/7 or 7/3 — pick whichever order you will use consistently, and note what each divisor means.
2
Set up the second fraction in the same order
Whichever quantity went on top in the first fraction goes on top again. This single consistency requirement prevents nearly every inverted answer.
3
Solve for the missing term
Cross multiply so the products along each diagonal are equal, then divide. Here 3 x d = 7 x 21, so d = 147 / 3 = 49.
4
Or use the unit rate instead
Compute 7 / 3 = 2.3333 per unit, then multiply by 21 giving 49. When the two routes disagree, one of your fractions was inverted.
5
Check the direction before accepting it
More units should cost more in a direct proportion. If the answer suggests twenty-one units cost less than three, the ratio has been flipped or the relationship is inverse rather than direct.

For worked examples, common mistakes and the limits of this formula, read the full How To Solve A Proportion page.