Proportion Calculator
Solve a proportion: find the missing value in a : b = c : d.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
A proportion states that two ratios are equal. Given three of the four values, cross multiplication gives the fourth — a calculation used constantly in scaling recipes, drawings and unit rates.
Worked example
calculated with the default values below
A 3 · B 4 · C 9 Missing value D 12.0000 · A ÷ B 0.750000 · C ÷ D 0.750000
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
d = b × c ÷ a (a : b = c : d)
- a
- Known term a
- b
- Known term b
- c
- Known term c
- d
- Unknown term
For a:b = c:d, d = b×c÷a; zero divisors are rejected.
Frequently asked questions
Why does solving for D use cross multiplication instead of subtraction?
A proportion says A/B equals C/D, so the missing D is B times C divided by A, not a difference between the ratios. With the defaults 3/4 equals 9/D the cross product gives D equals 4 times 9 divided by 3, or 12, and the tool also reports A divided by B as 0.75 and C divided by D as 0.75 to confirm the sides match. A must be nonzero; when A = 0, the calculator reports an input error and leaves the results blank.