Proportion calculator
Solve a : b = c : d for any of the four terms.
Fill in the fields and the result will appear here automatically.
Solve a/b = c/d for the selected term. The unknown field is hidden; enter only the three known values. Denominators b and d must remain nonzero after solving. The diagonally opposite term must also be nonzero for a unique answer using the selected formula. Zero numerators a or c are allowed. The result shows the missing term, completed proportion, quotient and cross products.
How it works
Formula and logic
For b ≠ 0 and d ≠ 0, a/b = c/d is equivalent to ad = bc. Hence a = bc/d, b = ad/c, c = ad/b and d = bc/a, requiring a nonzero divisor in the selected formula. The intermediate binary product is retained exactly before the quotient is rounded.
Example
In 2 : 3 = 4 : d the fourth term is 3 × 4 ÷ 2 = 6.
Fields and units
- Term to find — list option
- Term a — unitless
- Term b — unitless
- Term c — unitless
- Term d — unitless
How to use
- — Choose which term to find.
- — Fill in the three known terms.
- — Read the answer and the check.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: equal ratios with nonzero denominators
- Limitation
- All three known values must be finite. The missing term, quotient and displayed products must fit the numeric range without a nonzero value rounding to zero; otherwise an error is shown. Ordinary notation rounds to four decimal places; very small and large values use scientific notation.
FAQ
Why is one field hidden?
The term you are solving for is computed, so leaving it visible would invite a value that is then ignored.
Which term cannot be zero?
The original equality requires b ≠ 0 and d ≠ 0. The diagonally opposite term must also be nonzero for division in the chosen formula. A zero divisor can lead to no solution or many solutions; this page does not classify those cases.
Can the terms be negative?
Yes, finite negative and fractional values are allowed when the denominators and formula divisor are nonzero. A zero numerator is valid, but 0/0 is not a defined ratio.
What is the cross-product check?
The products a·d and b·c use the internally computed missing term before display rounding. This is a numeric check, not a proof of exact decimal data: the rounded term shown may not reproduce the products literally.