The standard proportion formula is a/b = c/d. Cross multiplication changes this into a × d = b × c. The equation can then be rearranged to calculate whichever value is missing.
Enter three values and leave one blank to solve a proportion, or enter all four values to check whether the ratios are equal.
Start with a/b = c/d and rearrange a × d = b × c for the unknown position.
Standard Proportion Formula
A proportion compares two ratios and states that they are equal.
The letters a and c are numerators, while b and d are denominators.
Neither denominator may equal zero.
Cross-Product Formula
Multiply a by d and multiply b by c.
If the original ratios are equal, these two products must match.
The Proportion Calculator displays both cross products.
Formula for Solving A
Begin with a times d equals b times c.
Divide both sides by d.
The resulting formula is a = (b × c) ÷ d.
Formula for Solving B
Rearrange the cross-product equation so b is isolated.
Divide a times d by c.
The formula is b = (a × d) ÷ c.
Formula for Solving C
Divide a times d by b.
This isolates c on one side of the equation.
The formula is c = (a × d) ÷ b.
Formula for Solving D
Divide b times c by a.
This isolates the second denominator.
The formula is d = (b × c) ÷ a.
Multiply the middle values and divide by d.
Multiply the outer values and divide by c.
Multiply the outer values and divide by b.
Multiply the middle values and divide by a.
Formula Example: Solve for D
Use the proportion 2/3 = 8/d.
Substitute the values into d = (b × c) ÷ a.
The result is d = (3 × 8) ÷ 2 = 12.
Formula Example: Solve for A
Use a/5 = 6/15.
Substitute into a = (b × c) ÷ d.
The calculation is a = (5 × 6) ÷ 15 = 2.
Formula Example: Solve for B
Use 4/b = 10/15.
Substitute into b = (a × d) ÷ c.
The calculation is b = (4 × 15) ÷ 10 = 6.
Formula Example: Solve for C
Use 3/5 = c/20.
Substitute into c = (a × d) ÷ b.
The calculation is c = (3 × 20) ÷ 5 = 12.
Why the Formula Works
Multiplying both sides of a/b = c/d by b and d removes the denominators.
This leaves a × d on one side and b × c on the other.
Because the same legal operation is performed on both sides, equality is preserved.
Formula Restrictions
The original denominators b and d cannot be zero.
When rearranging a formula, the value used as a divisor must also be nonzero.
A zero numerator may be valid, but it can create special cases when solving for a denominator.
Checking the Formula Result
Place the calculated value back into its original position.
Calculate a × d and b × c.
Equal products verify that the completed ratios are proportional.
Common Formula Errors
Do not use a × c = b × d.
Do not divide by a value that may be zero.
Preserve the original order of corresponding quantities.
Use parentheses around the multiplication before division when entering the formula.
Conclusion
The standard equation a/b = c/d becomes a × d = b × c.
Rearrange this equation according to the missing position.
Use the Proportion Calculator to select the missing value automatically.
FAQs
What is the general proportion formula?
The standard form is a/b = c/d.
What is the cross-product formula?
For equal ratios, a × d = b × c.
How do I solve for d?
Use d = (b × c) ÷ a.
Why can denominators not equal zero?
A ratio with a zero denominator is undefined.
How do I verify the formula result?
Substitute it into the proportion and compare the cross products.