| A | B | C | Fourth proportional | Note |
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Cross Multiplication Calculator: Fourth Proportional
This online tool lets you instantly calculate the fourth proportional using cross multiplication. Enter three known values of a proportion (A, B, C) and get the missing value D in one click. Ideal for rule-of-three problems, proportionality calculations and everyday problems.
What is cross multiplication?
Cross multiplication is a mathematical method for solving a proportion when three of the four values are known. If two quantities A and B are proportional to C and D, we write:
A / B = C / D
The cross multiplication rule says that the product of the extremes equals the product of the means: A × D = B × C. From this we derive the unknown value D (the fourth proportional) with the formula:
D = (B × C) / A
This technique is also known as the rule of three.
What is the fourth proportional?
The fourth proportional is the unknown value D in a proportion A:B = C:D. That is precisely what cross multiplication calculates: from three known terms, we determine the missing fourth term.
Fourth proportional example:
If 3 lb of apples cost $6, how much do 5 lb cost? We set up the proportion:
3 / 6 = 5 / D → D = (6 × 5) / 3 = $10
The fourth proportional here is $10. That is the result the calculator displays automatically.
How to use the cross multiplication calculator?
It's simple: fill in the three known values of your proportion, and the result (fourth proportional) is displayed automatically.
- Field A: first value of the proportion (e.g. 3 lb).
- Field B: value associated with A (e.g. $6).
- Field C: new value for which you are looking for the equivalent (e.g. 5 lb).
- Result field: the fourth proportional, calculated by cross multiplication, is displayed here (e.g. $10).
Cross multiplication use cases
Cross multiplication applies to many concrete situations:
- Cooking: adapting a recipe designed for 4 people to 6 people.
- Finance: calculating a prorated rent, salary or commercial discount.
- Geography: reading a map scale (1 in = 50 miles).
- Physics / chemistry: calculating concentrations or dosages.
- Construction: estimating an area or volume from a partial measurement.
Save and export the results
You can save your cross multiplication calculations by pressing the Save button. The results can then be exported in CSV or PDF format.
Keyboard shortcuts
m ⇝ Clear
f ⇝ Save