Rule of three
v1referenciaequivale_acantidadresultadoHow it is worked out
If one amount equals another, find what a third amount comes to at the same rate.
The rule of three solves proportions: cross multiply and divide. If 4 units cost 20, then 7 cost 20 times 7 divided by 4, which is 35. All it needs is for the relationship between the first two amounts to hold.
The expression that runs
equivale_a * cantidad / referenciaThe fields arrive with an example filled in: put your own numbers in and run it again. You can also edit the formula to fit your case.
What if the formula were yours?
This calculator is not hand-written: it is an Axioma formula. Open it in the editor to see how it is built, adapt it to your case and create the ones you need.
How cross multiplying works
The figures form two pairs: 4 equals 20, and 7 equals what you are after. Multiply the two amounts sitting diagonally from each other, 20 by 7, and divide by the one left over: 140 over 4 is 35.
It works because the ratio stays constant: if 4 are worth 20, each unit is worth 5, and seven units are worth 35. Cross multiplying does both of those steps at once.
Direct or inverse, which is not the same thing
This calculator solves the direct proportion, where both amounts move together: more units, more money; more kilometres, more fuel.
When one goes up as the other goes down the proportion is inverse and the arithmetic flips: if three people take six hours, six people take three, not twelve. There you multiply the two known amounts and divide by the third, which is a different formula and one you can write in the editor starting from this one.
Where it is used without being named
It is the calculation behind scaling a recipe up for more guests, mixing more paint at the same ratio, going from price per box to price per unit, or splitting a cost in proportion to what each person used.
It is worth checking the units match before working it out: if one side is in kilos and the other in grams the answer lands a thousand times off, and the formula has no way to warn you.
Frequently asked questions
- How do I know whether it is direct or inverse?
- Ask what happens if the first amount doubles. If the other doubles too it is direct; if it halves it is inverse, and the arithmetic changes.
- Can I use it with percentages?
- Yes, by treating the percentage as one of the amounts: if 250,000 is 100 %, then 15 % comes out of the same cross multiplication.
- What if one of the amounts is zero?
- If the known reference amount is zero there is no proportion to hold and the result does not exist: nothing can be divided by zero.