Online rule of three calculator + simple explanation

The rule of three is a useful mathematical tool for calculating a ratio of different values. So that you don't have to do this laboriously in your head, we have created a Online rule of three calculator developed.

With the rule of three calculator, you can quickly and easily calculate a ratio, which is useful for percentage calculations, for example.

Quick guide to the rule of three calculator

In our online rule of three calculator, all you have to do is enter your known values and the type of calculation.

Known relationship: Here you have to enter the ratio you know. E.g. 4 rolls cost CHF 6.
Ratio to be calculated: Here you can enter the result you want to know. For example, how much 5 rolls cost.
Type of calculation: For the type of calculation, you must choose between proportional and antiproportional. Proportional basically means "the more, the more", while antiproportional stands for "the more, the less". More rolls cost more, so in this case it would be proportional.

If you are unsure about the type of calculation, you will find explanations and examples for both cases below.

Then you can simply click on "Calculate rule of three" and get the result.

The most important facts at a glance

With a rule of three Values calculatedwhich in a certain Relationship with other values. In principle, three values are known and the fourth is to be calculated.

A distinction is made between a proportional and one antiproportional Calculation. The former applies in most cases and basically means "the more, the more". The second case stands for "the more, the less".

What is a rule of three?

A rule of three is a mathematical calculation in which you put three known quantities in relation to each other and thus determine a fourth quantity. The best-known application for the rule of three is calculating percentages.

The name of the rule of three could have two origins. It could either come from the fact that three values are used to calculate a third. However, many textbooks also explain that the calculation is carried out using three sets:

Known relationship
Relationship to a unit
Ratio to be calculated.

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How is the rule of three calculated?

Rule of three formula

The Formula for the rule of three consists as said of three sets and basically looks like this:

Three known variables are set in relation to each other
The known allocation is calculated back to one unit (i.e. 1)
The individual unit is now multiplied by the third variable.

In concrete terms, it looks like this:

If 12 apples cost CHF 3.60, how much do 8 apples cost?

12 apples are set in relation to CHF 3.60. We know that 12 apples cost 3.60.
Now we calculate this down to one unit, i.e. 1 apple. To do this, we calculate 3.60 / 12. 1 apple therefore costs CHF 0.30.
Now we multiply the individual unit by the third quantity. So we calculate CHF 0.3 * 8. The result is that 8 apples cost CHF 2.40.

Rule of three table

A table is often used for the calculation. This allows you to visualise how the values relate to each other in a proportional and antiproportional calculation.

This is how it looks for the example just mentioned with the apples:

The rule of three formulas and everyday examples

As the rule of three is somewhat difficult to understand in theory, we will give a few more examples here. However, the easiest way to do the calculation is of course with the rule of three calculator.

Formula proportional rule of three

Proportional means that the first value is in relation to the second, like the third to the fourth. The best way to illustrate this is with an example.

Let's assume that 3kg of potatoes cost CHF 5. How much will 2kg cost?

The ratio is therefore as follows:

3kg ⇒ CHF 5
2kg ⇒ ?

The result is CHF 3.33.

3kg is in relation to CHF 5, just as 2kg is in relation to CHF 3.33. If you have more potatoes, they will also cost more CHF.

The easiest way to proportional realise that the doubling of one value leads to the doubling of the other.

Formula antiproportional rule of three

Antiproportional is the opposite of proportional and means that the ratio is opposite. Here is another example:

Let's assume you drive 50km/h and reach your destination in 4 hours. How many hours do you need if you drive 100km/h?

The rule of three then looks like this:

50km/h ⇒ 4h
100km/h ⇒ ?

The result is 2h.

50km/h is therefore in inverse proportion to 4h, as 100km/h is to 2h. If the km/h increase, the hours decrease.

The easiest way to antiproportional realise that the Doubling one value leads to halving the other.

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When do you need the rule of three?

The rule of three is always needed when you want to put different values in relation to each other. This is often used for percentage calculations or when you want to know how much a certain number is worth if you know a different quantity (e.g. how much do 350g of strawberries cost if you know the price per kg?).

Rule of three in percentage calculation

The rule of three can also be used particularly well for calculating percentages. To do this, always calculate 1% first and then multiply it by the number of per cent you are looking for. An example:

If a TV costs CHF 800 new and is now written down by 30%, how much does it cost?

CHF 800 equals 100%, so now you have to calculate CHF 800 : 100 to know the price for 1%. With a 30% discount, the TV now costs 70% of the original price, so you calculate CHF 8 * 70. With the discount, it only costs CHF 560.

Here, too, the rule of three calculator is of course much faster.

About the author

Eric is the founder of Schwiizerfranke.com and certified IAF wealth advisor. Since 2019, he has been helping Swiss citizens to organise their finances comprehensibly, independently and efficiently.

📌 Note: This article is for information purposes only and does not constitute personalised investment advice.

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