Proportion Calculator

The Rule of Three is a mathematical calculation method to find a fourth unknown value from three known values. It is mainly used to solve ratio and proportion problems like 'If A is B, what is C?'. From daily shopping to recipe adjustments and business estimates, it is a highly versatile tool useful in a wide range of situations. Our tool fully supports three modes: Direct Proportion, Inverse Proportion, and Compound Proportion involving multiple conditions.

Cross Multiplication

A calculation method where you multiply the denominator and numerator in a cross pattern when two fractions are equal. It is used to convert A / B = C / X into A × X = B × C in direct proportion calculations. This allows the unknown value to be solved smoothly via an equation.

Direct Proportion

A relationship where an increase in one value leads to a proportional increase in another at a constant rate. For example, 'If you buy 5 apples at 100 yen each, it costs 500 yen'. This is the most frequently used proportion calculation in daily shopping and ingredient measuring.

Inverse Proportion

A relationship where an increase in one value leads to a decrease in another. It is used when calculating people and time, or speed and required time, such as 'A job that takes 10 hours for 3 people will be finished in 6 hours if 5 people work on it'.

Compound Proportion

A complex proportion calculation involving 3 or more variables. It involves a chain of multiple direct or inverse proportion conditions, enabling advanced predictions such as 'If 5 machines operating 8 hours a day can produce 100 items, how many can be produced if 3 machines operate for 10 hours?'.

Q.I don't know whether to use Direct or Inverse Proportion.

Think based on the criterion 'If one increases, does the other also increase?'. For example, if the purchase quantity increases, the price also increases, so it's 'Direct Proportion'. Conversely, if the number of workers increases, the time taken decreases, so choose 'Inverse Proportion' in that case.

Q.When is Compound Proportion used?

It is used for problems involving 3 or more variables. For example, when there is a baseline like 'A people working B hours make C products', it is ideal for calculations crossing multiple conditions, such as 'If D people work E hours, how many products will be made?'.

Q.What is the difference from Percentage calculation?

Percentage calculation is suitable for finding 'a portion of a whole' or 'rate of increase/decrease' (e.g., 20% off of 1000 yen is 800 yen). On the other hand, the Rule of Three is for 'predicting a new value from a known ratio', specialized for absolute value cross-multiplication like 'If 3 cost 500 yen, how much for 7?'.

Here are some specific use cases where the Rule of Three (proportion calculation) is useful.