Proportion Calculator

What is a proportion solver?

A proportion calculator finds an unknown value from three related quantities. That relationship can be a direct proportion, when both quantities increase or decrease together, or an inverse proportion, when one increases and the other decreases.

A proportion solver can work with a simple proportion or a compound proportion. Simple compares two quantities; compound is used when there are three or more. Each type is explained below, with its formula and examples.

Simple proportions

A simple proportion is used when there are two quantities and three values are known. The goal is to find the fourth. It can be direct or inverse, depending on whether the quantities change in the same direction or in opposite directions.

Direct proportion

A direct proportion applies when, as one quantity increases, the other also increases, and as one decreases, the other decreases. For example, a larger download takes longer. With values A, B, and C, the unknown is found as follows:

Direct proportion example

If downloading 5 GB takes 10 hours, how long will downloading 8 GB take?

Inverse proportion

An inverse proportion applies when, as one quantity increases, the other decreases. For example, more workers finish the same job in fewer days. The data layout is the same as in a direct proportion; what changes is the formula used to solve for X:

Inverse proportion example

If 5 workers take 10 days to do a job, how long will 8 workers take?

Compound proportions

A compound proportion is used when three or more quantities are involved. Each one can be direct or inverse relative to the value you are solving for. It is solved in steps: first one relationship, then the next using that result.

Compound proportion example

Problem

If 2 people take 6 hours to paint 1 room, how many hours will 4 people take to paint 3 rooms?

1. Identify the quantities: people, rooms, and hours.
2. For each quantity, decide whether it is direct or inverse relative to hours.
3. Solve in steps: first the inverse relationship, then the direct one.

Solution

First, classify each relationship:

1. People and hours: inversely proportional (more people, fewer hours).
2. Rooms and hours: directly proportional (more rooms, more hours).

Using an inverse proportion, calculate how long 4 people would take to paint 1 room:

It takes 4 people 3 hours to paint 1 room. Using a direct proportion, find the time for 3 rooms:

Therefore, 4 people will take 9 hours to paint 3 rooms.