This percentage calculator lets you calculate what percent a certain value is of the base (total value). In fact, if you know any two of the three (percent, value, base), it can calculate the unknown for you.

The calculator will give you not just the answer, but also the step by step solution.

Here's a quick overview of percentage and a few related concepts.

## Percentage

Percentage is a common way of expressing a fraction or ratio as a quantity out of hundred.

And just like fractions or ratios, percentages are used to compare two quantities. Here's an example.

Here's an example. Say there are $\hspace{0.2em} 50 \hspace{0.2em}$ marbles in a box and $\hspace{0.2em} 6 \hspace{0.2em}$ of those marbles are blue.

And if we wanted to say what portion of the marbles are blue, we could say $\hspace{0.2em} 6 \hspace{0.2em}$ out of $\hspace{0.2em} 50 \hspace{0.2em}$. Or $\hspace{0.2em} 12 \hspace{0.2em}$ out of $\hspace{0.2em} 100 \hspace{0.2em}$. Imagine two such boxes of marbles.

Now, instead of saying $\hspace{0.2em} 12 \hspace{0.2em}$ out of $\hspace{0.2em} 100 \hspace{0.2em}$, we could just say $\hspace{0.2em} 12 \hspace{0.2em}$ percent (written as $\hspace{0.2em} 12 \% \hspace{0.2em}$).

Percent simply means out of $\hspace{0.2em} 100 \hspace{0.2em}$. So, $\hspace{0.2em} 20 \% \hspace{0.2em}$ is another way of saying $\hspace{0.2em} 20 \hspace{0.2em}$ out of $\hspace{0.2em} 100 \hspace{0.2em}$.

When working with percentages, there are three quantities we need to keep in mind — total, part, and percent.

Going back to the previous marbles example,

- the "total" was $\hspace{0.2em} 50 \hspace{0.2em}$ (there were $\hspace{0.2em} 50 \hspace{0.2em}$ marbles in all),
- "part" was $\hspace{0.2em} 6 \hspace{0.2em}$ (we were concerned with the blue marbles and there were $\hspace{0.2em} 6 \hspace{0.2em}$ of them),
- and "percent" was $\hspace{0.2em} 20 \hspace{0.2em}$.

Moving ahead, the percent formula that connects the three quantities is as follows.

$\text{percent} \hspace{0.25em} = \hspace{0.25em} \frac{\text{part}}{\text{whole}} \times 100 \hspace{0.2em} \%$

We can rearrangle the above formula and make "part" the subject of the formula.

$\text{part} \hspace{0.25em} = \hspace{0.25em} \frac{\text{percent}}{100} \times \text{whole} \hspace{0.2em}$

Let's look on a couple of example problems to see this formula in action.

### Percentage Calculation — Examples

Example

In a class of $\hspace{0.2em} 30 \hspace{0.2em}$ students, there are $\hspace{0.2em} 12 \hspace{0.2em}$ boys and $\hspace{0.2em} 18 \hspace{0.2em}$ girls. What percentage of the class do girls represent?

Solution

We can find the percentage of girls using the formula we saw earlier, we have

$\begin{align*} \% \text{ of girls} \hspace{0.25em} &= \hspace{0.25em} \frac{\text{number of girls}}{\text{number of students}} \times 100 \hspace{0.2em} \% \\[1.75em] &= \hspace{0.25em} \frac{18}{30} \times 100 \hspace{0.2em} \% \\[1.75em] &= \hspace{0.25em} 60 \hspace{0.2em} \% \end{align*}$

So, girls form $\hspace{0.2em} 60 \hspace{0.1em} \% \hspace{0.2em}$ of the class.

Example

How much is $\hspace{0.2em} 15 \% \hspace{0.2em}$ of $\hspace{0.2em} 30 \hspace{0.2em}$?

Solution

This time, we'll need to use the second formula — the one for "part".

$\text{part} \hspace{0.25em} = \hspace{0.25em} \frac{\text{percent}}{100} \times \text{whole}$

Substituting the values, we get

$\begin{align*} 15 \hspace{0.15em} \% \hspace{0.5em} \text{of} \hspace{0.5em} 30 \hspace{0.25em} &= \hspace{0.25em} \frac{15}{100} \times 30 \\[1.75em] &= \hspace{0.25em} 4.5 \end{align*}$