Percentage Solver

A percentage solver helps you find the missing value in a percent problem: the part, the whole, or the percent. Most percentage questions reduce to one relationship, so once you identify those pieces, the calculation is usually straightforward.

Here are the three quantities to label first:

• part: the amount you are talking about
• whole: the full amount the part comes from
• rate: the percent, written as a decimal in equations

The key equation is

$$\text{part} = \text{rate} \times \text{whole}$$

where

$$\text{rate} = \frac{\text{percent}}{100}$$

If you know any two of the three values, you can solve for the third.

Percentage Solver Question Types

Most percent questions fit one of these patterns:

1. What is $p\%$ of $W$?
2. $P$ is what percent of $W$?
3. $P$ is $p\%$ of what number?

They all come from the same equation. The only thing that changes is which quantity is missing.

If the part is missing, multiply. If the whole is missing, divide the part by the rate. If the percent is missing, divide the part by the whole and convert the result to a percent.

Percentage Solver Formula

Use these forms depending on what you need to find.

When the whole and percent are known:

$$\text{part} = \frac{p}{100} \times \text{whole}$$

When the part and whole are known:

$$\text{percent} = \frac{\text{part}}{\text{whole}} \times 100\%$$

This requires $\text{whole} \ne 0$.

When the part and percent are known:

$$\text{whole} = \frac{\text{part}}{p/100}$$

This requires $p \ne 0$.

Worked Example: $18$ Is $30\%$ of What Number?

Here the part is $18$, and the percent is $30\%$. The whole is missing.

Convert the percent to a decimal:

$$30\% = 0.30$$

Now use

$$\text{whole} = \frac{\text{part}}{\text{rate}}$$

Then substitute:

$$\text{whole} = \frac{18}{0.30} = 60$$

So the whole is $60$.

Check it by going backward:

$$30\% \text{ of } 60 = 0.30 \times 60 = 18$$

This check is useful because percentage mistakes often come from swapping the part and the whole.

How to Identify the Whole in a Percent Problem

The whole is the base amount before the percent is taken. In the sentence "15 is $25\%$ of 60," the whole is $60$ because the $25\%$ refers to 60.

In word problems, the whole is often the original price, total number of items, full test score, or total population. If the wording feels unclear, ask: "Percent of what?" The answer to that question is usually the whole.

Common Percentage Mistakes

One common mistake is using $25$ instead of $0.25$ in the equation. In multiplication or division formulas, the rate should be a decimal unless you keep it as $25/100$.

Another mistake is mixing up the part and the whole. If you reverse them, a "what percent" answer can become far too large or far too small.

A third mistake is forgetting the denominator condition. The formula $\text{percent} = \frac{\text{part}}{\text{whole}} \times 100\%$ only works when the whole is not $0$.

Where Percentage Solvers Are Used

You use this idea in discounts, tax and tip calculations, test scores, financial summaries, and percentage change problems. Even when the wording changes, the structure is still part, rate, and whole.

That is why percent problems get easier once you stop memorizing separate tricks and start identifying the missing quantity.

Try Your Own Version

Try this: $45$ is what percent of $180$?

Start with

$$\text{percent} = \frac{\text{part}}{\text{whole}} \times 100\%$$

Then check whether your answer makes sense: since $45$ is one quarter of $180$, the percent should be less than $100\%$ and close to $25\%$.