How To Calculate Percentage

Most percentage questions are really one of two tasks: find what percent the part is of the whole, or find a percent of a number. Sorting out which one you have, then choosing the right base, solves nearly all of them. The two formulas:

A percentage is just a ratio on a scale of $100$: $75\%$ means $75$ out of $100$, or an equivalent fraction such as $\tfrac{3}{4}$. That shared scale is why percentages make grades, discounts, and survey results comparable.

When to use which formula

Use the first formula when you have two amounts and want their ratio as a percent — "what percent is $18$ out of $24$." Use the second when you know a percent and want the amount it represents — "$15\%$ of $80$." The deciding question is whether the percent is unknown (divide) or given (multiply). Either way the base is whatever you compare against, and if the base changes, the percentage changes.

The steps

1. Identify the whole. Decide which number is the full amount; the percentage is measured against that base.
2. Set up the operation. Put the part over the whole, or convert the percent to a decimal if you are finding a percent of a number.
3. Calculate and convert. Divide first when finding a percentage, then multiply by $100$ to write it as a percent.
4. Check the answer. Estimate whether the result fits the size of the part relative to the whole.

The whole procedure on one example

A student gets $18$ correct out of $24$. The part is $18$, the whole is $24$:

Divide first:

Then multiply by $100$:

So $18$ out of $24$ is $75\%$. Quick check: $18$ is three quarters of $24$, and three quarters is $75\%$.

For the other task — a percent of a number — convert and multiply. To find $15\%$ of $80$:

So $15\%$ of $80$ is $12$, which is a different question from "what percent is $12$ of $80$" (that one divides first).

Where each step tends to stall, and how to check

Step 1 (the whole): the denominator must be the full amount you compare against. If the question changes the base, the percentage changes too. Step 2 (convert the percent): $25\%$ means $0.25$, not $25$; skipping this makes the answer too large by a factor of $100$. Watch the neighbor concept: a plain percentage compares part to whole, while percent change compares the change to the original value,

which only applies when the original is not $0$. Step 4 (estimate): confirm the result matches the size relationship before trusting it.

Set up your own case with a sale price or a test score: name the whole first, then decide whether you divide to find a percentage or multiply to find a percent of a number. Percentages run through grades, discounts, tax, tips, interest, survey results, and data summaries, all because they put different-sized situations on one comparable scale.