How to Calculate Percentages

Percentages show up everywhere — discounts, tips, tax, test scores, interest rates. There are really only three calculations you need, and once you know which one a question is asking, the math is short.

1. Finding a percentage of a number

"What is 20% of 80?" is the most common percentage question, and it is just multiplication. Convert the percentage to a decimal (divide by 100) and multiply by the whole:

part = (percentage / 100) × whole

For 20% of 80: 20 / 100 = 0.20, and 0.20 × 80 = 16.

This is the calculation behind tips ("15% of $40"), discounts ("30% off $60"), and tax ("7% of $50"). The percentage is always the rate, the whole is always the thing the rate applies to, and the part is what you're solving for.

2. Percentage change (increase and decrease)

"A price went from $40 to $50 — what is the percent increase?" Here you compare the change to the original value:

percent change = (new − old) / old × 100

From $40 to $50: (50 − 40) / 40 × 100 = 10 / 40 × 100 = 25% increase.

If the value fell from $50 to $40: (40 − 50) / 50 × 100 = −10 / 50 × 100 = −20%, a 20% decrease. The sign tells you the direction; the magnitude is the size of the change relative to where you started.

Notice the denominator is always the original number. Going from $40 to $50 is a 25% increase, but going back from $50 to $40 is a 20% decrease — not 25%. The same $10 gap is a different percentage because the base changed. This asymmetry trips people up constantly.

3. What percentage one number is of another

"30 out of 120 people voted yes — what percentage is that?" Divide the part by the whole and multiply by 100:

percentage = (part / whole) × 100

30 / 120 × 100 = 0.25 × 100 = 25%. This is the calculation behind test scores (47 out of 50 = 94%), completion rates, and survey results.

If the result is over 100%, the part is larger than the whole — which makes sense for things like "this year's sales are 115% of last year's," but is meaningless for "what percent of the class passed" (that can't exceed 100%). The context tells you which results are sensible.

The classic trap: percent vs percentage points

When a headline says "interest rates rose 2%," it is ambiguous. If a rate goes from 4% to 6%, that is:

• A 2 percentage-point increase (the arithmetic difference: 6 − 4 = 2), or
• A 50% increase in the rate itself ((6 − 4) / 4 × 100 = 50).

These describe the same change very differently. "Percentage points" always means the simple difference between two percentages; "percent" means a relative change. Financial and political reporting frequently blurs this, and it can make a change sound far bigger or smaller than it is.

A quick mental shortcut

For everyday estimates, remember that 1% of a number is just that number divided by 100 — move the decimal two places. So 1% of 250 is 2.5, and 18% of 250 is 18 × 2.5 = 45. This lets you sanity-check any percentage quickly without a calculator, which is the whole point of being fluent with percentages.

Try it yourself

The Percentage Calculator handles all three operations above. For a discount-specific version, the Discount Calculator finds the sale price and the amount saved, and the Tip Calculator applies a percentage to a bill total.