Overview
Percent simply means "per hundred," and nearly every everyday percentage problem reduces to one of three basic patterns: finding a percentage of a number, expressing one number as a percentage of another, or measuring the percent change between two values. Once you can recognize which pattern a problem fits, the calculation itself is usually simple.
This guide covers all three patterns with the formulas and a worked example for each, since the most common source of percentage mistakes is applying the wrong pattern rather than doing the arithmetic wrong.
Percent of a number
To find P% of a number, multiply the number by P/100. This is the pattern behind discounts, tips, and sales tax estimates. For example, a 20% tip on a $45 bill is 45 × (20/100) = $9. This is the most common percentage calculation in daily life, and the one most calculators (including this one) are built around first.
Percent of total
To express one number as a percentage of another (what fraction of the whole does a part represent), divide the part by the whole and multiply by 100. For example, if 15 out of 60 students in a class chose a particular elective, that is (15 / 60) × 100 = 25%. This pattern is common in statistics, survey results, and any "what share of the total" question.
Percent change
Percent change measures how much a value increased or decreased relative to where it started, and the formula is ((new value − original value) / original value) × 100. The critical detail — and the most common mistake — is that you always divide by the original value, not the new one. If a price goes from $50 to $65, the percent increase is ((65 − 50) / 50) × 100 = 30%, not divided by 65.
Why percent change trips people up
A percent increase and the percent decrease that would reverse it are not the same number, which surprises people the first time they encounter it. A 50% increase from $100 takes you to $150 — but reversing that requires a decrease of exactly 33.3%, not 50%, because the second calculation divides by the new, larger original value ($150) rather than the original $100. Keeping track of which number is the "original" at each step is the key to avoiding this trap.
Frequently asked questions
How do I calculate a percentage increase or decrease?
Subtract the original value from the new value, divide that difference by the original value, then multiply by 100. A positive result is a percentage increase; a negative result is a percentage decrease.
Why is dividing by the wrong number a common percentage mistake?
Because it is easy to lose track of which value is the "original" (the denominator) once numbers start changing across multiple steps. Explicitly labeling which value is original before you set up the calculation — as described in this guide — helps avoid the error.
What is the difference between percentage points and percent?
Percentage points measure the raw difference between two percentages (going from 20% to 25% is a 5 percentage-point increase), while percent change measures that difference relative to the original percentage (a 25% relative increase in this example: (25−20)/20 × 100). The two describe the same change very differently, and mixing them up is a common source of confusion in statistics and news reporting.
Try the calculator
Use the free Percentage Calculator for live numbers, then come back to this guide anytime you need a quick refresher.