How to Calculate Percentage

Percentages show up everywhere — discounts, tips, grades, loan rates, and news headlines. Once you know the handful of formulas behind them, you can work out any of these by hand. This guide walks through the core percentage formula, finding a percentage of a number, percentage change, and the mistakes that catch people out.

The basic percentage formula

Every percentage calculation comes back to one relationship: a part compared with a whole. The formula is:

Percentage = (Part ÷ Whole) × 100

Divide the portion you are interested in by the total, then multiply by 100 to turn the decimal into a percent.

Worked example: a class has 30 students and 18 of them passed an exam. What percentage passed?

• Part = 18 (the students who passed)
• Whole = 30 (the total class)
• 18 ÷ 30 = 0.6
• 0.6 × 100 = 60%

So 60% of the class passed. The same structure works whether the whole is 30 students, 500 survey responses, or $2,000 in sales.

Finding a percentage of a number

Often you know the whole and the percentage, and you want the actual amount. Convert the percentage to a decimal, then multiply:

X% of Y = (X ÷ 100) × Y

Worked example: what is 15% of an $80 restaurant bill?

• 15 ÷ 100 = 0.15
• 0.15 × 80 = 12
• 15% of $80 is $12

A faster mental shortcut: 10% of 80 is 8, half of that (5%) is 4, so 15% is 8 + 4 = $12. Useful for tips and quick discounts.

Percentage change (increase and decrease)

Percentage change measures how much a value has grown or shrunk relative to where it started. The formula is:

Percentage change = ((New value − Old value) ÷ Old value) × 100

A positive result means an increase; a negative result means a decrease. The key detail is that you always divide by the old value — the starting point — not the new one.

Worked example (increase): a pair of shoes rises from $50 to $65. What is the percentage increase?

• 65 − 50 = 15
• 15 ÷ 50 = 0.3
• 0.3 × 100 = 30%
• The price increased by 30%

Worked example (decrease): the same shoes go on sale and drop from $65 back to $52. What is the percentage decrease?

• 52 − 65 = −13
• −13 ÷ 65 = −0.2
• −0.2 × 100 = −20%
• The price decreased by 20%

Notice that the same $13 move reads differently depending on the direction — a 30% increase one way is not a 30% decrease back the other. That asymmetry is built into how percentage change works.

Common percentage mistakes

The arithmetic is simple, but a few traps trip people up consistently. Watch for these:

• Dividing by the wrong number: in percentage change, always divide by the original value, not the new one. Dividing 15 by 65 instead of 50 in the example above would give the wrong answer.
• Confusing percentage points with percent change: if a bank rate moves from 4% to 5%, that is a 1 percentage point increase, but a 25% increase in the rate itself. They sound similar and mean very different things.
• Forgetting to multiply by 100: leaving the answer as 0.3 instead of 30% loses the conversion step. Always finish the formula.
• Adding percentages of different bases: a 20% raise followed by a 20% cut does not return you to the original — it nets to a 4% loss, because each percentage applies to a different starting value.
• Treating a discount plus tax as additive: a 30% discount and 8% tax are applied sequentially, not together, so they do not simply combine to 38%.

Real-world uses for percentages

Once the formulas are second nature, percentages turn up in nearly every part of daily life:

• Discounts and sales: a $120 jacket at 25% off saves (25 ÷ 100) × 120 = $30, for a final price of $90.
• Tips: 18% on a $65 meal is (18 ÷ 100) × 65 = $11.70, often rounded up to $12.
• Grades: scoring 87 out of 100 is 87%; scoring 43 out of 50 is (43 ÷ 50) × 100 = 86%.
• Interest and finance: a 5% APR on a $10,000 loan costs $500 in interest per year before compounding.
• Statistics and news: survey results, unemployment figures, and growth rates are almost always reported as percentages or percentage changes — making the distinction between the two all the more important.

For anything more involved — reverse percentages, compound growth, or multi-step change — a percentage calculator removes the arithmetic and lets you focus on the numbers themselves.

The bottom line

Nearly every percentage problem reduces to the same relationship: divide the part by the whole, then multiply by 100. For change, divide the difference by the original value. Keep straight which value is the base, never confuse percentage points with percent change, and you can work out discounts, tips, grades, and growth rates by hand.