A percentage expresses a number as a fraction of 100. It’s used everywhere — from exam scores and sale discounts to profit margins and interest rates. This guide covers the core percentage formula and every major variation you’ll actually need.
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Basic Percentage Formula
Percentage = (Value ÷ Total) × 100
Example: What percentage is 45 out of 60? (45 ÷ 60) × 100 = 75%.
To find a percentage of a number — e.g. “what is 20% of 150” — flip the formula:
Result = (Percentage ÷ 100) × Total
Example: 20% of 150 = (20 ÷ 100) × 150 = 30.
Percentage Increase Formula
% Increase = ((New Value − Old Value) ÷ Old Value) × 100
Example: a price rises from $80 to $92. ((92−80) ÷ 80) × 100 = 15% increase.
Percentage Decrease Formula
% Decrease = ((Old Value − New Value) ÷ Old Value) × 100
Example: a price drops from $80 to $68. ((80−68) ÷ 80) × 100 = 15% decrease.
Percentage Profit Formula
% Profit = ((Selling Price − Cost Price) ÷ Cost Price) × 100
Example: an item bought for $40 and sold for $50. ((50−40) ÷ 40) × 100 = 25% profit.
Percentage Loss Formula
% Loss = ((Cost Price − Selling Price) ÷ Cost Price) × 100
Example: an item bought for $40 and sold for $30. ((40−30) ÷ 40) × 100 = 25% loss.
Percentage Change Formula
Percentage change is the general term covering both increase and decrease — it uses the same formula as above but the sign tells you the direction:
% Change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result is an increase; a negative result is a decrease.
Frequently Asked Questions
Q: What’s the difference between percentage change and percentage difference?
A: Percentage change compares a value over time (old vs. new, with direction). Percentage difference compares two values without treating either as the “original” — it’s usually calculated as the absolute difference divided by the average of the two values.
Q: How do I calculate percentage points vs. percentage change?
A: Percentage points is the raw arithmetic difference between two percentages (e.g. 40% to 45% is a 5 percentage point increase), while percentage change expresses that same move relative to the starting value ((45−40)/40 × 100 = 12.5% increase).
Q: How do I reverse a percentage increase to find the original value?
A: Divide the new value by (1 + percentage/100). Example: if $115 is after a 15% increase, the original value is 115 ÷ 1.15 = $100.
Want to skip the manual math? Use our free Percentage Calculator for instant results on any of these calculations.