The Percentage Change Formula
Percentage change measures how much a value has increased or decreased relative to its original value. The formula is:
% Change = ((New Value − Old Value) ÷ |Old Value|) × 100
A positive result indicates an increase; a negative result indicates a decrease. The absolute value bars around "Old Value" handle cases where the original value is negative (e.g. a loss becoming a profit).
Worked Examples
Example 1: Price Increase
A product costs $80 and the price rises to $96.
% Change = ((96 − 80) ÷ 80) × 100 = (16 ÷ 80) × 100 = +20%
Example 2: Sales Decrease
A store sold 450 units last month and 360 this month.
% Change = ((360 − 450) ÷ 450) × 100 = (−90 ÷ 450) × 100 = −20%
Example 3: Stock Return
A stock was purchased at $120 and is now worth $145.
% Change = ((145 − 120) ÷ 120) × 100 = (25 ÷ 120) × 100 = +20.83%
Percentage Change vs. Percentage Point Change
This is one of the most commonly confused distinctions in everyday maths and journalism:
- Percentage change: measures the relative change from the original value. If an interest rate goes from 2% to 3%, the percentage change is ((3−2)÷2)×100 = +50%.
- Percentage point change: the arithmetic difference. 3% − 2% = +1 percentage point.
Both statements are technically correct, but they describe different things. Politicians and media outlets are frequently (sometimes deliberately) imprecise about which one they are reporting. Always check which is meant when reading a data-driven claim.
How to Find the Original Value Before a Percentage Change
A common mistake: if a product is on sale for $72 after a 20% discount, what was the original price?
Wrong approach: $72 + 20% of $72 = $72 + $14.40 = $86.40 ❌
Correct approach: The sale price is 80% of the original (100% − 20% = 80%). So original = $72 ÷ 0.80 = $90 ✓
The formula for recovering the original value after a percentage decrease: Original = Final ÷ (1 − discount/100)
After a percentage increase: Original = Final ÷ (1 + increase/100)
Compound Percentage Changes
Be careful with multiple percentage changes in sequence. A 10% increase followed by a 10% decrease does NOT bring you back to the starting value:
- Start: $100
- After +10%: $110
- After −10% of $110: $110 × 0.90 = $99
The result is $99, not $100. This is because the second percentage is calculated on a different base. Compound changes always need to be calculated sequentially — you cannot simply add or subtract the percentages.
Use the CalcDash Percentage Calculator
Our free Percentage Calculator handles all three common percentage problems: finding X% of a number, finding what percentage one number is of another, and calculating percentage change. Enter your values and get the result with the formula shown — no signup required.