Whether you are analyzing sales growth, tracking price changes, monitoring investment returns, or comparing test scores, knowing how to calculate percentage increase or decrease is a fundamental everyday skill. This guide covers every scenario with clear formulas, real-world examples, and a reference table — plus the common mistakes that trip people up.
Percentage Increase Formula
% Increase = ((New Value − Old Value) ÷ Old Value) × 100
Example: A product was $40 and is now $52. % Increase = ((52 − 40) ÷ 40) × 100 = (12 ÷ 40) × 100 = 30% increase.
Percentage Decrease Formula
% Decrease = ((Old Value − New Value) ÷ Old Value) × 100
Example: Revenue dropped from $80,000 to $64,000. % Decrease = ((80,000 − 64,000) ÷ 80,000) × 100 = (16,000 ÷ 80,000) × 100 = 20% decrease.
More Worked Examples
Example 1 — Salary increase: You earned $55,000 last year and received a raise to $60,500. % increase = ((60,500 − 55,000) ÷ 55,000) × 100 = (5,500 ÷ 55,000) × 100 = 10%.
Example 2 — Stock price drop: A share fell from $148 to $111. % decrease = ((148 − 111) ÷ 148) × 100 = (37 ÷ 148) × 100 = 25%.
Example 3 — Population growth: A city grew from 250,000 to 312,500 residents over a decade. % increase = ((312,500 − 250,000) ÷ 250,000) × 100 = 25%.
Example 4 — Finding the new value from a percentage change: A car worth $24,000 depreciates by 15% in its first year. New value = 24,000 × (1 − 0.15) = 24,000 × 0.85 = $20,400.
Percentage Change Reference Table
| Scenario | Old Value | New Value | % Change |
|---|---|---|---|
| Price rise | $100 | $125 | +25% |
| Price drop | $100 | $75 | −25% |
| Salary increase | $50,000 | $55,000 | +10% |
| Weight loss | 200 lbs | 180 lbs | −10% |
| Revenue growth | $1M | $1.3M | +30% |
Common Mistakes to Avoid
Using the wrong base value: Always divide by the original (old) value, not the new one. A price that rises from $80 to $100 is a 25% increase — not 20%. The 20% figure comes from dividing by the new value ($100), which is incorrect.
Confusing percentage points with percentage change: If an interest rate rises from 3% to 5%, it increases by 2 percentage points — but by 66.7% in relative terms. These are different measurements and are frequently confused in news reporting and financial documents.
Assuming increases and decreases cancel out: A 25% increase followed by a 25% decrease does not return to the original value. If something rises from $100 to $125 (+25%), then falls 25% from $125, it lands at $93.75 — not $100. The decrease applies to a higher base.
How to Find the Original Value Before a Percentage Change
If you know the final value and the percentage change, you can work backward to find the original: Original = New Value ÷ (1 + % change/100) for an increase, or Original = New Value ÷ (1 − % change/100) for a decrease.
Example: A price is now $90 after a 10% decrease. Original = 90 ÷ (1 − 0.10) = 90 ÷ 0.90 = $100.
Use Our Free Percentage Calculator
For quick calculations, use our free Percentage Calculator. It handles the most common percentage tasks — finding X% of a number, calculating percentage change, and more — without any sign-up required.
Frequently Asked Questions
How do I calculate percentage increase between two numbers?
Subtract the old value from the new value, divide by the old value, then multiply by 100. The result is the percentage increase. If the result is negative, it is a decrease rather than an increase.
What if the old value is zero?
If the original value is zero, the percentage change formula is undefined — you cannot divide by zero. In this case, it is more meaningful to simply state the absolute change (e.g., “increased from 0 to 50 units”) rather than express it as a percentage.
Can percentage change exceed 100%?
Yes. A 100% increase means the value doubled. A 200% increase means it tripled. There is no mathematical upper limit to percentage increase. For decreases, however, the maximum is 100% — a value cannot decrease by more than 100% of itself (that would bring it below zero, which may or may not be meaningful depending on context).