The percentage change formula is (New − Old) ÷ |Old| × 100. It measures how much a value has increased or decreased relative to its original, expressed as a percentage.
The percentage change formula is one of the most fundamental calculations in business and finance.
Percentage Change = (New Value - Old Value) / |Old Value| × 100
Step-by-Step Examples
Example 1: Revenue increase
Revenue grew from $800,000 to $1,000,000.
- Change = $1,000,000 − $800,000 = $200,000
- Percentage change = $200,000 ÷ $800,000 × 100 = +25%
Example 2: Cost reduction
Marketing spend dropped from $50,000 to $38,000.
- Change = $38,000 − $50,000 = −$12,000
- Percentage change = −$12,000 ÷ $50,000 × 100 = −24%
Example 3: Price increase
Product price raised from $49 to $69.
- Change = $69 − $49 = $20
- Percentage change = $20 ÷ $49 × 100 = +40.8%
Using Absolute Value in the Denominator
The formula uses |Old Value| (absolute value) in the denominator. This is important when the old value is negative: if last year's profit was −$100k and this year it's −$60k, the percentage improvement is (−60k − (−100k)) ÷ 100k = +40%, not −40%.
Percentage Change vs Percentage Points
These are not the same:
- Conversion rate moved from 4% to 5% — that's a 1 percentage point increase but a 25% relative increase
- Always clarify which you mean to avoid misinterpretation in reporting
CAGR (Compound Annual Growth Rate) is the mean annual growth rate of an investment or business metric over a period longer than one year, assuming growth compounded annually.
CAGR smooths out year-to-year volatility and expresses multi-year growth as a single annual rate.
CAGR = (End Value / Start Value)^1 / n - 1
where n is the number of years.
Why CAGR Is Better Than Simple Average
Suppose a metric grew: Year 1 +50%, Year 2 −33%, Year 3 +50%.
- Simple average growth: (+50 − 33 + 50) ÷ 3 = +22.3%
- Actual result: 1.5 × 0.67 × 1.5 = 1.507 — a 50.7% gain over 3 years
- CAGR: 1.507^(1/3) − 1 = 14.7% (more accurate)
CAGR in Practice
ARR CAGR: "We grew from $1M to $4M ARR in 3 years — what's our CAGR?" → 58.7%
Revenue benchmark: T2D3 (Triple-Triple-Double-Double-Double) implies a ~40% 5-year CAGR from $1M ARR
Investment return: "I invested $100k in 2019 and it's worth $200k in 2024 — what's my annual return?" → 14.87% CAGR
CAGR Limitations
CAGR assumes smooth, steady compounding — it masks volatility. A company that grew 200% one year and shrank 50% the next has a CAGR of 0% but went on a dramatic ride. Always accompany CAGR with annual growth data to show the full picture.