How to Calculate Percentage Change: A Complete Guide
Whether you are tracking stock performance, measuring business growth, analyzing scientific data, or just comparing two prices at the grocery store, calculating percentage change is essential. Here is exactly how to do it, with worked examples, the difference between percent change and percentage points, and the chained-change trap that catches even experienced analysts.
Try it: Percentage Change Calculator
Enter any two values and instantly see the percent change, growth factor, and reverse calculation.
Percentage Change Calculator
How Percentage Change Works
Find the Difference
Subtract the original value from the new value.
Divide by Original
Divide the difference by the absolute original value.
Multiply by 100
Convert to a percentage by multiplying by 100.
Common Applications
- Price changes: How much did a stock or product price increase?
- Growth rates: Revenue growth, population growth, or user growth
- Performance: Test score improvement, weight loss/gain percentage
- Budget variance: Actual vs. planned spending differences
The full calculator also supports multi-period change and chained percent changes.
Open the full math calculatorQuick Answer: Common Percentage Changes
Sign convention: positive = increase, negative = decrease. The formula is ((New − Old) / |Old|) × 100:
| From → To | Change | Formula |
|---|---|---|
| $80 → $100 | +25% | ((100 − 80) / 80) × 100 |
| $200 → $150 | −25% | ((150 − 200) / 200) × 100 |
| $50 → $75 | +50% | ((75 − 50) / 50) × 100 |
| $1,000 → $1,250 | +25% | ((1250 − 1000) / 1000) × 100 |
| −10 → +5 | +150% | ((5 − (−10)) / |−10|) × 100 |
| 100 → 80 → 100 | 0% net (not +25%) | −20% then +25% ≠ +5% |
Note: percentage change is not symmetric — going from $100 to $80 is −20%, but going from $80 back to $100 is +25%. The reference value matters. And chained changes do not add: a 20% loss followed by a 25% gain is not a 5% gain, it is a 0% net change.
The Percentage Change Formula
Percentage Change = ((New Value − Old Value) ÷ |Old Value|) × 100
A positive result means increase. A negative result means decrease.
The formula has three components: a numerator (the change itself), a denominator (the reference value), and a multiplier of 100 to convert the decimal to a percentage. The absolute value bars around the denominator are what make the formula work even when the old value is negative.
Example: Stock Price Increase
If a stock goes from $50 to $65:
((65 − 50) ÷ 50) × 100 = (15 ÷ 50) × 100 = 0.3 × 100 = +30%
The stock price increased by 30%. Conversely, if the stock later drops from $65 back to $50, the change is ((50 − 65) ÷ 65) × 100 = −23.1% — not −30%. The reference is the most recent value, not the original.
Example: Price Decrease
If a product drops from $200 to $150:
((150 − 200) ÷ 200) × 100 = (−50 ÷ 200) × 100 = −0.25 × 100 = −25%
The price decreased by 25%. To go back to the original $200 from $150 requires a +33.3% increase, not +25%.
Why Use Absolute Value for the Old Value?
Using the absolute value of the old value ensures the calculation works even when the old value is negative. For example, going from a loss of −$10M to a profit of +$5M: ((5 − (−10)) ÷ |−10|) × 100 = (15 ÷ 10) × 100 = +150%. The absolute value keeps the denominator positive and the sign of the answer meaningful.
Common Percentage Change Scenarios
| Scenario | From → To | Change |
|---|---|---|
| Revenue growth | $100K → $150K | +50% |
| Population change | 1M → 1.2M | +20% |
| Weight loss | 200 lbs → 180 lbs | −10% |
| Test score improvement | 72% → 85% | +18.1% |
| Inflation (CPI 2025 → 2026) | 315 → 325 | +3.2% |
| Year-over-year revenue | $2.4M → $2.7M | +12.5% |
Percent Change vs. Percentage Points (Easy to Confuse)
These are different concepts and confusing them is a common source of reporting errors:
- Percentage points (pp): the arithmetic difference between two percentages. Unemployment going from 4% to 5% is a 1 percentage point increase.
- Percent change: the relative change. Going from 4% to 5% is a ((5 − 4) ÷ 4) × 100 = 25% relative increase — but only 1 pp absolute.
News headlines that say "unemployment up 25%" when the rate went from 4% to 5% are technically correct on the relative metric but often misleading. Always check whether a report is using percentage points or percent change.
Chained Percentage Changes (The Trap)
Percent changes do not add when chained. A common mistake: "the stock lost 50% then gained 50%, so I'm even." False — you are down 25%.
- $100 → −50% → $50 → +50% → $75. Net change: −25%, not 0%.
- The fix: convert each percent change to a multiplier (1 + change), multiply them, and convert back.
- Multipliers: 0.50 × 1.50 = 0.75 → −25% net.
For multi-period growth tracking, this is exactly why compound interest and CAGR (compound annual growth rate) exist — they correctly handle the chained math.
Key Takeaways
- The percentage change formula works for any two values: ((New − Old) / |Old|) × 100
- A positive result means increase; negative means decrease
- Always use the absolute value of the original value as the denominator
- Percent change ≠ percentage points — 4% → 5% is 1 pp but 25% relative
- Chained percent changes do not add — use multipliers: (1+a)(1+b)−1
- Use our Percentage Change Calculator for instant results on any two values, or our Percentage Calculator for basic percent / discount / tip math
About this guide
Methodology: standard percentage change ((New − Old) ÷ |Old|) × 100 with sign convention. Chained change uses multiplicative composition (1+a)(1+b)−1, never additive. Percentage point vs. percent change distinction per BLS and Federal Reserve reporting standards. Reviewed by the Dr. Aaron Pak (Doctor of Kinesiology & Public Health) on October 9, 2026.