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Percentage change = ((New Value - Old Value) / Old Value) x 100. A price going from $80 to $100 is a 25% increase. Going from $100 to $80 is a 20% decrease. The percentages are different because the base changes.
That last sentence trips up more people than any other concept in percentage math. A 25% increase and a 20% decrease can describe the exact same two dollar amounts — it depends on which direction you are measuring. This guide breaks down the percentage change formula, shows where people get tripped up, and walks through the real-world scenarios you will actually use it for.
One formula handles both increases and decreases:
Percentage Change = ((New Value - Old Value) / Old Value) x 100
| Scenario | Old Value | New Value | Calculation | % Change |
|---|---|---|---|---|
| Salary raise | $50,000 | $55,000 | (55000 - 50000) / 50000 x 100 | 10% increase |
| Rent increase | $1,200/mo | $1,350/mo | (1350 - 1200) / 1200 x 100 | 12.5% increase |
| Stock drop | $150/share | $135/share | (135 - 150) / 150 x 100 | 10% decrease |
| Weight loss | 200 lbs | 180 lbs | (180 - 200) / 200 x 100 | 10% decrease |
| Price hike | $3.50/gal | $4.20/gal | (4.20 - 3.50) / 3.50 x 100 | 20% increase |
| Enrollment dip | 800 students | 720 students | (720 - 800) / 800 x 100 | 10% decrease |
| Revenue growth | $400K | $520K | (520 - 400) / 400 x 100 | 30% increase |
| Home value | $320,000 | $368,000 | (368000 - 320000) / 320000 x 100 | 15% increase |
Our Percentage Calculator handles these instantly — select the percentage change mode, type your two values, and get the result with the formula shown.
This is the single most counterintuitive thing about percentage change, and it matters for real financial decisions:
The reason: the denominator changes. A 50% increase uses the smaller original number as the base. A 50% decrease uses the larger number as the base. Same percentage, different absolute amounts.
| Loss | Amount Remaining | Gain Needed to Recover |
|---|---|---|
| 10% loss | $90 of $100 | 11.1% gain |
| 20% loss | $80 of $100 | 25% gain |
| 30% loss | $70 of $100 | 42.9% gain |
| 40% loss | $60 of $100 | 66.7% gain |
| 50% loss | $50 of $100 | 100% gain |
| 60% loss | $40 of $100 | 150% gain |
| 75% loss | $25 of $100 | 300% gain |
| 90% loss | $10 of $100 | 900% gain |
Year-over-year (YoY) growth uses the same formula but compares the same period across two years:
YoY is preferred over month-over-month for seasonal businesses because it compares the same season. A gym comparing January to December would show a spike every year just from New Year resolution sign-ups — not real growth.
When percentage changes stack over time, they compound. A 10% annual raise for 3 years is not a 30% total increase:
The extra 3.1% comes from compounding — each year's raise builds on the previous year's larger base. This is why compound interest grows faster than simple interest. Our Compound Interest Calculator models this over any time period.
This distinction matters enormously in finance and statistics, and confusing the two leads to serious misunderstandings:
Saying "interest rates increased 3%" is ambiguous — it could mean 5% to 8% (percentage points) or 5% to 5.15% (3% of 5%). Always specify "percentage points" when you mean the arithmetic difference.
You earn $62,000 and are offered $67,500 at a new company. Is that a good jump? Change = (67,500 - 62,000) / 62,000 x 100 = 8.9% increase. Industry standard for a job change is 10-20%, so this is on the low end. Use our Salary Calculator to compare the per-paycheck difference after taxes.
You invested $8,000 in an index fund and it is now worth $10,400. Return = (10,400 - 8,000) / 8,000 x 100 = 30% gain. But over how long? If that took 3 years, your CAGR is about 9.1% annually — reasonable for an index fund. Use our Compound Interest Calculator to model future growth.
If inflation is 4% per year and your salary stays flat, your purchasing power decreases by 4% annually. After 3 years of 4% inflation with no raise: your effective salary drops to $62,000 x 0.96 x 0.96 x 0.96 = $54,879 in today's dollars — an 11.5% real loss. Our Loan Calculator factors in interest rate changes driven by inflation.
Gas went from $3.25 to $3.90 per gallon. Change = (3.90 - 3.25) / 3.25 x 100 = 20% increase. If you drive 1,000 miles per month at 25 MPG, that is 40 gallons per month. Cost increase: 40 x $0.65 = $26 more per month. Use our Discount Calculator when hunting for savings to offset price hikes.
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