Percentage Change Calculator
Revenue moved from $48,000 to $54,500 — is that 13.5%? Enter any two values to get the exact percentage change, direction, and full calculation so you can explain the number clearly.
Last updated: April 2026
Percentage increase or decrease
Enter the original (old) value and the new value. A positive result is an increase; a negative result is a decrease.
Find the new value after a percentage change
Enter a starting value and a percentage change to find the resulting value.
How to calculate percentage change
The formula for percentage change is: ((New − Old) ÷ Old) × 100. A positive result means an increase; a negative result means a decrease.
Worked example: price increase from $80 to $100
((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 0.25 × 100 = 25% increase.
Worked example: price decrease from $200 to $150
((150 − 200) ÷ 200) × 100 = (−50 ÷ 200) × 100 = −25% (a 25% decrease).
Percentage change vs percentage points
These are frequently confused. If an interest rate rises from 2% to 3%, that is a 1 percentage point increase — but a 50% relative percentage change (because 1 is 50% of 2). Percentage points measure the absolute arithmetic difference. Percentage change measures the relative shift from the original value.
Common uses
Salary raises: if you earn $55,000 and get a raise to $57,750, that is ((57,750 − 55,000) ÷ 55,000) × 100 = 5% raise. The salary raise calculator extends this with an annual, monthly, weekly, and hourly breakdown, and the tip calculator applies the same percentage-of-a-number logic when calculating a restaurant gratuity.
Business pricing: if your cost rises and you need to recalculate your selling price to maintain margin, the profit margin calculator handles that alongside the percentage change. Discounts: a price drop from $120 to $90 is a 25% decrease — confirm it with the discount calculator to see exact savings. Inflation: if a basket of goods costs $400 one year and $418 the next, that is a 4.5% inflation rate for that basket.
How to find the new value after a percentage change
Multiply the original value by (1 + change ÷ 100) for an increase, or (1 − change ÷ 100) for a decrease. A 15% increase on $240: $240 × 1.15 = $276. A 15% decrease on $240: $240 × 0.85 = $204.
Reversing a percentage change
If a value increased by 25% to reach 500, the original was 500 ÷ 1.25 = 400. If it decreased by 25% to reach 500, the original was 500 ÷ 0.75 = 666.67. A common error is subtracting the percentage from the final value — 500 − 25% = 375 — which is wrong because it applies the percentage to the already-changed number rather than the original. Use the percentage of a number calculator to solve “X is P% of what number?” for any base-finding problem.
Compound growth and CAGR
Percentage change measures the shift between two specific points in time. Compound Annual Growth Rate (CAGR) expresses multi-year growth as a consistent annual rate. Formula: CAGR = (End ÷ Start)^(1÷Years) − 1. A portfolio growing from $10,000 to $16,105 over 5 years: (16,105 ÷ 10,000)^(0.2) − 1 = 1.6105^0.2 − 1 ≈ 10% CAGR. The simple percentage change over those 5 years was 61%, but the CAGR translates that into the equivalent steady annual rate — more useful for comparing investments over different time horizons.
Percentage change vs percentage points: a closer look
A tax rate rising from 20% to 25% is a 5 percentage point increase but a 25% relative increase. These describe the same event in completely different terms. Percentage points measure the absolute arithmetic difference between two percentages. The relative percentage change shows how large that shift is compared to where it started. In economic reporting, misusing these terms is a common source of misleading statistics — a headline claiming a “50% increase in the crime rate” sounds alarming, but if the rate went from 2% to 3%, the absolute increase is just 1 percentage point.
Percentage change with negative numbers
The formula still works when values are negative, but the result can be counterintuitive. The key is to always divide by the absolute value of the original. A temperature change from −10°C to −25°C: ((−25 − (−10)) ÷ |−10|) × 100 = (−15 ÷ 10) × 100 = −150%. If you mistakenly divide by −10 instead of its absolute value 10, you get +150% — the wrong sign and magnitude. A change from a negative to a positive value (e.g. a business moving from −$20,000 loss to +$5,000 profit) produces a result above 100%, which is mathematically correct but should be described in context as “moved from loss to profit” rather than a misleading percentage figure.
Real-world applications: population growth and inflation
Population growth rate uses the same formula: if a city had 480,000 residents in 2020 and 516,000 in 2025, the percentage change is ((516,000 − 480,000) ÷ 480,000) × 100 = 7.5% growth over five years. Dividing by the number of years gives an approximate annual rate of 1.5%. Inflation works identically: if a basket of goods cost $380 last year and costs $399 this year, that is ((399 − 380) ÷ 380) × 100 = 5% inflation for that basket. Both are direct applications of the percentage change formula, which is why it is one of the most used calculations in economics, demography, and business reporting.
Frequently asked questions
Formula: ((New − Old) ÷ Old) × 100. From $80 to $100: ((100 − 80) ÷ 80) × 100 = 25% increase.
Use the same formula. From 200 to 150: ((150 − 200) ÷ 200) × 100 = −25%. The negative sign shows it is a decrease.
$250 × 1.10 = $275. The increase is $25. Formula: $250 × (1 + 10 ÷ 100) = $250 × 1.10. To verify: 10% of $250 = $25, and $250 + $25 = $275.
If a pass rate goes from 60% to 75%, that is a 15 percentage point increase, but a 25% relative change (15 ÷ 60 × 100 = 25%). Percentage points are the arithmetic difference; percentage change is the relative difference from the original.
150 × 1.20 = 180. The increase is 30. Verified: ((180 − 150) ÷ 150) × 100 = 20%.
No. Starting at 100: up 30% = 130, then down 30% of 130 = 130 − 39 = 91. You end up 9% below where you started. This is because the second percentage is applied to a larger base. Percentage changes are not symmetrical.
Year-over-year (YoY) uses the same formula: ((This Year − Last Year) ÷ Last Year) × 100. If revenue was $480,000 last year and is $540,000 this year: ((540,000 − 480,000) ÷ 480,000) × 100 = 12.5% YoY growth. YoY is preferred over month-over-month for most business and economic metrics because it eliminates seasonal distortion — comparing December to November is misleading; comparing December to last December removes that noise.
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