Percentage Increase and Decrease Formula: How to Calculate with Examples

Percentage change measures how much a value has increased or decreased relative to its original amount, expressed as a percentage. It provides a standardized way to compare changes across different scales. For example, if a stock price moves from $50 to $55, saying it increased by $5 is accurate but incomplete. That same $5 increase on a $500 stock would be far less significant. Percentage change solves this by expressing the shift relative to the starting point: the first stock rose 10%, while the second rose only 1%. The general formula for percentage change is: Percentage Change = ((New Value - Old Value) / Old Value) x 100. If the result is positive, it represents an increase. If the result is negative, it represents a decrease. Percentage change is one of the most frequently used calculations in everyday life. You encounter it when checking how much your rent went up, evaluating whether your investment portfolio gained or lost value, comparing this quarter's sales to last quarter, or figuring out how much you save during a sale. Understanding this single formula gives you a powerful tool for making sense of changes in almost any context. The key thing to remember is that percentage change always describes a movement from one specific value to another. It has a clear starting point (the old value) and an ending point (the new value), and the direction matters.

The percentage increase formula calculates how much a value has grown relative to its original amount. The formula is: Percentage Increase = ((New Value - Old Value) / Old Value) x 100. Example 1: Salary Raise. Your annual salary increased from $52,000 to $55,640. What is the percentage increase? Difference: $55,640 - $52,000 = $3,640. Divide by original: $3,640 / $52,000 = 0.07. Multiply by 100: 0.07 x 100 = 7%. Your salary increased by 7%. Example 2: Rent Increase. Your monthly rent went from $1,200 to $1,350. Difference: $1,350 - $1,200 = $150. Divide by original: $150 / $1,200 = 0.125. Multiply by 100: 0.125 x 100 = 12.5%. Your rent increased by 12.5%. Example 3: Website Traffic. Your blog had 4,500 visitors last month and 6,300 this month. Difference: 6,300 - 4,500 = 1,800. Divide by original: 1,800 / 4,500 = 0.4. Multiply by 100: 0.4 x 100 = 40%. Website traffic increased by 40%. In each case, the process is identical: subtract the old value from the new value, divide by the old value, and multiply by 100. The formula works with any unit, whether dollars, people, kilograms, or clicks. The units cancel out, leaving you with a pure percentage.

The percentage decrease formula works the same way as the increase formula, but the new value is smaller than the old value, producing a negative result. You typically express this as a positive number followed by the word 'decrease.' The formula is: Percentage Decrease = ((Old Value - New Value) / Old Value) x 100. Example 1: Sale Price. A jacket originally priced at $120 is now on sale for $84. Difference: $120 - $84 = $36. Divide by original: $36 / $120 = 0.30. Multiply by 100: 0.30 x 100 = 30%. The jacket is discounted by 30%. Example 2: Stock Loss. You bought a stock at $45 per share and it dropped to $38.25. Difference: $45 - $38.25 = $6.75. Divide by original: $6.75 / $45 = 0.15. Multiply by 100: 0.15 x 100 = 15%. Your stock decreased by 15%. Example 3: Weight Loss. A person weighed 185 pounds and now weighs 170.2 pounds. Difference: 185 - 170.2 = 14.8. Divide by original: 14.8 / 185 = 0.08. Multiply by 100: 0.08 x 100 = 8%. Their weight decreased by 8%. Note that you can also use the general percentage change formula for decreases. Plugging in a new value smaller than the old value will automatically give a negative result: ((38.25 - 45) / 45) x 100 = -15%. The negative sign indicates a decrease.

These two concepts sound similar but serve different purposes. Confusing them leads to incorrect conclusions, especially in data analysis and reporting. Percentage change measures the shift from one specific value to another over time or due to an event. It has a clear direction: value A changed to value B. The formula uses the original value as the denominator. Example: sales grew from $10,000 to $12,000, a 20% increase. Percentage difference compares two values where neither is clearly the 'original.' It measures how far apart two values are relative to their average. The formula is: Percentage Difference = (|Value A - Value B| / ((Value A + Value B) / 2)) x 100. Example: Company A's revenue is $10,000 and Company B's revenue is $12,000. The percentage difference is ($2,000 / $11,000) x 100 = 18.2%. Notice that the percentage change (20%) and percentage difference (18.2%) give different results for the same two numbers. This is because the denominator differs: one uses the starting value, the other uses the average. When should you use which? Use percentage change when comparing the same thing at two different points in time, such as this year's revenue vs last year's, or a stock price before and after an event. Use percentage difference when comparing two distinct things that exist simultaneously, such as the test scores of two students or the prices of two competing products. Choosing the wrong formula will give a misleading number.

Percentage change calculations appear in virtually every field. Here are some of the most common real-world applications. Price changes and inflation. Governments track the Consumer Price Index (CPI) as a percentage change to measure inflation. When you hear that inflation is 3.2%, it means the average price of a basket of goods increased 3.2% compared to the same period last year. Understanding this helps you evaluate whether your salary is keeping pace with the cost of living. Salary negotiations. When discussing a raise, percentage terms are more meaningful than absolute amounts. A $5,000 raise means very different things depending on whether your current salary is $40,000 (12.5% increase) or $150,000 (3.3% increase). Expressing raises as percentages also allows fair comparisons across different pay levels. Investment returns. Portfolio performance is always measured in percentage terms. If your investment grew from $10,000 to $11,500 over a year, that is a 15% return. This percentage allows you to compare your performance against benchmarks like the S and P 500 index, regardless of how much money you invested. Business metrics. Companies track percentage changes in revenue, customer acquisition, churn rate, and conversion rate. A marketing team might report that email open rates increased from 18% to 22%, a percentage change of 22.2%. These metrics guide strategic decisions. Science and engineering. Measurement error is expressed as a percentage. If a thermometer reads 102 degrees but the actual temperature is 100 degrees, the percentage error is 2%. This standardization makes it possible to compare accuracy across instruments with different scales.

Mistake 1: Dividing by the wrong value. The most frequent error is dividing by the new value instead of the old value. If a price increased from $80 to $100, the correct calculation is ($20 / $80) x 100 = 25%. Dividing by $100 gives 20%, which is wrong. Always divide by the original, starting, or 'before' value. Mistake 2: Confusing percentage points with percentage change. If an interest rate moves from 4% to 5%, it increased by 1 percentage point, not 1%. The actual percentage change is ((5 - 4) / 4) x 100 = 25%. This distinction matters enormously in finance and economics. Mistake 3: Assuming percentage changes are reversible. A 50% increase followed by a 50% decrease does not return you to the starting value. Starting at $100: a 50% increase gives $150. A 50% decrease of $150 gives $75, not $100. This asymmetry catches many people off guard. Mistake 4: Adding percentages from different bases. If your portfolio gained 10% one year and 20% the next, the total gain is not 30%. On a $1,000 investment: year 1 gives $1,100, and year 2 gives $1,320 (20% of $1,100). The actual total gain is 32%, due to compounding. Mistake 5: Ignoring the sign. A percentage change of -15% is a decrease, not an increase. When reporting results, always be explicit about the direction. Saying 'prices changed by 15%' is ambiguous; saying 'prices decreased by 15%' is clear.

Sometimes you know the final value and the percentage change, but you need to find the original value. This is called a reverse percentage calculation, and it is particularly useful for finding pre-discount prices or pre-tax amounts. Finding the original value after an increase. If a price increased by 20% and the new price is $180, what was the original price? The new price equals the original times 1.20 (since a 20% increase means the new value is 120% of the original). So: Original = $180 / 1.20 = $150. Finding the original value after a decrease. A shirt is on sale for $56 after a 30% discount. What was the original price? The sale price equals the original times 0.70 (since a 30% decrease means the new value is 70% of the original). So: Original = $56 / 0.70 = $80. The general formulas are: Original Value = New Value / (1 + Percentage Increase / 100) for increases, and Original Value = New Value / (1 - Percentage Decrease / 100) for decreases. A common mistake is to simply apply the percentage to the new value. For instance, if a $56 shirt is 30% off, some people calculate 30% of $56 ($16.80) and add it back to get $72.80. This is incorrect because the 30% was applied to the original price, not the sale price. The correct original price is $80, and 30% of $80 is indeed $24, which gives the sale price of $56.

Test your understanding with these practice problems. Try solving each one before reading the solution. Problem 1: A house was valued at $320,000 last year and is now valued at $348,800. What is the percentage increase? Solution: ($348,800 - $320,000) / $320,000 x 100 = $28,800 / $320,000 x 100 = 9%. The house value increased by 9%. Problem 2: A company's workforce shrank from 1,250 employees to 1,075. What is the percentage decrease? Solution: (1,250 - 1,075) / 1,250 x 100 = 175 / 1,250 x 100 = 14%. The workforce decreased by 14%. Problem 3: After a 15% raise, your new salary is $63,250. What was your original salary? Solution: Original = $63,250 / 1.15 = $55,000. Your original salary was $55,000. Problem 4: A laptop costs $680 after a 20% discount. What was the original price? Solution: Original = $680 / 0.80 = $850. The original price was $850. Problem 5: An investment gained 12% in year one, then lost 8% in year two. Starting with $5,000, what is the final value and overall percentage change? Solution: After year 1: $5,000 x 1.12 = $5,600. After year 2: $5,600 x 0.92 = $5,152. Overall change: ($5,152 - $5,000) / $5,000 x 100 = 3.04%. The investment gained 3.04% overall, not 4% (12% - 8%). Problem 6: A store raised prices by 25% and then offered a 25% discount. Is the final price the same as the original? Solution: Starting at $100: after a 25% increase, the price is $125. After a 25% discount, the price is $125 x 0.75 = $93.75. The final price is 6.25% less than the original, not the same.