How to Calculate Percent Change (Increase and Decrease)
Percent change is one of the most used calculations in business, finance, and everyday life — and one of the most frequently gotten wrong. Whether you are tracking a price increase, measuring a weight loss goal, calculating investment returns, or reporting sales growth, the percent change formula is your essential tool. This guide explains the correct formula for both increases and decreases, common mistakes to avoid, and how to use our free percentage calculator to get the right answer every time.
The Percent Change Formula Explained
Percent change measures how much a value has changed relative to its starting point, expressed as a percentage. The formula is: Percent change = ((New Value − Old Value) / Old Value) × 100 For an increase, the result is positive. For a decrease, the result is negative. Example of a percent increase: A house was valued at £250,000 two years ago and is now worth £290,000. Percent change = ((290,000 − 250,000) / 250,000) × 100 = (40,000 / 250,000) × 100 = 16% increase. Example of a percent decrease: A product's price dropped from £45 to £36. Percent change = ((36 − 45) / 45) × 100 = (−9 / 45) × 100 = −20% (a 20% decrease). The formula is always the same regardless of whether the change is an increase or decrease. The sign of the result tells you the direction. Some calculators report the absolute change and the direction separately to avoid confusion with negative percentages. One critical point: the denominator is always the original (old) value, never the new one. This is where most errors occur. Dividing by the new value instead of the old value gives an incorrect result. In the house example above, dividing by 290,000 instead of 250,000 gives 13.79% instead of 16% — both answers are plausible, which is why this error persists unnoticed.
Percent Increase: Worked Examples
Percent increase appears whenever a value grows over time or a price rises. Here are six common real-world examples with complete calculations. Salary raise: Current salary £32,000, new salary £34,500. Percent increase = ((34,500 − 32,000) / 32,000) × 100 = (2,500 / 32,000) × 100 = 7.81%. A useful number to know when comparing a job offer to an industry benchmark. Inflation impact: A grocery basket cost £85 last month and costs £89.50 this month. Percent increase = ((89.50 − 85) / 85) × 100 = (4.50 / 85) × 100 = 5.29%. This is the personal inflation rate for that household on that basket. Website traffic: A website had 12,000 visitors in January and 15,500 in February. Percent increase = ((15,500 − 12,000) / 12,000) × 100 = (3,500 / 12,000) × 100 = 29.17% growth. Product price markup: A retailer buys a product for £18 wholesale and sells it for £27. Percent increase = ((27 − 18) / 18) × 100 = (9 / 18) × 100 = 50% markup. Bodyweight goal: A person weighing 70 kg gains 3 kg of muscle. Percent increase = ((73 − 70) / 70) × 100 = (3 / 70) × 100 = 4.29% weight increase. Investment return: An investment of £5,000 grew to £6,400. Percent increase = ((6,400 − 5,000) / 5,000) × 100 = (1,400 / 5,000) × 100 = 28% return on investment. In each case, the formula is identical. The only variable is which value is 'old' and which is 'new'. Our calculator makes this explicit with labelled input fields.
Percent Decrease: Worked Examples
Percent decrease applies whenever a value falls — whether it is a sale price, a declining metric, or a weight loss goal. The formula is the same as percent change, producing a negative result when new is less than old. Sale discount: An item normally priced at £120 is on sale for £84. Percent decrease = ((84 − 120) / 120) × 100 = (−36 / 120) × 100 = −30% (30% discount). Business loss: A store sold 840 units in Q1 and 693 units in Q2. Percent decrease = ((693 − 840) / 840) × 100 = (−147 / 840) × 100 = −17.5% decrease in sales. Calorie reduction: Daily calorie intake dropped from 2,400 to 1,900 as part of a diet. Percent decrease = ((1,900 − 2,400) / 2,400) × 100 = (−500 / 2,400) × 100 = −20.83% reduction. Property depreciation: A car was worth £22,000 when new and is now worth £14,500 after three years. Percent decrease = ((14,500 − 22,000) / 22,000) × 100 = (−7,500 / 22,000) × 100 = −34.09%. Error rate improvement: A manufacturing process had a 4.8% defect rate and improved to a 3.1% defect rate. Percent decrease = ((3.1 − 4.8) / 4.8) × 100 = (−1.7 / 4.8) × 100 = −35.42% reduction in defect rate. Note the last example carefully: the percent change in the defect rate is 35.42%, but the change in percentage points is only 1.7. These are different quantities — confusing them is a common error in quality reporting. Our related article covers the percentage vs percentage points distinction in detail.
Multi-Step and Compound Percent Changes
When a value changes by a percentage multiple times, the results do not simply add up. This is because each subsequent change is applied to the most recent value, not the original — a property known as compound growth or compounding. Example: A price increases by 10% and then by 10% again. Intuition might suggest a 20% total increase. The actual result: if the original price is £100, a 10% increase gives £110. A second 10% increase on £110 gives £121 — a 21% total increase from the original, not 20%. To find the equivalent single percent change for a series of percent changes, multiply the growth factors. Each change is expressed as a factor: a 10% increase is 1.10, a 5% decrease is 0.95. Multiply all factors together and subtract 1 to get the total percent change. Example: A value increases by 15%, then decreases by 8%, then increases by 3%. Total factor = 1.15 × 0.92 × 1.03 = 1.0904. Total percent change = (1.0904 − 1) × 100 = 9.04% net increase — not 10% (15 − 8 + 3). This matters in investment return calculations (compounded annual returns), inflation tracking (cumulative inflation over multiple years), and growth projections (year-over-year growth rates). Financial calculators and spreadsheet CAGR functions handle this automatically, but understanding the underlying principle prevents misinterpretation of compound growth figures. For simple before/after comparisons without compounding, our percentage calculator's percent change mode gives the correct single-step result. For compounded multi-period analysis, use each result as the new starting value for the next calculation.
Frequently Asked Questions
- What is the formula for percentage increase?
- Percentage increase = ((new value − old value) / old value) × 100. The result is positive when the new value is greater than the old value. Always divide by the original (old) value, not the new one. Example: a price that goes from £80 to £100 has a percentage increase of ((100 − 80) / 80) × 100 = 25%.
- What is the formula for percentage decrease?
- The formula is identical to percentage increase: ((new value − old value) / old value) × 100. When the new value is less than the old value, the result is negative, indicating a decrease. Example: a price that falls from £100 to £80 has a percent change of ((80 − 100) / 100) × 100 = −20%. Some calculators report this as '20% decrease' to avoid confusion with the negative sign.
- Can a percent change be greater than 100%?
- Yes. If a value more than doubles, the percent increase exceeds 100%. Example: a follower count that grows from 500 to 1,800 increased by ((1,800 − 500) / 500) × 100 = 260%. There is no mathematical upper bound on percent increase. For percent decrease, the result cannot exceed −100%, since a value cannot fall below zero (in most real-world contexts).