Prices go up, salaries get revised, stock values swing, and a diet slowly brings your weight down. In every one of these situations, the most useful way to describe what happened is a percentage change. Saying that a phone is now 5,000 cheaper tells you something, but saying it is 20% cheaper tells you far more, because the percentage lets you compare it with any other product regardless of its price.
This guide explains percentage increase and decrease from the ground up. You will learn the formulas, how to apply them step by step, how to work backwards from a final value, why successive changes behave strangely, and which mistakes catch out even confident learners. If you are new to the subject, it helps to first read our beginner guide on how to calculate percentage. When you want an instant answer, our free percentage calculator can verify your work.
Quick Answer: Percentage Change Formulas
Percentage increase = ((New Value − Old Value) ÷ Old Value) × 100
Percentage decrease = ((Old Value − New Value) ÷ Old Value) × 100
Example: if a price rises from 800 to 920, the increase is 120, and (120 ÷ 800) × 100 = 15%. If it falls from 920 to 800, the decrease is also 120, but (120 ÷ 920) × 100 ≈ 13.04%.
What Is Percentage Change?
Percentage change measures how much a quantity has moved relative to its starting value, expressed as a share of 100. The key phrase is “relative to its starting value”. An increase of 10 means something very different when the starting number is 20 than when it is 2,000. In the first case the value has grown by half; in the second, by only half of one percent.
Two words appear in every percentage change problem. The old value (also called the original, initial or reference value) is where you started. The new value (also called the final value) is where you ended up. The percentage change is the difference between them, divided by the old value, multiplied by 100. If the new value is higher, you have an increase. If it is lower, you have a decrease.
Because the old value is the base of the calculation, it is always the number that goes at the bottom of the fraction. Almost every error in this topic comes from dividing by the wrong number.
How to Calculate Percentage Increase
Use this formula when the new value is larger than the old one:
Percentage increase (%) = ((New − Old) ÷ Old) × 100
Step-by-Step Method
- Subtract the old value from the new value to find the increase.
- Divide that increase by the old value.
- Multiply the result by 100.
- Add the percent sign.
Example 1: Salary Hike
An employee’s monthly salary rises from 40,000 to 44,000. The increase is 44,000 − 40,000 = 4,000. Divide by the old value: 4,000 ÷ 40,000 = 0.10. Multiply by 100 and the answer is 10%.
Example 2: Website Visitors
A blog gets 50,000 visitors in March and 56,500 in April. The increase is 6,500, and 6,500 ÷ 50,000 = 0.13, so traffic grew by 13%.
Example 3: Increase Above 100%
A small business earned 20,000 last year and 50,000 this year. The increase is 30,000, and 30,000 ÷ 20,000 = 1.5, which is 150%. A percentage increase can easily go beyond 100% whenever the new value is more than double the old one.
How to Calculate Percentage Decrease
Use this formula when the new value is smaller than the old one:
Percentage decrease (%) = ((Old − New) ÷ Old) × 100
The only change is that you subtract the new value from the old, so that the result is positive. Some people prefer to use the single formula ((New − Old) ÷ Old) × 100 for both cases and simply read a negative answer as a decrease. Both approaches give the same size of change.
Example 1: Price Drop
A laptop falls in price from 60,000 to 51,000. The decrease is 9,000. Dividing, 9,000 ÷ 60,000 = 0.15, so the price dropped by 15%.
Example 2: Weight Loss
Someone goes from 80 kg to 72 kg. The decrease is 8 kg, and 8 ÷ 80 = 0.10, so they lost 10% of their body weight.
Example 3: Falling Sales
Monthly sales drop from 250 units to 200 units. The decrease is 50, and 50 ÷ 250 = 0.20, so sales fell by 20%.
How to Increase or Decrease a Number by a Percentage
Often you already know the percentage and need the new value. There is a fast way to do this using a multiplier.
- To increase a number by r%, multiply it by (1 + r ÷ 100).
- To decrease a number by r%, multiply it by (1 − r ÷ 100).
Here are some worked examples:
- Increase 250 by 12%: 250 × 1.12 = 280.
- Increase 2,000 by 18%: 2,000 × 1.18 = 2,360.
- Decrease 900 by 40%: 900 × 0.60 = 540.
- Decrease 500 by 35%: 500 × 0.65 = 325.
The multiplier method is quicker than finding the percentage first and then adding or subtracting, because it needs only one multiplication. It is the same idea behind our guide on how to calculate discount, where paying 80% of the price is the same as taking 20% off.
| Change | Multiplier | Change | Multiplier |
|---|---|---|---|
| +5% | 1.05 | −5% | 0.95 |
| +10% | 1.10 | −10% | 0.90 |
| +15% | 1.15 | −15% | 0.85 |
| +20% | 1.20 | −20% | 0.80 |
| +25% | 1.25 | −25% | 0.75 |
| +50% | 1.50 | −50% | 0.50 |
Working Backwards to Find the Original Value
Sometimes you know the final value and the percentage change, and you want to know where you started. Reverse the multiplier by dividing instead of multiplying.
Original = Final ÷ Multiplier
Example 1: After an Increase
A monthly rent is 1,150 after a 15% increase. The multiplier is 1.15, so the original rent was 1,150 ÷ 1.15 = 1,000.
Example 2: After a Decrease
A jacket costs 1,200 after a 20% discount. The multiplier is 0.80, so the original price was 1,200 ÷ 0.80 = 1,500.
A very common mistake is to calculate 20% of the final price and add it back. Twenty percent of 1,200 is 240, giving 1,440, which is wrong. The 20% discount was taken from the original price, not from the sale price, so you must divide.
Successive Percentage Changes
When two or more changes happen one after another, each new percentage applies to the value left by the previous change. You cannot simply add the percentages together. Instead, multiply the multipliers.
Example 1: Two Increases
A price rises by 10% and then by another 10%. Starting at 100, the first rise gives 110, and the second rise adds 11, giving 121. The total increase is 21%, not 20%. In multiplier form, 1.10 × 1.10 = 1.21.
Example 2: Increase Then Decrease
A value goes up by 20% and then down by 20%. Starting at 100, it rises to 120, then falls by 24 (which is 20% of 120) to reach 96. The net result is a 4% decrease. In multiplier form, 1.20 × 0.80 = 0.96.
Example 3: Growth Over Several Years
A deposit of 5,000 grows by 8% each year for three years. The multiplier is 1.08 × 1.08 × 1.08 = 1.259712, so the final amount is 5,000 × 1.259712 = 6,298.56. This repeated percentage growth is exactly how interest works in practice, which we explain in our guide to compound interest.
Why Increase and Decrease Are Not Symmetrical
A surprising fact about percentages is that going up and going down by the same percentage does not bring you back to the start. The reason is the base changes. A 50% rise on 100 gives 150, but a 50% fall from 150 gives 75, which is a net loss of 25%.
This asymmetry also tells you how big a rebound you need after a loss:
- After a 10% fall, you need an 11.1% rise to recover.
- After a 20% fall, you need a 25% rise (80 → 100).
- After a 50% fall, you need a 100% rise (50 → 100).
- After a 75% fall, you need a 300% rise (25 → 100).
Investors in particular should remember this. The deeper the drop, the disproportionately larger the climb required to get back to even.
Percentage Difference vs Percentage Change
Percentage change has a clear direction and a clear starting point. Percentage difference is used when neither value is “the original” and you just want to compare two numbers fairly. The formula divides the gap by the average of the two values:
Percentage difference = (|A − B| ÷ ((A + B) ÷ 2)) × 100
For example, two shops sell the same item for 80 and 120. The gap is 40 and the average is 100, so the percentage difference is 40%. Notice that if you called 80 the old value you would get a 50% increase, and if you called 120 the old value you would get a 33.3% decrease. The symmetric formula avoids this confusion when no natural starting point exists.
Percentage change should also be kept separate from percentage points. If an interest rate moves from 6% to 8%, it has risen by 2 percentage points, but that is a 33.3% relative increase. News reports often mix these up, so always check which one is meant. Our article on how inflation is calculated gives more real examples.
Real-Life Applications
Prices and Shopping
Whenever a shop changes a price, percentage change shows whether the deal is truly good. A product reduced from 2,500 to 2,000 is a 20% reduction. You can also compare offers using our guide on GST calculation, since tax is another percentage added on top.
Salary and Career
Appraisals are usually announced as percentage hikes. If your salary of 55,000 rises by 8%, your new pay is 55,000 × 1.08 = 59,400. Understanding the percentage lets you compare your raise with inflation and with offers elsewhere. You can also see how take-home pay changes in our article on in-hand salary calculation.
Business and Marketing
Revenue growth, conversion rate changes and cost reductions are all tracked as percentage changes. If monthly revenue climbs from 12 lakh to 15 lakh, the growth is 3 ÷ 12 = 25%. Comparing percentage growth across months or products shows what is really working. For profit-related percentages, read about profit margin vs markup and how to calculate ROI.
Investments
Returns on stocks, mutual funds and deposits are reported as percentage changes. If an investment grows from 20,000 to 23,000, it has returned 15%. A fall from 23,000 to 20,000 is only a 13.04% loss, which is the asymmetry discussed earlier.
Health and Fitness
People track weight loss, body fat reduction and improvements in running time as percentages. A fall from 30% to 27% body fat is 3 percentage points, or a 10% relative reduction. To understand these measurements better, see our guide on body fat percentage.
Population and Statistics
Governments and researchers report population growth, unemployment shifts and literacy improvements as percentage changes so that regions of different sizes can be compared. To summarise such data, you may also need mean, median and mode.
Common Mistakes to Avoid
- Dividing by the new value. The old value is always the base. Dividing by the new value gives the wrong answer.
- Adding successive percentages. A 10% rise followed by another 10% rise is 21% overall, not 20%.
- Assuming a rise and a fall of the same percentage cancel out. They do not, because the base changes.
- Calculating the reverse incorrectly. To undo a percentage change, divide by the multiplier rather than applying the opposite percentage.
- Mixing up percent and percentage points. Always state which one you mean.
- Using zero as the old value. If the old value is zero, percentage change is undefined, because you cannot divide by zero. Use the absolute change instead.
- Ignoring negative numbers. When values are negative, the standard formula can give misleading signs. Use the absolute value of the old number in the denominator and interpret the result with care.
Practice Questions
- A value rises from 60 to 75. What is the percentage increase?
- A value falls from 480 to 360. What is the percentage decrease?
- Increase 2,000 by 18%.
- Decrease 900 by 40%.
- After a 25% increase, a value is 750. What was the original?
- A price rises by 50% and then falls by 50%. What is the net change?
Answers
- (15 ÷ 60) × 100 = 25% increase
- (120 ÷ 480) × 100 = 25% decrease
- 2,000 × 1.18 = 2,360
- 900 × 0.60 = 540
- 750 ÷ 1.25 = 600
- 1.50 × 0.50 = 0.75, so a 25% net decrease
Frequently Asked Questions
What is the formula for percentage increase?
Percentage increase = ((New Value − Old Value) ÷ Old Value) × 100. Subtract, divide by the old value, then multiply by 100.
What is the formula for percentage decrease?
Percentage decrease = ((Old Value − New Value) ÷ Old Value) × 100. The only difference is the order of subtraction.
How do I increase a number by a percentage?
Multiply the number by (1 + percentage ÷ 100). To raise 250 by 12%, multiply by 1.12 to get 280.
Why is a 50% rise followed by a 50% fall not zero?
The second percentage is applied to a bigger base. From 100 you go to 150, and 50% of 150 is 75, which leaves you at 75, a net loss of 25%.
How do I find the original value after a percentage increase?
Divide the final value by the multiplier. If a price is 1,150 after a 15% rise, the original is 1,150 ÷ 1.15 = 1,000.
Can a percentage decrease be more than 100%?
No. A positive quantity cannot fall by more than all of itself. A percentage increase, on the other hand, has no upper limit.
How do I calculate percentage change between two negative numbers?
Use the same formula but divide by the absolute value of the old number, and interpret the sign carefully. Many analysts avoid percentage change in this case and report the absolute difference instead.
Conclusion
Percentage increase and decrease boil down to a single idea: measure the change against the starting value. Remember the formula ((New − Old) ÷ Old) × 100, use multipliers such as 1.15 and 0.85 for quick forward calculations, divide by the multiplier to work backwards, and multiply multipliers when changes happen in a chain. Keep in mind that a rise and a fall of equal percentages do not cancel out, because the base shifts each time.
With these tools you can judge discounts, salary hikes, investment returns and business growth with confidence. For a fast, error-free answer, use our free percentage calculator, and keep learning with these related guides: