Percentage increase and decrease both use the same core formula — the only thing that changes is whether the result comes out positive or negative.
% Change = ((New Value − Old Value) ÷ |Old Value|) × 100
A positive result means an increase. A negative result means a decrease. That's the whole rule — the formula does the work of telling you which direction the change went. (The vertical bars mean "absolute value"; they only make a difference when the old value is negative.)
Step by Step
- Subtract the old value from the new value to get the change.
- Divide that change by the old value — the starting point.
- Multiply by 100 to turn the decimal into a percentage.
- Read the sign: positive is an increase, negative is a decrease.
Percentage Increase, Worked Example
Say a salary goes from $50,000 to $56,000. Plug it in:
((56,000 − 50,000) ÷ 50,000) × 100 = (6,000 ÷ 50,000) × 100 = 12%
That's a 12% increase.
Percentage Decrease, Worked Example
A jacket priced at $80 goes on sale for $60:
((60 − 80) ÷ 80) × 100 = (−20 ÷ 80) × 100 = −25%
The negative sign tells you it's a decrease — a 25% discount.
More Everyday Examples
| Situation | Old | New | Calculation | Result |
|---|---|---|---|---|
| Monthly rent | $1,200 | $1,290 | 90 ÷ 1,200 | +7.5% |
| Exam score | 64 | 80 | 16 ÷ 64 | +25% |
| Streaming subscription | $9.99 | $12.99 | 3 ÷ 9.99 | ≈ +30.03% |
| Electricity bill | $150 | $120 | −30 ÷ 150 | −20% |
| Town population | 25,000 | 23,500 | −1,500 ÷ 25,000 | −6% |
Notice the subscription row: a $3 rise sounds small, but relative to a $9.99 starting price it is a 30% increase. Percentage change is useful precisely because it puts changes of different sizes on the same scale.
Applying an Increase or Decrease to a Number
Often you know the percentage and need the new value. Multiply by 1 plus the change (as a decimal) for an increase, or 1 minus it for a decrease:
New = Old × (1 + % ÷ 100) or New = Old × (1 − % ÷ 100)
A 12% raise on $50,000: 50,000 × 1.12 = $56,000. A 25% price cut on $80: 80 × 0.75 = $60. These are the same examples as above, just worked in the other direction.
Finding the Original Value (Reverse Percentages)
If a price is $69 after a 15% increase, the original was 69 ÷ 1.15 = $60. A very common error is to take 15% off $69 instead, which gives $58.65 — wrong, because the 15% was calculated on $60, not on $69. Likewise, if a car is worth $14,400 after losing 20% of its value, it was worth 14,400 ÷ 0.80 = $18,000.
The Most Common Mistake
People often divide by the wrong number — using the new value as the base instead of the old one. In the jacket example, dividing the $20 difference by the sale price ($60) instead of the original price ($80) gives 33%, not 25%. The base for percentage change is always the starting value, never the ending one.
A few other errors come up regularly:
- Forgetting to multiply by 100. A result of 0.12 is 12%, not 0.12%.
- Dropping the sign. Writing "25%" for the jacket hides the fact that the price went down. Say "−25%" or "a 25% decrease".
- Comparing changes from different bases. A 50% rise in a small number (2 → 3 complaints) is not more important than a 10% rise in a large one (1,000 → 1,100). Always look at the absolute numbers alongside the percentage.
- Rounding too early. Keep full precision until the final step, especially when chaining several changes together.
Percentage Change vs. Percentage Points
These two get mixed up constantly. If an interest rate moves from 5% to 7%, that's a 2 percentage point increase, but a 40% percentage increase (since (7−5)/5 × 100 = 40%). "Percentage points" describes the raw difference between two percentages; "percentage change" describes that difference relative to the starting value. Financial and news reporting frequently conflates the two, so it's worth checking which one a source actually means.
Successive Changes Don't Simply Add Up
Because each percentage is calculated on the current value, consecutive changes multiply rather than add:
- Up 10%, then down 10%: $100 → $110 → $99. Overall
1.10 × 0.90 = 0.99, a 1% loss, not zero. - Up 50%, then down 50%:
1.50 × 0.50 = 0.75, a 25% loss overall. - 5% a year for three years:
1.05 × 1.05 × 1.05 ≈ 1.1576, about 15.76% in total — slightly more than 15%, because each year's growth builds on the last.
The same logic explains why a loss is harder to recover from than it looks:
| Drop | Remaining value | Increase needed to recover |
|---|---|---|
| 10% | 90% | ≈ 11.1% |
| 20% | 80% | 25% |
| 25% | 75% | ≈ 33.3% |
| 50% | 50% | 100% |
Increases Above 100%
A decrease can never go beyond −100% (that would mean the value dropped below zero from a positive start), but an increase has no upper limit. Keep these in mind:
- A 100% increase means the value doubled (10 → 20).
- A 200% increase means it tripled (10 → 30), not doubled.
- "Three times as much" and "200% more" describe the same thing; "300% more" would be four times as much.
Quick Mental Math Tips
- Work out 10% of the old value first; then count how many 10% steps fit into the change. From 40 to 52, the change is 12 and 10% of 40 is 4, so that's three steps: 30%.
- If the new value is half the old, it's −50%; if it's a quarter less, −25%. Fractions are often faster than division.
- Ask whether the answer is plausible: a change smaller than the old value must be under 100%.
Don't want to do the arithmetic by hand? Our Percentage Calculator and Percentage Difference Calculator handle both increase and decrease instantly. If you are comparing two values with no clear starting point, read Percentage Difference vs. Percentage Change first.
Frequently Asked Questions
What if the old value is zero?
Percentage change is undefined when you start from zero, because you cannot divide by zero. Going from 0 to 40 sales is not an "infinite" increase in any useful sense — report the absolute change ("up 40 sales") instead.
How do I calculate percentage change in Excel or Google Sheets?
With the old value in A2 and the new value in B2, enter =(B2-A2)/ABS(A2) and format the cell as a percentage. The ABS keeps the sign correct if the old value is ever negative.
How do I find the average yearly growth over several years?
Don't divide the total change by the number of years. Use the compound annual growth rate: (End ÷ Start)^(1 ÷ Years) − 1. Growth from 100 to 150 over four years is 1.5^0.25 − 1 ≈ 10.67% a year, not 12.5%.
Is a 100% decrease possible?
Yes — it means the value fell all the way to zero, such as a fee being removed entirely. Anything beyond −100% would require the value to become negative, which only makes sense for quantities like profit or temperature.
Try it yourself: compare a bill or price from this month with last month's, work out the change with the four steps above, and check your answer in the Percentage Calculator. For the basics behind every formula here, see How to Calculate Percentage.