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How to Calculate Percentage Increase and Decrease
Percentage change has one formula, but the order of the numbers decides whether your answer is right or backwards. Here is the formula, three worked examples, and the traps that catch people out.
Percentage change is one formula used in both directions. You subtract the starting value from the ending value, divide by the starting value, then multiply by 100. If the answer is positive it is an increase; if it is negative it is a decrease. There is no separate 'decrease formula' to memorise.
The formula
The denominator is always the old value — the number you are measuring from. That single detail is responsible for most wrong answers, because it is easy to divide by whichever number happens to be larger.
Written out as steps: find the difference, divide that difference by the original amount, multiply by 100, and attach a sign or the word 'increase' or 'decrease' so the direction is unambiguous.
Percentage change = ((New value - Old value) / Old value) x 100
Worked example: a rent increase
Your rent goes from 1,200 to 1,320 a month. The difference is 120. Divide 120 by the original 1,200 and you get 0.10. Multiplied by 100, that is a 10% increase.
Notice what happens if you divide by the new value instead: 120 divided by 1,320 is 0.0909, or 9.09%. That number is not wrong in the abstract — it is the increase expressed as a share of the new rent — but it is not the percentage increase, and quoting it to a landlord or in a budget spreadsheet will quietly understate what changed.
Worked example: a price drop
A monitor listed at 340 is now 289. The difference is 289 - 340 = -51. Divide by the original 340 to get -0.15, which is -15%: a 15% decrease.
Keeping the subtraction in the order 'new minus old' means the sign does the work for you. You do not have to decide in advance whether the change is up or down; a negative result tells you.
Worked example: reversing a change is not symmetrical
This is the result that surprises people most. If a value falls by 20% and then rises by 20%, you do not get back to where you started.
Start at 500. A 20% decrease removes 100, leaving 400. A 20% increase on 400 adds 80, giving 480 — not 500. The second percentage was applied to a smaller base, so it moved fewer units.
To undo a 20% fall you need a 25% rise, because 100 divided by 400 is 0.25. The general rule: to reverse a decrease of p, you need an increase of p / (1 - p). A 50% loss needs a 100% gain to recover.
Percentage change versus percentage points
When the thing you are measuring is itself a percentage, the difference between the two numbers is measured in percentage points, not percent. A rate that moves from 4% to 5% has gained one percentage point, which is a 25% increase in the rate. Both statements are true and they describe very different sized changes, which is exactly why the distinction matters when you are reading a rate change on a loan or a savings account.
| Scenario | Correct description | Common mis-statement |
|---|---|---|
| A savings rate moves from 4% to 5% | Up 1 percentage point, or up 25% | 'Up 1 percent' |
| A tax rate moves from 20% to 22% | Up 2 percentage points, or up 10% | 'Up 2 percent' |
| A pass rate falls from 80% to 76% | Down 4 percentage points, or down 5% | 'Down 4 percent' |
Where this comes up in ordinary decisions
In a monthly budget in particular, percentage change is more informative than the raw difference. Groceries rising by 40 tells you less than groceries rising by 12%, because the percentage is comparable across categories of very different sizes.
- Comparing this year's electricity bill to last year's to see whether usage or the tariff changed.
- Checking whether a pay rise keeps pace with rising costs.
- Working out how much a subscription has crept up over three renewals.
- Measuring whether a spending category in your budget actually shrank or just looked smaller against a bigger total.
- Sanity-checking a 'discount' by comparing it to the price the item sat at a month ago.
Where percentage change calculations go wrong
- Dividing by the new value instead of the old one. Always divide by where you started.
- Averaging percentage changes across periods. Three months of +10%, -10% and +10% does not average to +3.33%; compound them instead (1.10 x 0.90 x 1.10 = 1.089, so +8.9%).
- Mixing percent and percentage points when the underlying figure is a rate.
- Calculating a percentage change from a base of zero. It is mathematically undefined, and any tool that reports a number there is inventing one.
- Rounding intermediate steps. Round only at the end, or small errors accumulate across a multi-step calculation.
Assumptions and limits
The formula assumes the two values are genuinely comparable: same unit, same period length, same basis. Comparing a 28-day February bill to a 31-day January bill produces a percentage change that mostly measures the calendar, not your usage. Normalise to a daily figure first if the periods differ.
It also assumes the starting value is meaningful. Percentage change from a very small base is technically correct but practically misleading — going from 2 sales to 4 is a 100% increase and tells you almost nothing about the business.
Finally, a percentage change describes what happened between two points. It is not a forecast. Extending last quarter's growth rate forward assumes conditions repeat, which is an assumption you are making, not something the arithmetic supports.
Use the original value as the denominator
For percentage increase or decrease, the original amount is the reference point. If a price moves from 80 to 100, the change is 20 and the percentage increase is 20 ÷ 80 = 25%, not 20%. Keeping the original value visible beside the formula is a simple way to avoid reversing the denominator.
Frequently asked questions
Is there a different formula for percentage decrease?
No. The same formula covers both. If you subtract in the order 'new value minus old value', a decrease simply produces a negative result.
How do I find the percentage change when one value is negative?
The formula becomes unreliable, because dividing by a negative base flips the sign of the result. For figures that can go negative, such as profit, report the absolute change in currency instead, or state clearly that you moved from a loss to a profit.
What is the difference between percentage change and percentage difference?
Percentage change has a clear before and after, and divides by the before. Percentage difference compares two values with no natural order and divides by their average, so it gives the same answer whichever one you list first.
If something increases by 100%, has it doubled?
Yes. A 100% increase adds the original amount again. A 200% increase triples it, because you add twice the original.
Why does a 20% increase followed by a 20% decrease not return to the starting value?
The second 20% is taken from the increased value, so the two percentages use different bases.
What is the difference between percentage change and percentage points?
Percentage change compares relative movement between values. Percentage points describe the direct difference between two percentages, such as 40% to 45% being a 5-point increase.
Conclusion
Percentage change is a one-line formula with one thing to get right: divide by the value you started from. Keep the subtraction in the order new minus old, watch for the percent versus percentage-point distinction whenever the underlying figure is itself a rate, and remember that percentage moves in opposite directions do not cancel out. Those three habits cover almost every situation where this calculation shows up in everyday budgeting and price comparison.
Figures in this article are illustrative. Results depend on your own rates, fees, taxes and circumstances, and are for educational and planning purposes rather than financial advice.