Percentage Change Calculator
Find the percent increase or decrease between two values: with the formula, the substitution, and the absolute difference shown.
Details
Percent change
+25%
100 → 125, increase
This works out the percentage change between two values, or applies a percentage increase or decrease to a starting number.
It returns the change as a percentage, the amount of the change in ordinary numbers, and the final value.
What percentage change measures
Percentage change measures how much something moved, relative to where it started. A price going from 50 to 75 rose by 25, and because it started at 50 that is a 50% increase.
The starting value is what you divide by, and it is the whole reason percentage change can be confusing. The same 25 measured against a starting point of 75 would be a much smaller percentage.
That asymmetry has real consequences: a 50% rise followed by a 50% fall does not bring you back to where you began. It leaves you 25% down.
Always divide by where it started, never by where it ended. Dividing by 75 instead would give 33.3%, which answers a different question entirely.
What to enter
- What do you want to do?
- Find the change between two values, or apply a percentage increase or decrease to a starting value.
- Starting value
- Where it began. This is the divisor, so getting it right decides the answer.
- New value
- Where it ended up. Lower than the start gives a negative result, which simply means a decrease.
Change, difference and points
- Percentage change
- Divide by the starting value. Used when something moved over time: prices, salaries, populations.
- Percentage difference
- Divide by the average of the two. Used when neither value is a starting point, such as comparing two measurements. See the percent difference calculator.
- Percentage points
- The plain gap between two percentages. A rate moving from 2% to 4% rose by 2 points, but that is a 100% increase.
- Percentage of a number
- A different question again, handled by the percentage calculator.
What this assumes
The starting value is not zero. Any change from zero is undefined as a percentage, because you cannot divide by it.
How to calculate a percentage change
Find the difference, divide by the starting value, then turn it into a percentage.
- new − old
- The change. Negative means it went down
- ÷ old
- The starting value, always
Subtract. New value minus old value. Keep the sign: negative is a decrease.
Divide by the old value. This is where the answer is decided. Dividing by the new value answers a different question.
Multiply by 100. That turns the decimal into a percentage.
To apply a change instead, multiply. Up 20% means × 1.20. Down 20% means × 0.80.
See a worked example: why up 50% then down 50% loses money
- Starting value
- 100
- Then
- +50%, then −50%
Up 50%: 100 × 1.5 = 150.
Down 50%: 150 × 0.5 = 75.
You are 25% below where you started, despite the two percentages looking like they cancel.
The reason is the base changed. The rise was 50% of 100, but the fall was 50% of 150, which is a much bigger amount.
75, a net loss of 25%
Frequently asked questions
- How do I calculate a percentage increase?
Subtract the old value from the new one, divide by the old value, then multiply by 100. Going from 50 to 75 is 25 ÷ 50 × 100 = a 50% increase.
To apply an increase rather than measure one, multiply by 1 plus the decimal: a 20% rise is × 1.20.
- What is a 5% increase of $100?
$105. Multiply 100 by 1.05, or work out 5% of 100 (which is 5) and add it on.
The same method scales: 5% more than $250 is 250 × 1.05 = $262.50.
- How do I calculate a 20% increase?
Multiply by 1.20. A price of 80 becomes 80 × 1.20 = 96; a salary of $50,000 becomes $60,000.
Watch the reverse: taking 20% back off 96 gives 76.80, not 80, because the 20% now comes off a bigger number. To undo it, divide by 1.20.
- How do I calculate a 2.5% increase?
Multiply by 1.025. A $40,000 salary rising 2.5% becomes $41,000, an increase of $1,000.
For any awkward percentage, the rule is the same: move the decimal two places left and add 1. 2.5% becomes 0.025, so the multiplier is 1.025.
- Do I divide by the old value or the new one?
Always the old one. Percentage change measures movement relative to where you started.
Going from 50 to 75 is a 50% increase, because 25 ÷ 50 = 0.5. Dividing by 75 would give 33.3%, which is the answer to 'what share of the new value was the change'.
- Why isn't a 50% fall the opposite of a 50% rise?
Because each percentage is taken from a different base. Rising 50% from 100 gives 150, and falling 50% from 150 gives 75.
To reverse a 50% rise you need a 33.3% fall. To reverse a 20% fall you need a 25% rise. The larger the move, the bigger the gap.
- What's the difference between percentage change and percentage points?
If an interest rate moves from 2% to 4%, that is a rise of 2 percentage points but a 100% increase.
Both are correct, and the difference is often exploited in reporting, because 100% sounds far more dramatic. Use points whenever you are comparing two figures that are already percentages.
- How do I apply a percentage increase in one step?
Multiply by 1 plus the decimal. Up 20% is × 1.20, and down 20% is × 0.80.
To reverse it, divide. If a price is 120 after a 20% rise, the original was 120 ÷ 1.20 = 100. Subtracting 20% instead would wrongly give 96.
- Can percentage change be more than 100%?
An increase can, easily. Going from 10 to 30 is a 200% increase, meaning it tripled.
A decrease cannot go below −100%, because that would mean losing more than everything. A value falling to zero is exactly −100%.
Problems people actually run into
Averaging percentage changes
Gaining 50% one year and losing 50% the next does not average to zero. It leaves you 25% down, because the second percentage applied to a larger base.
Averaging percentage changes across periods is nearly always wrong. The honest figure is the compound result, which is what you get by multiplying the factors: 1.5 × 0.5 = 0.75.
Subtracting a discount to find the original price
An item costs 80 after 20% off. Adding 20% back gives 96, not 100, because the 20% is now being taken from the smaller figure.
Divide instead: 80 ÷ 0.80 = 100. This is the same trap as margin versus markup, and it appears constantly in retail arithmetic.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 12, 2026
