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Percentage Change Calculator
Work out percentage change, percentage increase and percentage decrease between two numbers. Free, instant, no signup.
Calculator
How do you calculate percentage change?
Percentage change = ((new − old) ÷ old) × 100. Positive is an increase; negative is a decrease.
Why is a fall from 100 to 80 only −20% when 80 to 100 is +25%?
The base changed. The same £20 move is a fifth of 100 but a quarter of 80.
Is percentage change the same as percentage points?
No. Percentage change is relative to the start. Percentage points are the raw gap between two percents.
How much do you need to gain back after a loss?
Required gain = 1 ÷ (1 − loss) − 1. A 20% fall needs 25% back, and a 50% fall needs 100%. The table below gets less cheerful as it goes.
Do two percentage changes add up?
No, they multiply. Up 10% then down 10% leaves you at 1.10 × 0.90 = 0.99 of where you started, so you are down 1% despite the moves "cancelling out".
How do you find the original number before a percentage change?
Original = new ÷ (1 + change). A £120 price after a 20% rise started at 120 ÷ 1.2 = £100. Taking 20% off £120 gives £96, which is the classic wrong answer.
How much you need to gain back after a fall
Required gain = 1 ÷ (1 − fall) − 1. Starts at £100. Worked out from that formula, not from any market.
| Fall | What is left | Gain to get back to £100 |
|---|---|---|
| −5% | £95 | 5.3% |
| −10% | £90 | 11.1% |
| −20% | £80 | 25.0% |
| −25% | £75 | 33.3% |
| −30% | £70 | 42.9% |
| −50% | £50 | 100.0% |
| −75% | £25 | 300.0% |
| −90% | £10 | 900.0% |
The formula
Percentage change = ((new − old) ÷ old) × 100 A positive result is an increase. A negative result is a decrease. Absolute percentage change = |percentage change| (the size of the move, ignoring direction). Going the other way: New value = old × (1 + percentage ÷ 100)
Worked example
A share goes from £80 to £100.
Percentage change = ((100 − 80) ÷ 80) × 100 = 25%
So the share rose 25%.
Going the other way: £80 rises by 25%.
New value = 80 × (1 + 25 ÷ 100) = 80 × 1.25 = £100.
If it fell from £100 to £80:
Percentage change = ((80 − 100) ÷ 100) × 100 = −20%
Same pounds lost, different percent, because the starting point changed. That asymmetry trips people up.
Methodology
How it calculates
- Compares two numbers relative to the starting value.
- Also supports solving for the new value given an old value and a percent move.
Formula
Percentage change = ((new − old) ÷ old) × 100 A positive result is an increase. A negative result is a decrease. Absolute percentage change = |percentage change| (the size of the move, ignoring direction). Going the other way: New value = old × (1 + percentage ÷ 100)
Assumptions
- No units conversion. Both numbers must share the same unit.
- Not financial advice; education only.
Edge cases
- Old value of zero cannot be used as a base for percentage change.
- A rise from 80 to 100 is +25%; a fall from 100 to 80 is −20% (base changed).
Sources
None. Pure maths; no external rate or spec feed.
FAQ
What is the difference between percentage change and percentage points?
Percentage change is relative to the starting number. Percentage points are the raw gap between two percentages. If a rate moves from 2% to 3%, that is a rise of 1 percentage point, but a 50% percentage change.
Why is a fall from 100 to 80 only −20%, when 80 to 100 was +25%?
Because the base changed. From 80 the move of 20 is a quarter of the start. From 100 the same 20 is a fifth. Always check which number you are dividing by.
Can I use this for prices, salaries and portfolio returns?
Yes. Any two numbers that share the same unit work. For multi-year returns, CAGR is usually clearer than a single percentage change.
Does this use live market data?
No. You type the numbers. Nothing is fetched from markets, so there is no data licence and no delay.
Not financial advice. This calculator is for education only. Double-check results before you make money decisions. Past moves do not predict future ones.