Percentage increase calculator
Percentage change is always measured against the starting value. A fall is the same calculation with a negative result.
Result
- Increase
- 25.00%
- Absolute change
- 20.00
- Multiplier
- ×1.2500
Worked examples
A price rise
Rent goes from $1,200 to $1,320 a month.
- 1320 − 1200 = 120
- 120 ÷ 1200 = 0.1
- 0.1 × 100 = 10
A 10% increase.
A fall
Website traffic drops from 8,400 to 7,140 visits.
- 7140 − 8400 = −1260
- −1260 ÷ 8400 = −0.15
A 15% decrease.
Change is always measured against the start
Percentage change divides by the original value, never the new one. That single choice is what makes increases and decreases asymmetric, and it is the source of most confusion about the topic.
Going from 80 to 100 is a 25% increase, because 20 is a quarter of 80. Coming back down from 100 to 80 is a 20% decrease, because the same 20 is now a fifth of 100. The journey is identical; the base changed, so the percentage did too.
Multipliers are easier for chained changes
For anything involving more than one step, convert to a multiplier: a 10% rise is ×1.1, a 10% fall is ×0.9. Then multiply them together rather than adding percentages.
A 10% rise followed by a 10% fall is 1.1 × 0.9 = 0.99, a net loss of 1%. Adding the percentages would have told you nothing changed, which is wrong. This matters for anything compounding: investment returns, inflation, population growth.
Reversing a percentage change
To undo an increase you divide, not subtract. If a price includes a 20% markup and you want the original, divide by 1.2 rather than taking 20% off — taking 20% off the marked-up price gives you a different, smaller number.
This is the most common error in VAT and sales-tax arithmetic. A $120 total that includes 20% tax has a pre-tax value of $100, not $96.
Formula
change % = ((new − old) ÷ old) × 100
Worth knowing
- A rise from 80 to 100 is a 25% increase, but the fall from 100 back to 80 is only a 20% decrease — the base changed.
Percentage change as a multiplier
Converting to a multiplier is what makes repeated changes tractable — multiply them rather than adding the percentages.
| Change | Multiplier | Reverse it by |
|---|---|---|
| +5% | ×1.05 | ÷1.05 (−4.76%) |
| +10% | ×1.1 | ÷1.1 (−9.09%) |
| +20% | ×1.2 | ÷1.2 (−16.67%) |
| +25% | ×1.25 | ÷1.25 (−20%) |
| +50% | ×1.5 | ÷1.5 (−33.33%) |
| +100% | ×2 | ÷2 (−50%) |
| −10% | ×0.9 | ÷0.9 (+11.11%) |
| −25% | ×0.75 | ÷0.75 (+33.33%) |
| −50% | ×0.5 | ÷0.5 (+100%) |
Why increases and decreases are not symmetric
| Start | Change | End | To get back |
|---|---|---|---|
| 100 | +10% | 110 | −9.09% |
| 100 | +25% | 125 | −20% |
| 100 | +50% | 150 | −33.33% |
| 100 | +100% | 200 | −50% |
| 100 | −10% | 90 | +11.11% |
| 100 | −50% | 50 | +100% |
Frequently asked questions
How do I calculate percentage increase?
Subtract the old value from the new, divide by the old value, then multiply by 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%.
Is percentage decrease calculated the same way?
Yes, and it is the same formula. A negative result means a decrease. From 100 to 80: (80 − 100) ÷ 100 × 100 = −20%.
Why is a 25% increase reversed by only a 20% decrease?
Because the base changes. The 25% is a share of 80, the 20% is a share of 100. The same absolute change of 20 is a different fraction of each.
How do I combine two percentage changes?
Multiply the multipliers instead of adding the percentages. A 10% rise then a 5% rise is 1.1 × 1.05 = 1.155, a 15.5% total increase — not 15%.
What if the starting value is zero?
Percentage change is undefined. Dividing by zero has no answer, so growth from nothing has to be described in absolute terms instead.
How do I calculate percentage change over several periods?
Multiply the multipliers. Three consecutive 10% rises are 1.1³ = 1.331, a 33.1% total increase rather than 30%.
What is the average annual growth rate?
Take the nth root of the total multiplier, where n is the number of periods. Growth from 100 to 150 over 3 years is 1.5^(1/3) = 1.1447, about 14.5% a year.
Why can a percentage decrease never exceed 100%?
Because a 100% decrease removes the entire quantity. Anything beyond that would take the value below zero, which most quantities cannot do.
What does a 200% increase mean?
The value tripled. A 100% increase is a doubling, so a 200% increase adds twice the original on top of it.
How do I find the original value after a percentage increase?
Divide by the multiplier. If a value is 138 after a 15% rise, the original was 138 ÷ 1.15 = 120.