How to use this calculator
Pick the question you’re asking from the menu:
- Percentage change from an old to a new value. Enter the old and new values. You get the percent increase or decrease, the change in value, the growth factor and a note on what it takes to get back.
- Increase or decrease a value by a percentage. Enter a starting value, choose increase or decrease, and enter the percentage.
- Original value before a percentage change. Enter the value after the change and the percentage, and the calculator works backward to the starting value.
- Percentage points vs. percent. Enter two rates, such as interest rates or test pass rates, to see the change both ways.
The working appears under every answer, so you can follow it or repeat it by hand. For other percentage questions, such as “what is 15% of 80” or “45 is what percent of 60,” use the general percentage calculator.
The percentage change formula
Percentage change compares the change with where you started:
A positive result is a percentage increase and a negative result is a percentage decrease. If the old value is negative, the calculator divides by its size (absolute value) so that a rise always comes out positive.
Applying a change and undoing one both use the multiplier, 1 plus the change as a decimal. A 12% increase multiplies by 1.12; a 15% decrease multiplies by 0.85. To find the value before a change, divide by the multiplier instead:
Worked examples
Percentage increase. Your rent rises from $1,250 to $1,400 a month. The change is 1,400 − 1,250 = 150, and 150 ÷ 1,250 = 0.12, so that’s a 12% increase. To get back down to $1,250, the rent would have to fall by 10.71%, because that cut would be measured from the larger $1,400.
Percentage decrease. A stock falls from $80 to $60. The change is −20, and −20 ÷ 80 = −0.25: a 25% decrease. Getting back to $80 needs a 33.33% gain.
Applying a change. Increase 80 by 25%: 80 × 1.25 = 100. Decrease 200 by 15%: 200 × 0.85 = 170.
Reversing a change. A price is $1,400 after a 12% increase. The original was 1,400 ÷ 1.12 = $1,250. A jacket on sale for $68 at 15% off had an original price of 68 ÷ 0.85 = $80.
Percentage points. A savings rate goes from 4% to 5%. That’s a rise of 1 percentage point, and a 25% increase in the rate itself (1 ÷ 4 × 100).
What it takes to get back
A change and its reverse are never the same size, because the second change starts from a different number. These figures come from the calculator’s “getting back” note:
| Change | Change needed to return to the start |
|---|---|
| +5% | −4.76% |
| +10% | −9.09% |
| +20% | −16.67% |
| +25% | −20% |
| +50% | −33.33% |
| +100% | −50% |
| −5% | +5.26% |
| −10% | +11.11% |
| −20% | +25% |
| −25% | +33.33% |
| −50% | +100% |
| −75% | +300% |
The asymmetry grows quickly with the size of the drop. A portfolio that loses 75% has to quadruple, a 300% gain, just to break even. It’s also why a 20% price cut followed by a 20% increase leaves the price 4% below where it started. The formula is −p ÷ (100 + p) × 100, where p is the original change.
Percentage points vs. percent
When the values you’re comparing are already percentages, such as interest rates, tax rates, unemployment or poll results, there are two honest ways to describe a change, and they give very different numbers:
- Percentage points subtract one rate from the other. A mortgage rate moving from 6% to 7% is up 1 percentage point.
- Percent change compares that gap with the starting rate. The same move is a 16.67% increase in the rate.
Both are correct; they answer different questions. Use percentage points when you’re describing the rate itself and percent when you’re describing how much it changed relative to where it was. The “points” mode shows both side by side, so you can quote whichever one you mean.
Tips for accurate percentage changes
- Always divide by the old value. That’s what makes it a change “from” something. Dividing by the new value is a common slip that understates increases and overstates decreases.
- Don’t add percentage changes. Two years of 10% growth is 1.1 × 1.1 = 1.21, a 21% rise, not 20%. Our compound interest calculator applies this over many years, and the inflation calculator does it with real price data.
- Stacked discounts multiply too. 25% off and then another 10% off is 32.5% off in total. The discount calculator handles stacked discounts and sales tax.
- Keep the sign. A −8% change and an 8% decrease are the same thing; write one or the other, not “−8% decrease.”
- For comparing two values with no “before,” such as two quotes or two measurements, percentage difference (relative to their average) is fairer. The percentage calculator has a mode for it.
Assumptions and rounding
The calculator removes floating-point noise before showing results, displays values to up to 4 decimal places and percentages to 2, and marks rounded figures in the steps with ≈. A change from zero has no percentage, so it asks for a nonzero old value. In reverse mode, a decrease must be less than 100%, since after a 100% drop every starting value ends at zero.
Frequently asked questions
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value, and multiply by 100. Rent that goes from $1,250 to $1,400 changed by (1,400 − 1,250) ÷ 1,250 × 100 = 12%. A positive answer is an increase and a negative answer is a decrease.
What's the difference between percentage increase and percentage change?
Percentage change is the general term, and it can be positive or negative. A percentage increase is simply a positive percentage change, and a percentage decrease is a negative one written without the minus sign. The formula is the same for both.
Why does a 50% drop need a 100% gain to recover?
Each percentage is measured from a different starting point. Halving 100 leaves 50, and getting from 50 back to 100 means adding another 50, which is 100% of 50. In general, the smaller the value after a fall, the larger the percentage gain needed to recover.
How do I find the original number before a percentage increase?
Divide the new number by 1 plus the percentage as a decimal. If a price is $1,400 after a 12% increase, the original was 1,400 ÷ 1.12 = $1,250. Taking 12% off $1,400 instead gives $1,232, which is wrong because the 12% was a share of the original.
What is the difference between a percentage point and a percent?
A percentage point is the plain difference between two percentages, while percent change measures that difference relative to the starting rate. An interest rate going from 4% to 5% rose by 1 percentage point, but by 25% in relative terms. News reports usually mean percentage points when they say a rate "rose 1%".
Can I calculate a percentage change from zero?
No. Any change from zero is infinitely large in percentage terms, because you would be dividing by zero. Report the change as an absolute amount instead, such as "from 0 to 40 sales," or compare against a different, nonzero baseline.
Updated November 2026. Results are estimates for educational purposes and depend on the inputs you provide.