Percent change describes how much a quantity grew or shrank relative to where it started. A rise from 80 to 92 is a 12-unit change, and because 12 is 15% of 80, it is a 15% increase. This percent change calculator takes an old value and a new value and returns the percentage increase or decrease, the absolute change, the symmetric "percent difference" used when neither value is the natural starting point, and the reverse change that would undo it.
For the basic "what is X% of Y" questions use the percentage calculator; for prices after a markdown use the discount calculator.
How to use the percent change calculator
- Enter the old, or starting, value. This is the reference the change is measured against.
- Enter the new value.
- A positive result is an increase and a negative result is a decrease.
- Use percent difference when comparing two values with no natural "before", such as prices at two stores.
Formula
Dividing by the absolute value of the old number keeps the sign meaningful when the starting value is negative: going from −10 to −5 is reported as a 50% increase. Percent change from zero has no defined value.
Worked example
A student's quiz score rose from 80 to 92.
- Change: 92 − 80 = 12 points.
- Percent change: 12 ÷ 80 × 100 = +15%.
- Percent difference: 12 ÷ ((92 + 80) ÷ 2) × 100 = 12 ÷ 86 × 100 = 13.95%.
- Reverse change: going from 92 back to 80 is (80 − 92) ÷ 92 × 100 = −13.04%.
Why a 50% drop needs a 100% gain to recover
Percent changes are measured from different bases, so they don't cancel. If a value falls 50% from 200 to 100, getting back to 200 requires a 100% increase, because the gain is measured against the smaller number. Likewise a 20% rise followed by a 20% fall leaves you 4% below where you started: 100 × 1.2 × 0.8 = 96. The calculator's "reverse change" line shows this asymmetry for your numbers.
| Decrease | Increase needed to recover |
|---|---|
| 10% | 11.11% |
| 20% | 25% |
| 25% | 33.33% |
| 33.33% | 50% |
| 50% | 100% |
| 75% | 300% |
Percent change vs percentage points
When the quantities are themselves percentages, say a pass rate, be careful with wording. A pass rate rising from 60% to 75% has gone up by 15 percentage points, but the percent change is (75 − 60) ÷ 60 = 25%. News reports and school data use both, so check which is meant. Enter 60 and 75 above to see the percent change; the absolute change line gives the percentage-point change.
For several periods of growth in a row, multiply the growth factors rather than adding the percentages: +10% then +10% is 1.1 × 1.1 = 1.21, a 21% total increase.
Caveats and assumptions
- Percent change from an old value of zero has no defined value; the calculator reports this rather than a misleading number.
- With negative starting values, the sign follows the direction of movement on the number line.
- Percent difference is symmetric and is not the same as percent change; use it only when neither value is the baseline.
- Results are rounded to two decimal places for display.
Frequently asked questions
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 92: 12 ÷ 80 × 100 = 15%.
How do I calculate percentage decrease?
Use the same formula; the result is negative. From 50 to 40: (40 − 50) ÷ 50 × 100 = −20%, a 20% decrease.
What is the difference between percent change and percent difference?
Percent change measures against the old value. Percent difference measures against the average of the two values, so it gives the same answer whichever value you list first.
Why can’t I calculate percent change from zero?
Dividing by zero has no defined result. Report the absolute change instead, for example "rose from 0 to 12".
If a price rises 25% and then falls 25%, is it back to the original?
No. 100 × 1.25 × 0.75 = 93.75, so it ends 6.25% below where it started.
Sources
- OpenStax Prealgebra 2e — 6.2 Solve General Applications of Percent (percent increase and decrease) — percent increase and decrease method
- OpenStax Prealgebra 2e — 6.1 Understand Percent — percent as a ratio per hundred
- NIST Special Publication 811 — Guide for the Use of the International System of Units — guidance on expressing values and percentages
This calculator gives estimates for planning and education. Check measurements, local codes, supplier specs and your school's official policy before relying on a result. See our disclaimer and how we build and check calculators.