To calculate a percentage increase, compare how much a value changed with where it started. The starting value is the baseline: a rise of 10 is a big change from 20, but a small change from 1,000. That is why the same difference can represent very different percentages.
The method works for a price, score, measurement, quantity, or other number that can be compared consistently. First identify the original value and the new value; then calculate the difference and express it as a fraction of the original. The same process gives a negative answer for a decrease.
The percentage increase formula
Use this formula when the original value is nonzero:
Percentage change = ((new value − original value) ÷ original value) × 100
If the new value is greater than the original, the result is positive and describes an increase. If the new value is lower, the result is negative; its magnitude describes the decrease. For example, a result of −12% means the value fell by 12% relative to its starting amount.
Some calculators use the absolute value of the original number in the denominator, written as |original value|. For ordinary quantities with a positive starting point, that gives the same answer as dividing by the original. For numbers that may be negative, such as a financial balance moving through zero, decide which convention is appropriate before interpreting a percentage: a percent change can be ambiguous when the baseline is negative.
Which number is the baseline?
The denominator is the starting value, not the ending value and not the difference. A useful way to remember the order is “change compared with what you had.” Label the values before doing arithmetic: old = 80, new = 100. The change is 100 − 80 = 20, and the baseline is 80.
Do not swap the two values simply because the smaller number looks more convenient. Percentage comparisons are directional. Going from 80 to 100 is a 25% increase; going back from 100 to 80 is a 20% decrease. The size of the numerical difference is 20 both ways, but each change is measured against a different starting point.
Worked examples: increases and decreases
Example 1: a price goes up
A monthly service fee changes from $48 to $60. Subtract the original price from the new price: $60 − $48 = $12. Divide that increase by the starting price: $12 ÷ $48 = 0.25. Convert the decimal to a percentage by multiplying by 100: 25% increase.
Check the result by applying it to the base: 25% of $48 is $12, and $48 + $12 = $60. If a percentage is being used for a real bill or contract, distinguish a percentage change in the listed price from any taxes, fees, or other changes that occurred at the same time.
Example 2: a value goes down
A container holds 250 milliliters before a process and 210 milliliters afterward. The signed change is 210 − 250 = −40. Divide by the original: −40 ÷ 250 = −0.16. Multiplying by 100 gives −16%, which can be stated as a 16% decrease.
For a decrease, you can also calculate the drop as a positive amount first: (250 − 210) ÷ 250 × 100 = 16%. Both descriptions communicate the same change. Keep the original amount in the denominator in either version.
Example 3: a percentage-point change is different
Suppose a survey result moves from 40% to 50%. The absolute difference is 10 percentage points. The relative percentage increase is (50 − 40) ÷ 40 × 100 = 25%. “Up 10 percentage points” and “up 25 percent” describe different things. Use percentage points when subtracting one percentage rate from another; use percentage change when comparing the difference with the former rate.
Why a zero starting value is a special case
If the original value is zero, the formula asks you to divide by zero. That operation is undefined, so there is no finite percentage increase or decrease from zero under the standard formula. Going from 0 visitors to 25 visitors is a gain of 25 visitors, but it is not accurately described as a 100% increase. There was no nonzero baseline against which to measure the gain.
Report the absolute change instead, or choose a separate meaningful comparison period with a nonzero starting value. If an application requires a percentage, explain the limitation rather than quietly substituting another denominator. The Kinsad Percentage Calculator has a percentage-change mode that takes the original and new values; when the original is zero, that calculation is not defined.
How to reverse a percentage increase or decrease
To recover an original amount from a final amount, undo the multiplier; do not simply subtract or add the same percentage to the final amount. An increase of p% multiplies the starting value by 1 + p/100. Therefore:
Original after an increase = final value ÷ (1 + p/100)
For a 15% increase, divide the final value by 1.15. If a marked price is now $115 after a 15% increase, $115 ÷ 1.15 = $100. The original was $100. Subtracting 15% of $115 would give $97.75, which is not the original, because the 15% increase was calculated on $100, not $115.
To reverse a decrease of p%, divide the final amount by 1 − p/100. For an item that costs $84 after a 30% discount, calculate $84 ÷ 0.70 = $120. The original price was $120. Adding 30% of $84 would produce $109.20, which is still short of the original.
Equal increases and decreases do not cancel
Suppose a number starts at 100, rises by 20%, and then falls by 20%. The rise gives 100 × 1.20 = 120. The decrease is 20% of the new base, 120, so the result is 120 × 0.80 = 96. The final value is 4% below the starting value, not back at 100.
For the reverse trip from 120 to 100, the decrease is 20 ÷ 120 = 16.67%, approximately. Each percentage is tied to its own starting value. This is why a discount followed by a same-sized markup, or a loss followed by an equal percentage gain, may not restore the original.
A quick process to check your answer
- Name the comparison: identify the old value and the new value, in the same units.
- Find the signed difference: subtract old from new.
- Use the original as the baseline: divide the difference by the old value.
- Convert to percent: multiply by 100 and include the sign or state increase/decrease.
- Check plausibility: multiply the original by the resulting factor and see if it reaches the new value.
Keep extra decimals during intermediate steps and round the final result to a precision useful for the task. If figures are estimates, excessive decimal places can suggest a level of certainty the source data does not support. OpenStax explains the relationship among a percent, its base, and the resulting part in its Understanding Percent lesson; the same base-first thinking makes a percent-change calculation easier to audit.
Common mistakes to avoid
- Dividing by the new value: standard percentage change is measured from the old value.
- Dropping units or context: make sure both values refer to the same thing and period.
- Confusing a percent with a percentage point: subtracting two rates gives points; relative change requires division by the earlier rate.
- Calling a zero-baseline change 100%: the formula has no defined percentage result when the original is zero.
- Reversing the percentage against the wrong base: undo an increase with division by its growth factor; undo a decrease by division by the remaining fraction.
Frequently asked questions
What is the difference between percentage increase and percentage change?
Percentage change is the general signed comparison. A positive result is an increase; a negative result is a decrease. People often say “percentage increase” specifically when the new value is higher.
Can the percentage decrease be more than 100%?
For nonnegative values decreasing to zero, the decrease is 100%. A result below zero would mean the value crossed below zero, which may need a different interpretation than an ordinary decrease.
Can I use the same formula for measurements in different units?
Convert them to the same unit first. Comparing 2 meters directly with 250 centimeters without conversion would mix units and produce a meaningless result.