A percentage increase calculator finds the percent change between an initial value and a final value — the standard way to express how much something grew or shrank relative to where it started. Prices, salaries, populations, website traffic, and investment returns are all routinely reported this way because a relative change is more meaningful than a raw difference.
Enter the starting value and the ending value. The calculator returns the signed percentage change (positive for an increase, negative for a decrease), the absolute change, and the exact formula with your numbers substituted in, so every result is easy to verify by hand.
The Percent Change Formula
Percentage change compares the difference between two values to the original value:
Percentage change = (final − initial) ÷ |initial| × 100
Three points about this formula:
- The initial value goes in the denominator — always divide by where you started, not where you ended.
- The absolute value in the denominator keeps the direction of the change correct even when the initial value is negative (for example, a company going from −$50,000 to −$20,000 in profit is a 60% improvement).
- The sign of the result carries meaning: +25% is a 25% increase, −25% is a 25% decrease.
The formula breaks down when the initial value is 0: any change from zero is infinite in percentage terms, so the calculator reports an error rather than a misleading number.
Percent Increase vs Percentage Difference
These two terms are often mixed up but answer different questions:
- Percent increase/decrease is directional: it compares a new value against an original value, dividing by the original. Going from 200 to 250 is a 25% increase; going from 250 to 200 is a 20% decrease. The percentages differ because the base differs.
- Percentage difference is non-directional: it compares two values of equal standing, dividing by their average: |a − b| ÷ ((a + b) ÷ 2) × 100. For 200 and 250 that is 50 ÷ 225 × 100 ≈ 22.22%.
Use percent change when there is a clear "before" and "after" (a price rise, a raise, growth over time). Use percentage difference when neither value is the baseline, such as comparing prices at two different stores.
Worked Examples: A Raise and a Price Drop
Example 1 — salary increase. Your pay rises from $52,000 to $58,500.
- Absolute change: 58,500 − 52,000 = 6,500.
- Divide by the initial value: 6,500 ÷ 52,000 = 0.125.
- Multiply by 100: a +12.5% increase.
Example 2 — discounted TV. A television drops from $800 to $620.
- Absolute change: 620 − 800 = −180.
- Divide by the initial value: −180 ÷ 800 = −0.225.
- Multiply by 100: a −22.5% change, i.e. a 22.5% decrease.
Reverse check for example 1: 12.5% of 52,000 is 6,500, and 52,000 + 6,500 = 58,500 — the numbers close the loop, confirming the answer.
Frequently Asked Questions
How do you calculate percentage increase?
Subtract the initial value from the final value, divide by the initial value, and multiply by 100: (final − initial) ÷ initial × 100. Going from 200 to 250 gives (250 − 200) ÷ 200 × 100 = 25%, a 25% increase.
How do you calculate percentage decrease?
Use the same formula — the result simply comes out negative. From 250 down to 200: (200 − 250) ÷ 250 × 100 = −20%, a 20% decrease. Reports often drop the minus sign and state "a 20% decrease" instead.
Why is a 25% increase not undone by a 25% decrease?
Because the base changes. Increasing 200 by 25% gives 250, but decreasing 250 by 25% removes 62.50, landing at 187.50, not 200. To undo a 25% increase you need a 20% decrease, since 50 is 20% of the new base of 250.
What is the difference between percent change and percentage difference?
Percent change is directional and divides by the initial value — right for before-and-after comparisons. Percentage difference is non-directional and divides by the average of the two values — right when neither number is the baseline. For 200 and 250, percent change is 25% but percentage difference is about 22.22%.
Can percentage increase be more than 100%?
Yes. A value that more than doubles has increased by over 100%. Growing from 40 to 100 is (100 − 40) ÷ 40 × 100 = 150%. A 100% increase means exactly doubling; a 200% increase means tripling the original value.