How to calculate percentage increase (formula and examples)
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How do you calculate percentage increase?
Subtract the old value from the new one, divide the difference by the old value, then multiply by 100. A subscription that rises from 80 to 100 dollars increased by (100 - 80) ÷ 80 × 100 = 25 percent, because the change is measured against the starting value.
Your streaming subscription went from 80 to 100 dollars a year. Is that a 20% increase, or 25%? The question hides a choice of reference: 20 is 20% of 100, but 25% of 80. The correct answer is 25%, and once the formula is in your head, you can settle any price hike, salary raise or traffic spike in ten seconds. This guide covers the formula, worked examples with real numbers, the asymmetry that makes losses harder to recover than gains, and the percentage-point distinction that headlines mangle.
The percentage increase formula
Percentage increase always measures the change relative to the starting value:
percentage increase = (new - old) ÷ old × 100
Three steps, in order:
- Subtract the old value from the new one to get the raw change.
- Divide that change by the old value, not the new one.
- Multiply by 100 to turn the decimal into a percentage.
For the subscription: (100 - 80) ÷ 80 × 100 = 20 ÷ 80 × 100 = 25%. The division by the old value is the whole trick. The change is judged against where you started, because that is what "increase" means: how much more you pay compared to before. The same definition appears in Reed College's primer on percentage change, which works it through a wage rising from 4 to 5 dollars per bushel, a 25 percent raise by the same division.
⚠️ Common mistake: Dividing by the new value instead of the old one shrinks every increase. The 80-to-100 move becomes 20 ÷ 100 = 20% instead of 25%, and the error grows with the size of the change: a price that doubles shows up as a 50% increase. Anchor the division to the value you started from.
Run 80 to 100 in change mode and read the calculation line, spelled out step by step, under the result.
Worked examples with real numbers
A few common situations, computed with the same one-line formula:
| Situation | Old value | New value | Calculation | Increase |
|---|---|---|---|---|
| Monthly rent | 1,200 | 1,320 | 120 ÷ 1,200 × 100 | 10% |
| Annual salary | 54,000 | 58,320 | 4,320 ÷ 54,000 × 100 | 8% |
| Website traffic | 8,400 | 12,600 | 4,200 ÷ 8,400 × 100 | 50% |
| Grocery item | 2.49 | 2.99 | 0.50 ÷ 2.49 × 100 | 20.08% |
The formula also works in reverse. If the new value is smaller, the result comes out negative and you are looking at a percentage decrease. A stock that falls from 150 to 120 has changed by (120 - 150) ÷ 150 × 100 = -20%. One formula handles both directions, which is why calculators call it "percentage change" rather than maintaining two separate modes. Averages behave the same way: when a monthly metric jumps around, compare its average across periods before reading too much into a single increase.
The asymmetry trap: +25% then -25% is not zero
Increases and decreases of the same percentage do not cancel each other, because each one is measured on a different base.
Start at 100. Add 25% and you reach 125. Now remove 25%: that 25% is computed on 125, so you subtract 31.25 and land on 93.75. You end up 6.25% below where you started.
The same asymmetry explains why a big loss is so hard to recover. A portfolio that drops 50% needs a 100% gain to get back to even: from 200 down to 100, then 100 has to double to reach 200 again. To undo an increase of X%, the exact decrease needed is X ÷ (100 + X) × 100; to undo a decrease, the required gain grows faster than the loss:
| Loss | Gain needed to break even |
|---|---|
| -10% | +11.1% |
| -20% | +25% |
| -25% | +33.3% |
| -50% | +100% |
🚫 Avoid: Adding percentages across periods. Two price increases of 10% compound to 21%, not 20%, because the second one applies to an already-raised base: 100 × 1.1 × 1.1 = 121. The gap looks small over two steps and widens fast over many, which is how yearly inflation figures produce decade totals that surprise people.
Percent versus percentage points
News reports mix these up all the time. When an interest rate moves from 5% to 7%, two different statements are both true:
- The rate rose by 2 percentage points (the raw gap: 7 - 5).
- The rate rose by 40 percent (the relative change: 2 ÷ 5 × 100).
"Points" compare percentages by subtraction; "percent" compares them by division. The EU's data visualisation guide insists on the same discipline for charts and reports: call the result of subtracting two percentages a difference in percentage points, and reserve "percent" for the relative change. The full distinction, with more examples, sits in our glossary entry on the percentage point.
💡 Good to know: The Reed College primer calls the gap a favorite tool of anyone with something to sell: a mortgage rate climbing from 4% to 6% is a 50 percent increase in the interest you pay, yet "up 2 points" sounds like a rounding error. Same move, two framings, and the framing usually gets chosen by whoever benefits from it.
Reverse percentage: finding the original value
You know the result and the percentage, and you want the starting point. A jacket costs 90 after a 25% discount: what was the original price? Adding 25% back to 90 gives 112.50, which is wrong. The discounted price is 75% of the original, so divide instead:
original = final ÷ (1 + increase ÷ 100) for an increase, or original = final ÷ (1 - decrease ÷ 100) for a discount.
Here: 90 ÷ 0.75 = 120. The jacket started at 120. Same logic for prices that include tax: an item priced 108 with 8% sales tax baked in cost 108 ÷ 1.08 = 100 before tax. The rule of thumb: undo a percentage by dividing by its multiplier, never by applying the opposite percentage.
Apply a 25% discount to 120 in decrease mode and confirm the jacket lands at 90, then reverse your own receipts.
Quick checklist
- Divide by the old value, the one you started from.
- A negative result means a decrease. The formula handles both directions.
- Say "points" when subtracting two percentages, "percent" when dividing them.
- To reverse a percentage, divide by the multiplier instead of subtracting.
- When the numbers get messy, 2.49 to 2.99 rather than 80 to 100, hand the arithmetic to the percentage calculator and keep your attention on what the result means.
With the formula and these reflexes, a price tag, a payslip or a headline becomes something you can verify in seconds, and the verification is usually one division.
Frequently asked questions
What is the difference between percentage increase and percentage change?
Direction. Percentage change is the umbrella term: (new - old) ÷ old × 100, with a sign that tells the story. A positive result is a percentage increase, a negative one a percentage decrease. In practice you compute the same division either way, which is why one formula covers a raise, a discount and a stock drop. The sign convention pays off in spreadsheets, where a column of changes can be summed, averaged and sorted without splitting rises and falls into separate cases.
Can a percentage increase be more than 100 percent?
Yes, and it happens whenever a value more than doubles. Going from 8,400 to 25,200 site visits is (25,200 - 8,400) ÷ 8,400 × 100 = 200%. The vocabulary trips people here:
- A 100% increase means the value doubled.
- A 200% increase means it tripled.
- Increasing to 200% of the original is doubling, not tripling.
Watch the preposition: "increased by 200%" and "increased to 200%" describe different outcomes, and marketing copy has been known to pick whichever sounds bigger.
Why does a 50% loss need a 100% gain to break even?
Because the gain is computed on the smaller, post-loss base. Lose 50% of 200 and you hold 100; the missing 100 now equals 100% of what you have left. The percentages refuse to cancel since each references a different starting point. The rule scales in both directions: a 20% loss needs a 25% gain and a 90% loss needs a 900% gain. Run any pair through the percentage calculator to see the recovery math, and distrust any comparison that nets out gains and losses by adding their percentages.
How do I find the original price before an increase?
Divide the final price by the growth multiplier. An increase of p percent multiplies the original by (1 + p ÷ 100), so undoing it means dividing by that same factor. A bill of 240 after a 20% increase started at 240 ÷ 1.2 = 200. Two checks keep you out of trouble:
- Never subtract the percentage from the final value; 240 minus 20% gives 192, which is wrong.
- Verify by going forward: 200 × 1.2 = 240, so the answer holds.
The same division recovers pre-tax prices and pre-raise salaries.
Does the formula work for grades and averages too?
The formula applies to any pair of numbers, grades included. A class grade that climbs from 80 to 88 improved by 10%, and a semester average moving from 3.0 to 3.3 rose by the same relative amount. Two related questions have their own dedicated math, though: turning category scores into one class grade is a job for the weighted grade calculator, and working out the exam score a target requires is covered in the score you still need on the final. Percentage increase measures movement between two values; those guides produce the values worth comparing.
Frequently asked questions
Flavio builds every tool on this site and writes about the small calculations that have big consequences. Find him on LinkedIn