How to Calculate Percentage Increase and Decrease (With Worked Examples)
Your rent went from $800 to $920. Your shop’s sales jumped from 400 orders to 520. A jacket dropped from $120 to $84. In each case, the raw difference only tells half the story — the percentage change tells you how big that move really is. Percentage increase and decrease turn “it went up by 120” into “it went up by 15%”, a figure anyone can compare, whatever the starting number was.
The percentage change formula
There is only one formula to learn, and it works for both increases and decreases:
Percentage change = ((new value − old value) ÷ old value) × 100
If the answer is positive, it is a percentage increase. If it is negative, it is a percentage decrease — just drop the minus sign when you say “down by X%”.
Walk through it with the rent example: the new rent is $920, the old rent was $800. Subtract: 920 − 800 = 120. Divide by the old value: 120 ÷ 800 = 0.15. Multiply by 100: 15%. The rent rose by 15%.
The most common mistake is dividing by the new value instead of the old one. The old value is always the baseline — the “from” number. Change is always measured relative to where you started.
Method 1: Calculate percentage change online in seconds (fastest)
Doing the subtraction and division by hand is easy, but it is also easy to slip a decimal, especially with awkward numbers. Our free Percentage Calculator has a dedicated percentage-change mode that does it instantly, entirely in your browser, so your numbers are never uploaded anywhere. Here is how to use it:
- Choose the “percentage increase/decrease” mode on the calculator.
- Enter the old value in the first field and the new value in the second.
- Read the result instantly — it tells you the percentage and whether it is an increase or a decrease.
- Try variations. Wondering what a 10% rise on your current salary would be? Change the numbers and compare outcomes side by side.
- Use it for reverse checks too. If a price fell by 30% to $84, you can work back to the original $120 (84 ÷ 0.70).
There is no signup, no limit on how many calculations you run, and no record of what you typed.
Worked examples
Example 1 — A salary raise: Your salary rises from $50,000 to $56,000. The difference is $6,000. Divide by the old salary: 6,000 ÷ 50,000 = 0.12, so the raise is 12%. A colleague whose salary rose from $30,000 to $33,600 also got 12% — the same percentage, even though the dollar amount is smaller.
Example 2 — A price drop: A laptop falls from $900 to $720. The difference is −180. Divide by 900: −180 ÷ 900 = −0.20, so the price decreased by 20%.
Example 3 — Business growth: Monthly orders grow from 400 to 520. The increase is 120, and 120 ÷ 400 = 0.30, so orders grew by 30%.
Example 4 — A fall that looks small but is not: Website visitors drop from 10,000 to 8,500. That is a 15% decrease — worth investigating, even though 8,500 still sounds like a lot.
Percentage change vs percentage points
This distinction trips up even professional reports. If an interest rate rises from 5% to 8%, that is a 3 percentage point increase — but a 60% relative increase (3 ÷ 5 = 0.60). News headlines sometimes say “interest rates up 60%” when they mean 3 points, which sounds far more dramatic.
The rule: use “percentage points” when you are comparing two percentages directly, and “percent” when you are describing the relative change. A jump from 1% to 2% is one percentage point, but a 100% increase. Keeping them straight makes your own reports honest and helps you spot when someone else’s are not.
Why increases and decreases are not symmetric
Here is a trap that catches almost everyone. If a price rises by 25% and then falls by 25%, it does not return to the original price. Start at $100: a 25% rise gives $125. A 25% fall from $125 removes $31.25, leaving $93.75 — not $100.
The reason is that the second change uses a different baseline. To undo a 25% increase, you need a 20% decrease (25 ÷ 125 = 0.20). Likewise, after a 50% fall, you need a 100% rise just to get back to where you started. This asymmetry matters for investments, discounts and price negotiations: recovering from a loss always takes a bigger percentage gain than the loss itself.
Common problems — and what to do
- You divided by the new value: Recalculate with the old value as the denominator. The baseline is always the “from” number.
- Your increase and decrease do not cancel out: That is normal, not an error — see the asymmetry section above. Work each step from its own starting value.
- You are comparing two percentages: Report the difference in percentage points, and only use the relative percent change when that is genuinely what you mean.
- The percentage looks absurdly large: Small baselines produce huge percentages. A rise from 2 sales to 10 is a 400% increase, but it is still only 8 extra sales. Always show the raw numbers alongside big percentages.
- You need the original value after a change: Divide the new value by (1 + rate) for an increase, or (1 − rate) for a decrease. A $84 sale price after 30% off means the original was 84 ÷ 0.70 = $120. For dedicated sale-price math, see our discount and percentage guide.
Frequently asked questions
How do you calculate percentage increase?
Subtract the old value from the new value, divide the result by the old value, and multiply by 100. For example, a price rising from $50 to $65 is ((65 − 50) ÷ 50) × 100 = 30% increase. The old value is always the baseline you divide by.
How do you calculate percentage decrease?
Use the same formula: ((new value − old value) ÷ old value) × 100. A negative answer means a decrease — a price falling from $900 to $720 gives −20%, which you report as a 20% decrease. The calculator’s percentage-change mode labels the direction for you.
What is the difference between percent and percentage points?
A move from 5% to 8% is a 3 percentage point increase, but a 60% relative increase (3 ÷ 5). Use percentage points when comparing two percentages directly, and percent when describing the relative change from a baseline.
Why does a 25% rise followed by a 25% fall not return to the original price?
Because the second change uses a different baseline. A 25% rise on $100 gives $125, and a 25% fall from $125 removes $31.25, leaving $93.75. To undo a 25% increase you need a 20% decrease, not 25%.
How do I find the original value after a percentage change?
Divide the new value by (1 + rate) for an increase, or (1 − rate) for a decrease. If $84 is the price after 30% off, the original was 84 ÷ 0.70 = $120. For sale prices specifically, a dedicated discount calculator is even more direct.
The short answer
Percentage change = ((new value − old value) ÷ old value) × 100, with the old value always as the baseline. A positive result is an increase, a negative one is a decrease — or skip the arithmetic and use the free Percentage Calculator. Remember that percentage points and percent are different things, and that gains and losses never cancel symmetrically.
