How to Calculate Percentage Increase or Decrease
The one formula for percentage increase or decrease, with worked examples both ways, a quick reference table, and the common mistakes that throw people off.
How to Calculate Percentage Increase or Decrease
To learn how to calculate percentage increase or decrease, use one formula: subtract the old value from the new value, divide by the old value, then multiply by 100. A positive result is a percentage increase; a negative result is a percentage decrease. In short, percentage change equals (new minus old) divided by old, times 100.
That single formula handles prices, salaries, traffic, weight, scores, and any other measurement that moves between two points in time. Below you will find the formula broken down, fully worked examples for both directions, a quick-reference table, and the mistakes that trip people up. When you want the answer instantly, our Percentage Calculator does the math for you.
The Formula, Explained
Percentage change measures how much a value has grown or shrunk relative to where it started. The starting number is always the denominator, which is the single most important rule to remember.
Percentage change = ((New value − Old value) / Old value) × 100
- If the result is positive, it is a percentage increase.
- If the result is negative, it is a percentage decrease (drop the minus sign and call it a decrease).
- If the result is zero, nothing changed.
The reason you always divide by the old value is that percentage change asks "relative to the starting point, how big was the move?" Dividing by the new value answers a different, usually wrong, question.
Increase and decrease are not symmetric
Here is the counterintuitive part most people miss. A 50 percent increase followed by a 50 percent decrease does not return you to the start. Go from 100 up 50 percent to 150, then down 50 percent of 150, and you land at 75, not 100. The percentages are measured against different bases, so they do not cancel out.
Worked Example: Percentage Increase
Your monthly website traffic rose from 4,000 visits to 5,200 visits. What is the percentage increase?
- Subtract: 5,200 − 4,000 = 1,200.
- Divide by the old value: 1,200 / 4,000 = 0.3.
- Multiply by 100: 0.3 × 100 = 30.
Traffic grew by 30 percent. Notice the denominator is the original 4,000, not the new 5,200. Using the wrong base is the most common error in percentage math.
Worked Example: Percentage Decrease
A jacket dropped from a price of 80 dollars to 60 dollars. What is the percentage decrease?
- Subtract: 60 − 80 = −20.
- Divide by the old value: −20 / 80 = −0.25.
- Multiply by 100: −0.25 × 100 = −25.
The price fell by 25 percent. The negative sign signals a decrease; you simply report it as "a 25 percent decrease." The method is identical to an increase; only the sign of the result changes.
Quick Reference Table
Here are common changes calculated with the same formula so you can sanity-check your own work.
| Old value | New value | Change | Result |
|---|---|---|---|
| 50 | 75 | (75−50)/50 × 100 | +50% increase |
| 200 | 150 | (150−200)/200 × 100 | −25% decrease |
| 1,000 | 1,100 | (1100−1000)/1000 × 100 | +10% increase |
| 120 | 90 | (90−120)/120 × 100 | −25% decrease |
| 8 | 10 | (10−8)/8 × 100 | +25% increase |
Real-World Scenarios Where This Matters
Percentage change is not abstract math; it is the language of everyday money and performance decisions. Seeing it applied makes the formula stick.
Salary and raises
You earn 50,000 a year and are offered 54,000. The raise is (54,000 − 50,000) / 50,000 × 100, which is an 8 percent increase. If next year inflation runs at 6 percent, your real gain is only about 2 percentage points of purchasing power, a reminder that nominal raises and real raises differ.
Discounts and sales
A 90 dollar item is marked down to 63 dollars. The discount is (63 − 90) / 90 × 100, a 30 percent decrease. To check a "40 percent off" claim quickly, multiply the original by 0.60; if the sale price matches, the claim is honest.
Business metrics
Monthly revenue moves from 12,000 to 13,800. That is a 15 percent increase, the kind of figure that drives growth reports. Track it consistently using the same base each period so trends are comparable rather than misleading.
Working Backwards: Apply a Percentage
Sometimes you know the percentage and need the new value. To increase a number by a percentage, multiply by (1 + the rate); to decrease, multiply by (1 − the rate).
- Increase 250 by 12 percent: 250 × 1.12 = 280.
- Decrease 250 by 12 percent: 250 × 0.88 = 220.
This shortcut is faster than calculating the change amount separately and adding it back, and it is how spreadsheets and calculators do it under the hood.
Percentage points vs. percentages
If an interest rate moves from 4 percent to 6 percent, that is a 2 percentage point rise but a 50 percent increase in the rate itself ((6−4)/4 × 100). Mixing these up is a classic reporting error. Percentage points describe the absolute gap between two percentages; percentage change describes the relative move.
Finding the original value after a change
A trickier but common question is working out the starting number when you only know the final value and the percentage change. The mistake people make is subtracting the percentage from the final figure, which gives the wrong answer. Instead, divide. If a price is 120 after a 20 percent increase, the original is 120 / 1.20, which equals 100, not 120 minus 20 percent. Likewise, if a value is 90 after a 25 percent decrease, the original is 90 / 0.75, which equals 120. This "reverse percentage" comes up constantly with tax-inclusive prices and discounted totals, so it is worth practicing until the divide-don't-subtract instinct is automatic.
Mental Math Shortcuts
You do not always have a calculator handy, and a few tricks make percentage change quick to estimate in your head. These will not replace a precise tool, but they help you sanity-check results and catch obvious errors before they spread into a report or a budget.
- Ten percent is easy. Move the decimal one place left. Ten percent of 240 is 24, so a rise from 240 to 264 is about 10 percent.
- Build from ten. Five percent is half of ten percent; twenty percent is double. So twenty percent of 240 is 48.
- One percent for fine tuning. Move the decimal two places. One percent of 240 is 2.4, useful for odd figures like 3 or 7 percent.
- Halving and doubling. A change from 50 to 75 is clearly a quarter more, so 25 percent, no formula needed.
The goal of mental math is not perfect accuracy; it is a fast gut check. If a tool tells you a price rose 300 percent when you expected 30, your estimate flags the slipped decimal instantly. Estimate first, then confirm the exact figure with a calculator for anything that matters.
Common Mistakes to Avoid
- Dividing by the new value. Always divide by the original (old) value.
- Assuming increases and decreases cancel. A 20 percent rise then a 20 percent fall leaves you below where you started.
- Confusing percentage points with percent change. They are different measures.
- Forgetting the sign. A negative result is a decrease, not an error.
- Rounding too early. Keep full precision until the final step to avoid drift.
Calculate It Instantly
Once you understand the formula, the arithmetic is the only slow part, and that is exactly what a tool is for. Drop your old and new values into the Percentage Calculator to get the increase or decrease in one step, then explore more math helpers in the Online Calculators hub. For quick currency math while you are at it, see our USD to INR guide.
Frequently Asked Questions
What is the formula for percentage increase or decrease?
Percentage change equals (new value minus old value), divided by the old value, multiplied by 100. A positive result is an increase and a negative result is a decrease. Always divide by the original value.
How do I calculate a percentage increase?
Subtract the old value from the new value, divide that difference by the old value, then multiply by 100. For example, going from 4,000 to 5,200 is (5,200 minus 4,000) divided by 4,000 times 100, which equals a 30 percent increase.
How do I calculate a percentage decrease?
Use the same formula; the result will be negative. For example, a price falling from 80 to 60 is (60 minus 80) divided by 80 times 100, which equals minus 25, reported as a 25 percent decrease.
Why do I divide by the old value and not the new one?
Percentage change measures the move relative to the starting point, so the original value is the reference. Dividing by the new value answers a different question and gives the wrong percentage.
Does a percentage increase then the same percentage decrease return the original number?
No. The two percentages are taken from different bases. A 50 percent increase from 100 gives 150, and a 50 percent decrease from 150 gives 75, not 100.
What is the difference between percentage points and percent change?
Percentage points are the absolute gap between two percentages, such as 4 percent to 6 percent being 2 points. Percent change is the relative move, which here is a 50 percent increase. They are not interchangeable.
How do I increase or decrease a number by a percentage?
To increase, multiply by (1 plus the rate as a decimal); to decrease, multiply by (1 minus the rate). For example, 250 increased by 12 percent is 250 times 1.12, which equals 280.