How to Calculate Percentage Change (Increase and Decrease)

Percentage change is the difference between a new value and an old value, divided by the old value, times 100. The mistakes almost always come from dividing by the wrong number or confusing a percentage change with a percentage point, so both are covered below alongside worked examples. A percentage change calculator takes the old and new values and returns the signed result.

The Percentage Change Formula

Percentage Change = (New Value − Old Value) ÷ Old Value × 100

Find the raw difference, divide it by the original value to express it as a fraction of where you started, then multiply by 100.

The sign gives the direction: positive is an increase, negative is a decrease. The old value is always the reference point in the denominator; dividing by the new value instead is the most common error. (The calculator divides by the absolute value of the old number, so a change from −20 to −10 reports +50%, a move toward zero; when the old value is negative, read the sign with care.)

Worked Example: Calculating a Percentage Increase

Suppose your monthly rent rose from $1,200 to $1,380. To find the percentage increase, plug the numbers into the formula.

First, find the difference: $1,380 − $1,200 = $180. Next, divide by the original value: $180 ÷ $1,200 = 0.15. Finally, multiply by 100: 0.15 × 100 = 15%.

Your rent increased by 15%. Notice that the $1,200 starting value anchors the calculation. If you had mistakenly divided the $180 difference by the new $1,380, you'd get roughly 13%, understating the increase you actually absorbed.

The same arithmetic covers website traffic climbing from 4,000 to 5,200 visits (a 30% increase) or revenue growing from $2 million to $2.5 million (a 25% increase). To go the other way, from a starting value and a known percentage to the new value, multiply by (1 + the rate): $1,200 × 1.15 = $1,380.

Worked Example: Calculating a Percentage Decrease

Decreases use the exact same formula; you simply end up with a negative result. Imagine a jacket originally priced at $80 is now on sale for $60.

Find the difference: $60 − $80 = −$20. Divide by the original value: −$20 ÷ $80 = −0.25. Multiply by 100: −0.25 × 100 = −25%.

The jacket's price dropped by 25%. The negative sign marks the decrease, and the original $80 price is again the reference point. In everyday language you'd say the price "fell 25%" rather than reciting the minus sign.

Percentage Change vs. Percentage Points

A percentage point is the simple arithmetic difference between two percentages; a percentage change measures how much one value changed relative to another. Headlines mix the two up constantly.

Imagine an interest rate rises from 4% to 6%. The increase is 2 percentage points (6 − 4). But the percentage change is (6 − 4) ÷ 4 × 100 = 50%. Both statements are correct, yet they describe very different magnitudes. Saying "rates rose 50%" sounds alarming, while "rates rose 2 percentage points" sounds modest, even though they describe the identical event.

Whenever the two values are themselves percentages (unemployment rates, approval ratings, interest rates), say which one you mean.

Percentage Difference vs. Percentage Change

Percentage difference is for comparing two values when neither is the "starting" point. Instead of dividing by the old value, you divide by the average of the two.

Percentage Difference = |Value A − Value B| ÷ ((Value A + Value B) ÷ 2) × 100

Comparing two products priced at $40 and $50, the percentage difference is |40 − 50| ÷ 45 × 100 = 22.2% (rounded). Because the average is the reference, the answer is the same whichever value you list first; percentage change, by contrast, depends on which value is the original. Use percentage change when there is a clear before-and-after and percentage difference when comparing two equivalent items.

Where You'll Use It

Percentage change quantifies a raise (a jump from $55,000 to $60,500 is a 10% increase), an investment's growth, a price rise or a sale discount. In reporting it sits behind quarterly sales growth, year-over-year inflation and population change, and it makes different scales comparable: a $5 increase is 50% on a $10 item and 0.5% on a $1,000 item.

Pitfalls to Avoid

The most counterintuitive trap is that percentage changes don't simply cancel out. A 50% drop followed by a 50% rise does not return you to where you started.

Say a stock falls 50% from $100 to $50. If it then rises 50%, it climbs by half of $50, which is $25, landing at $75, not the original $100. To fully recover from a 50% loss, you'd actually need a 100% gain. This asymmetry exists because each percentage change is calculated against a different base value, so the same percentage applied to a smaller number yields a smaller absolute amount.

Other frequent mistakes: dividing by the new value instead of the old, forgetting to multiply by 100, and adding successive percentages together instead of applying them one after another (a 10% rise followed by a 10% rise is 21%, not 20%).