How to Calculate Percentage Change (With Real Examples)

Percentage change is one of those things everyone needs occasionally and almost no one can do correctly under pressure. Was that price a 20% increase or a 16.7% increase? Did your investment grow 8% or 12%? Is a "25% off" sign followed by a "25% off" the same as 50% off?

This guide covers the percentage change formula, the three variations people actually need (forward change, reverse change, and "X is what percent of Y"), and the mistakes that catch people out. If you just need to compute one, the Uttir Percentage Calculator has all three modes in one place.

The percentage change formula

The formula for percentage change is:

((new − old) / |old|) × 100

The absolute value on the old value is the part most people miss. It ensures that a $100 → $80 change and an $80 → $100 change give the same magnitude (20%), just with opposite signs.

Worked example: a price increase

A product was $80 and is now $100. The percentage change is:

((100 − 80) / |80|) × 100 = (20 / 80) × 100 = 25%

Positive — that's a price increase of 25%.

Worked example: a price decrease

A product was $100 and is now $80. The percentage change is:

((80 − 100) / |100|) × 100 = (−20 / 100) × 100 = −20%

Negative — that's a price decrease of 20%.

Worked example: population growth

A city had 1.2 million people in 2010 and 1.35 million in 2020. The percentage change is:

((1,350,000 − 1,200,000) / |1,200,000|) × 100 = (150,000 / 1,200,000) × 100 = 12.5%

Population grew by 12.5% over the decade.

The "X is what percent of Y" formula

Different question, same calculator. This is the "what percentage of the total is this number" formula:

(X / Y) × 100

Worked example: test score

You got 42 out of 50 on a test. What percent is that?

(42 / 50) × 100 = 84%

Worked example: budget

You spent $320 of a $1,000 monthly budget on rent. What percent of your budget is rent?

(320 / 1,000) × 100 = 32%

The "what is X% of Y" formula

And the third mode — computing a value from a percentage:

Y × (X / 100)

Worked example: sales tax

The pre-tax price is $84.50. Sales tax is 8.875%. How much is the tax?

84.50 × (8.875 / 100) = 84.50 × 0.08875 = $7.50 (rounded to the cent)

Worked example: tip

The bill is $46. You want to leave an 18% tip. How much?

46 × (18 / 100) = 46 × 0.18 = $8.28

For a bill this size with a tip, the Uttir Tip Calculator does the full math including split between people.

The three mistakes everyone makes

Mistake 1: Dividing by the wrong number

When calculating percent change, divide by the old value, not the new. When calculating "X is what percent of Y," X is the part and Y is the whole — divide X by Y, not the other way around.

Classic trap: "I got a 10% raise, so my new salary is 110% of my old one." Correct. But then "I got a 10% raise, so my raise is 10% of my new salary." Wrong — the raise is 10% of the old salary, not the new one. They happen to be close when the raise is small, but the difference grows as the raise gets bigger.

Mistake 2: Forgetting the absolute value in the denominator

If a stock price went from $50 to $30, the change is −40%. If a stock price went from $30 to $50, the change is +66.7%. They are not the same magnitude, even though the difference is the same $20. The percentage change depends on the base.

The formula uses |old| so that "what percentage did this change by" has the same magnitude regardless of direction. But the answer is signed — the sign tells you which way.

Mistake 3: Treating sequential percentages as additive

A 20% increase followed by a 20% decrease is not a 0% net change. Starting from $100: a 20% increase brings you to $120. A 20% decrease brings you to $96, not back to $100. The decrease is taken from the new, larger base.

This is also why "25% off followed by 25% off" is not 50% off. $100 − 25% = $75, then $75 − 25% = $56.25. That's a 43.75% effective discount, not 50%.

Real-world uses

Percentage change shows up everywhere. Here are the most common ones with the right approach for each.

Year-over-year revenue growth

Use the standard formula: ((this year − last year) / |last year|) × 100. If last year was $4.2M and this year is $5.1M, growth is 21.4%. Track this monthly, quarterly, and annually — each gives a different lens on the same data.

Investment returns

Use the same formula, but remember to account for deposits and withdrawals if they happened during the period. The simple percentage change formula assumes the only change is the value itself. For investments with cash flow, use a money-weighted return (XIRR) or time-weighted return (TWR) instead.

Discount stacking

To find the effective discount from two stacked coupons, multiply the remaining fractions: 20% off then 10% off leaves 0.8 × 0.9 = 0.72, so 28% off. Don't add them. This is the same math as Mistake 3 above.

Grade weighting

If the final is worth 25% of your grade and you have a 85% in the class so far, the formula for what you need on the final is: (target × 1.0) − (85% × 0.75) all divided by 0.25. The Uttir Grade Calculator does this in one click — including the case where you've already secured the grade and the answer is "0 needed."

FAQ

Is a percentage change the same as a percentage point change?

No. A percentage change is the relative shift between two values. A percentage point change is the absolute difference between two percentages. If interest rates went from 4% to 5%, that's a 1 percentage point increase but a 25% relative increase. News articles mix these up constantly.

Can percentage change be more than 100%?

Yes. A $50 stock that goes to $200 has increased by 300%. Percentage change is unbounded above and below — there's no rule that caps it at 100%.

What if the old value is 0?

Division by zero. The formula is undefined. "How much did revenue grow from $0 to $5M?" is a meaningful question, but the answer can't be expressed as a percentage. In practice, you describe it as "from nothing to $5M" or pick a different baseline.

What about negative values?

Percentage change with a negative baseline is awkward. "How much did a −5% loss grow to a −2% loss?" doesn't have a clean answer. The formula still works mechanically — ((−2 − (−5)) / |−5|) × 100 = 60% — but interpreting it requires care. The 60% number doesn't mean what most people expect.