The Percentage Formula Everyone Gets Wrong (And How to Actually Do It)

Somewhere between grade school math and real life, most people lost the thread on percentages. Not the concept — everyone knows roughly what 20% off means. The problem is the calculation: which number goes on top, which goes on the bottom, and why does doing it backwards give you a completely different answer.

This matters more than it sounds. Percentage change calculations show up in salary negotiations, investment returns, discount pricing, grade curves, inflation comparisons, and medical statistics. Getting it wrong doesn't just produce a wrong number — it produces a confidently wrong number, which is worse.

Here's the correct formula, why it works, and where people consistently trip over it.

The Core Formula (And Why It's Built the Way It Is)

Percentage change — whether an increase or a decrease — uses a single formula:

Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100
If the result is positive → it's an increase
If the result is negative → it's a decrease

The original value is always the denominator. That's the part people get wrong. You're measuring the change relative to where you started — so the starting point is what you divide by.

A quick example: a product costs $65 last year and $78 this year. The change is $13. Divided by the original $65, that's 0.20. Multiply by 100: a 20% increase. If you accidentally divided by $78 instead of $65, you'd get 16.7% — wrong, and in this case, misleadingly smaller.

Percentage Increase: The Formula in Action

You use percentage increase when the new value is higher than the original. Common situations: salary raises, price hikes, investment gains, year-over-year revenue growth.

Percentage Increase = ((New − Original) ÷ Original) × 100

Your salary goes from $62,000 to $67,000:
  ($67,000 − $62,000) ÷ $62,000 = 0.0806
  0.0806 × 100 = 8.06% raise

That 8.06% sounds different from "they gave me $5,000 more." Both are true. The percentage tells you how significant the change is relative to what you were already making — which is what matters when you're comparing raises across different salary levels.

Percentage Decrease: Same Formula, Negative Result

Nothing changes in the formula — a decrease just produces a negative number.

Percentage Decrease = ((New − Original) ÷ Original) × 100

A stock drops from $240 to $186:
  ($186 − $240) ÷ $240 = −0.225
  −0.225 × 100 = −22.5%

The negative sign is the signal that it's a decrease. Some contexts strip the negative and just say "22.5% decrease" — both mean the same thing as long as the direction is clear. One thing worth knowing: a percentage increase and decrease of the same number are not reversible. If that stock drops 22.5%, it needs a 29% gain just to return to $240. This is because the base changes — the gain is calculated on the lower starting point.

Finding What Percentage One Number Is of Another

This is a slightly different question — not "how much did it change" but "what share of the whole is this part." The formula is simpler:

Percentage = (Part ÷ Whole) × 100

What percentage of 240 is 60?
  (60 ÷ 240) × 100 = 25%

You scored 47 out of 60 on a test:
  (47 ÷ 60) × 100 = 78.3%

This version shows up constantly: budget breakdowns, nutritional labels, test scores, market share figures, survey results. The logic is always the same — put the part over the whole.

Percentage Points vs. Percentage Change: The Distinction That Trips Up Everyone

This is where most people — including journalists, politicians, and financial analysts — make embarrassing errors.

Percentage points = the raw arithmetic difference between two percentages.

Percentage change = how much one percentage changed relative to itself.

An interest rate moves from 3% to 4.5%. That is 1.5 percentage points — but it is a 50% increase in the rate itself. These are both accurate descriptions of the same event. They are not interchangeable. When you see a percentage changing in a headline, ask: percentage of what? Compared to what base? The answer changes the meaning entirely.

Real-World Examples That Make the Formula Click

Every one of these uses the identical formula. The only thing that changes is which numbers you plug in.

How to Work Backwards: Finding the Original Value

Sometimes you know the final value and the percentage change — and need to recover the original. This comes up in sale pricing, tax calculations, and reverse-engineering reported figures.

For a percentage INCREASE:
  Original = New Value ÷ (1 + Percentage as decimal)
  A price is $94.60 after a 15% increase. What was the original?
  $94.60 ÷ 1.15 = $82.26

For a percentage DECREASE:
  Original = New Value ÷ (1 − Percentage as decimal)
  A price is $76.50 after a 10% discount. What was the original?
  $76.50 ÷ 0.90 = $85.00

This is also how you verify a claimed discount. If something is marked "was $120, now $89" — check: ($89 ÷ $120) × 100 = 74.2%, meaning you're paying 74.2% of the original, which is a 25.8% discount.

Calculate percentage change instantly →

Where People Get This Wrong in the Real World

Salary negotiations. A counter-offer of "$5,000 more" sounds the same whether your salary is $45,000 or $145,000. In percentage terms it isn't — it's 11.1% and 3.4% respectively. Knowing the percentage keeps you anchored to what the raise actually means relative to your current compensation.

Investment returns. A fund up 30% one year and down 30% the next is not back to even. It's down 9% overall. A $10,000 investment becomes $13,000 after a 30% gain. That $13,000 dropping 30% lands at $9,100. Percentages applied to changing bases compound in ways that flat numbers obscure.

Discounts stacked on discounts. A 20% off sale with an additional 10% off coupon is not 30% off. The 20% comes off first (you pay 80%), then 10% comes off that (you pay 72% of original). Total effective discount: 28%, not 30%. Retailers know this. Now you do too.

Frequently Asked Questions

How do you calculate percentage increase?

Subtract the original value from the new value, divide by the original value, then multiply by 100. Formula: ((New − Original) ÷ Original) × 100. Example: a price rising from $80 to $100 is ((100 − 80) ÷ 80) × 100 = 25% increase.

How do you calculate percentage decrease?

Same formula as percentage increase — the result is simply negative when the new value is lower. ((New − Original) ÷ Original) × 100. A price dropping from $100 to $80 is ((80 − 100) ÷ 100) × 100 = −20%. The negative sign tells you it's a decrease.

What is the difference between percentage change and percentage points?

Percentage points measure the absolute arithmetic difference between two percentages. Percentage change measures the relative change. If an interest rate goes from 4% to 6%, that is 2 percentage points — but it is a 50% increase in the rate itself. Confusing the two is one of the most common errors in financial and political reporting.

How do you find what percentage one number is of another?

Divide the part by the whole, then multiply by 100. What percentage is 45 of 180? (45 ÷ 180) × 100 = 25%. This applies to test scores, budget breakdowns, nutritional values, and any situation where you need to express one number as a share of another.

Why does a 50% increase followed by a 50% decrease not get you back to the original number?

Because the base changes. A 50% increase on $100 brings you to $150. A 50% decrease on $150 brings you to $75 — not $100. The decrease is calculated on the new, higher base. This is why percentage changes are not symmetrical and why you should always note what value a percentage is being applied to.