Percentage change measures how much a value has grown or shrunk relative to its starting point. It answers questions like "how much did sales increase?" or "by what percent did the price drop?" — and it's one of the most useful calculations in everyday math, business reporting, and data analysis.
This guide covers the formula, worked examples, edge cases, and the mistakes that catch people most often.
Quick Answer
Use this formula:
Percentage Change = ((New Value − Original Value) / |Original Value|) × 100
- Positive result: increase
- Negative result: decrease
- Zero result: no change
If you want a faster check, use the percentage change calculator and verify the same values with the percentage calculator.
The Percentage Change Formula
Percentage Change = ((New Value − Original Value) / |Original Value|) × 100
That's it. Three steps:
- Subtract: New minus Original gives the absolute change.
- Divide: Divide by the absolute value of the Original to get the relative change.
- Multiply by 100: Convert the decimal to a percentage.
A positive result is an increase. A negative result is a decrease.
Quick Example
Your electricity bill was $120 last month and $150 this month.
- Difference: 150 − 120 = 30
- Divide: 30 / 120 = 0.25
- Convert: 0.25 × 100 = 25% increase
Percent Increase vs. Percent Decrease
The formula is the same in both cases — only the sign changes.
| Scenario | Original | New | Calculation | Result |
|---|---|---|---|---|
| Price went up | $80 | $100 | (100 − 80) / 80 × 100 | +25% |
| Price went down | $100 | $80 | (80 − 100) / 100 × 100 | −20% |
| Revenue doubled | $5,000 | $10,000 | (10000 − 5000) / 5000 × 100 | +100% |
| Stock halved | $200 | $100 | (100 − 200) / 200 × 100 | −50% |
| No change | 450 | 450 | (450 − 450) / 450 × 100 | 0% |
Notice the second row: going from $100 down to $80 is −20%, not −25%. The base number matters — and that asymmetry is the source of the most common mistake with percentage change.
The Reversal Trap: Why +25% and −25% Don't Cancel
This confuses almost everyone the first time:
- Start with 100
- Increase by 25%: 100 × 1.25 = 125
- Decrease by 25%: 125 × 0.75 = 93.75 — not 100
The increase adds 25% of 100 (= 25), but the decrease removes 25% of 125 (= 31.25). The base changed, so the same percentage refers to a different amount.
To reverse a percentage change:
- Reversing a +X% increase requires a decrease of: X / (1 + X/100) %
- Reversing a −X% decrease requires an increase of: X / (1 − X/100) %
| Original Change | Reverse Needed |
|---|---|
| +10% increase | −9.09% decrease |
| +25% increase | −20% decrease |
| +50% increase | −33.33% decrease |
| +100% increase (doubled) | −50% decrease (halved) |
| −20% decrease | +25% increase |
| −50% decrease | +100% increase |
This is why headlines like "Stock drops 30% then recovers 30%" are misleading — the stock hasn't actually recovered to its original price.
Percentage Change vs. Percentage Difference vs. Percentage Points
These three concepts sound similar but mean different things. Using the wrong one produces confusing or incorrect results.
Percentage Change
Measures growth or decline from a specific starting value. It's directional — the result has a sign.
- Use when: one value is clearly "before" and the other is "after."
- Example: Revenue went from $200K to $260K → +30% change.
Percentage Difference
Compares two values symmetrically by dividing by their average: ((|A − B|) / ((A + B) / 2)) × 100.
- Use when: neither value is the baseline (e.g., comparing two cities' populations).
- Example: City A has 50,000 people, City B has 60,000. Percentage difference = 10,000 / 55,000 × 100 ≈ 18.2%.
Percentage Points
The arithmetic difference between two percentages.
- Use when: both values are already percentages.
- Example: Unemployment drops from 6% to 4.5%. That's a 1.5 percentage point decrease — but a 25% percentage change.
Mixing up "percentage change" and "percentage points" is extremely common in news reporting and can dramatically misrepresent the magnitude of a shift.
When the Original Value Is Zero
If the original value is zero, the formula produces a division-by-zero error. This is mathematically undefined — there is no meaningful "percentage change from zero."
In practice, when this comes up (e.g., going from 0 sales to 15 sales), you have a few options:
- Report the absolute change instead ("+15 units")
- Describe it qualitatively ("new activity — previously zero")
- Use a small non-zero baseline if your context allows it (common in financial modeling, but state the assumption clearly)
There is no universally correct workaround. The honest answer is that percentage change from zero is undefined.
Changes Greater Than 100%
A percentage change exceeding 100% means the value more than doubled.
| Multiplier | Percentage Change | Plain English |
|---|---|---|
| ×2 | +100% | Doubled |
| ×3 | +200% | Tripled |
| ×5 | +400% | Quintupled |
| ×10 | +900% | 10× growth |
This is straightforward once you remember that +100% means "one full original value was added." Each additional 100% adds another full copy of the original.
On the decline side, percentage change cannot go below −100% (which means the value reached zero). A −100% change means the entire value was lost.
Compounding: Repeated Percentage Changes
When percentage changes happen in sequence, they multiply — they don't add.
Example: A stock gains 20% one year and 15% the next.
- After year 1: $100 × 1.20 = $120
- After year 2: $120 × 1.15 = $138
- Total change: ($138 − $100) / $100 × 100 = +38% (not 35%)
The extra 3% comes from earning 15% on the $20 gain from year 1 (0.15 × 20 = 3).
This compounding effect means:
- Successive gains produce a total larger than their sum.
- Successive losses produce a total smaller than their sum (the damage compounds less because each loss shrinks the base).
- A gain followed by an equal loss always results in a net loss (see the reversal trap above).
Worked Examples
Example 1: Rent Increase
Your rent goes from $1,400/month to $1,540/month.
- Difference: 1,540 − 1,400 = 140
- Divide: 140 / 1,400 = 0.10
- Multiply: 0.10 × 100 = +10% increase
Example 2: Weight Loss
A person goes from 185 lbs to 170 lbs.
- Difference: 170 − 185 = −15
- Divide: −15 / 185 = −0.08108
- Multiply: −0.08108 × 100 ≈ −8.1% decrease
Example 3: Negative to Positive
Temperature goes from −5°C to 15°C.
- Difference: 15 − (−5) = 20
- Divide: 20 / |−5| = 4.0
- Multiply: 4.0 × 100 = +400% change
Note: Percentage change with negative starting values is technically valid but can be counterintuitive. Some contexts (like temperature) are better served by stating the absolute difference.
Example 4: Percentage Points in Context
A website's conversion rate goes from 2.0% to 2.5%.
- Percentage point change: 2.5% − 2.0% = +0.5 percentage points
- Percentage change: (2.5 − 2.0) / 2.0 × 100 = +25%
Saying "conversions increased by 25%" and "conversions increased by 0.5 percentage points" describe the same event. Which framing to use depends on context — the percentage change (25%) sounds dramatic; the percentage point change (0.5 pp) sounds modest. Both are accurate.
Common Mistakes
-
Swapping old and new values. The original value goes in the denominator. Reversing them changes both the magnitude and the sign.
-
Confusing percentage change with percentage points. An interest rate moving from 3% to 4% is a 1 percentage point increase — not a 1% increase. It's actually a 33.3% increase.
-
Assuming symmetry. A 20% increase and 20% decrease don't cancel out. Always check which direction you're computing from.
-
Adding sequential changes. Two consecutive 10% increases give +21%, not +20%. Multiply the factors: 1.10 × 1.10 = 1.21.
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Using zero as a baseline. The formula is undefined when the original value is zero. Report absolute change instead.
-
Ignoring the base in comparisons. "Sales grew by 200%" from a base of 3 units means 9 units. Percentage change on tiny numbers can produce enormous-sounding results that aren't practically significant.
Quick Reference: Percentage Change Cheatsheet
| If You Know | Formula |
|---|---|
| Old value and new value | ((New − Old) / |Old|) × 100 |
| Old value and % change | New = Old × (1 + Change/100) |
| New value and % change | Old = New / (1 + Change/100) |
| % to reverse a +X% increase | X / (1 + X/100) |
| % to reverse a −X% decrease | X / (1 − X/100) |
Frequently Asked Questions
How do you calculate percentage change between two numbers?
Use the formula: ((New − Old) / |Old|) × 100. Subtract the original from the new, divide by the absolute value of the original, and multiply by 100. The sign tells you the direction — positive for increase, negative for decrease.
What is the percentage change from 50 to 75?
(75 − 50) / 50 × 100 = +50%. The value increased by half of the original.
What is the percentage change from 75 to 50?
(50 − 75) / 75 × 100 = −33.33%. Notice this is not −50% — the base is different.
How do I calculate percent increase?
It's the same formula as percentage change. If the result is positive, you have a percent increase. Percentage Change = ((New − Old) / |Old|) × 100.
How do I calculate percent decrease?
Same formula. If the result is negative, you have a percent decrease. For example, going from 200 to 150: (150 − 200) / 200 × 100 = −25%.
Is percentage change the same as growth rate?
In most everyday and business contexts, yes — "growth rate" refers to percentage change over a time period. In statistics and finance, "growth rate" sometimes implies compounding or annualization, so the context matters.
Can percentage change be negative?
Yes. A negative percentage change means a decrease. For example, −15% means the value dropped by 15% of its original amount.
What is the percentage change if the value doubles?
If something doubles, the percentage change is +100%. Tripling is +200%, quadrupling is +300%, and so on.
How do I find the original value if I know the new value and the percentage change?
Rearrange the formula: Original = New / (1 + Change/100). For example, if the new price is $90 after a +20% increase: 90 / 1.20 = $75.
Why does the order of values matter?
Because the original value is the denominator. Going from 100 to 150 is +50%, but going from 150 to 100 is −33.3%. The percentage change depends on which value you start from.
How is percentage change used in business?
Revenue growth, cost reduction, conversion rate changes, churn rate shifts, year-over-year comparisons, and budget variance analysis all rely on percentage change. It normalizes absolute numbers so you can compare performance across different scales.
What's the difference between percentage change and ratio?
Percentage change expresses how much a value shifted relative to its starting point. A ratio expresses how two values relate (e.g., 3:2). They're connected: a ratio of new/old of 1.25 corresponds to a +25% change.
How do I calculate percentage change in a spreadsheet?
In Excel or Google Sheets: =(B1-A1)/ABS(A1)*100 where A1 is the old value and B1 is the new value. Or use =(B1/A1)-1 and format the cell as a percentage.