Percentage Change Calculator
Enter an original value and a new value to calculate the percentage increase or decrease, with full step-by-step working.
For more options, use the full percentage change calculator or the percentage calculator.
What Is Percentage Increase and Decrease?
When a value changes — a price, a salary, a test score, an energy bill — you often need to express that change as a proportion of where it started. That proportion, multiplied by 100, is the percentage change. It tells you how large a change is relative to the original, which makes comparisons meaningful across different scales.
Percentage change is a measure of how much a quantity has increased or decreased relative to its original value. If the new value is greater than the original, the result is a percentage increase. If less, it is a percentage decrease. The formula is: ((New Value − Original Value) ÷ Original Value) × 100. A positive result means an increase; a negative result means a decrease.
This calculation is built into Common Core Math Standard 7.RP.3, appears in business analysis, finance, science, and everyday contexts including retail pricing, salary negotiations, and reading news headlines. For a broader grounding in numerical summaries, the descriptive statistics guide covers how percentage change fits into data analysis.
The Percentage Change Formula
One formula covers both percentage increases and decreases. The critical rule: always divide by the original value — the starting point — not the new value.
New = the new (final) value
Original = the starting (old) value
Positive result → increase
Negative result → decrease
When separate formulas are clearer:
Both formulas give the same magnitude — only the sign changes. The decrease formula subtracts in reverse order to produce a positive result, which is easier to read in context.
A negative output from the unified formula confirms a decrease. Example: ((80 − 100) ÷ 100) × 100 = −20%. This is a 20% decrease — the negative sign indicates direction, not an error in the arithmetic.
How to Calculate Percentage Increase
Follow this four-step process for any percentage increase. The same steps are captured in the HowTo structured data for search engines.
- 1Find the difference. Subtract the original value from the new value: New − Original. This gives the absolute size of the increase.
- 2Divide by the original. Divide the difference by the original (starting) value. This converts the change into a decimal proportion.
- 3Multiply by 100. Multiply the decimal by 100 to express the change as a percentage.
- 4Interpret the result. A positive number is a percentage increase. Add the % symbol to your answer.
Example 1 — Retail Price Increase
Calculating a price increase percentage
A pair of running shoes cost $95 in January and $114 in October. By what percentage did the price increase?
Difference: 114 − 95 = 19
Divide by original: 19 ÷ 95 = 0.2
Multiply by 100: 0.2 × 100 = 20
✓ The price increased by 20%
Example 2 — Salary Raise
Calculating a pay increase as a percentage
Maya's annual salary increased from $52,000 to $58,240. What percentage raise did she receive?
Difference: 58,240 − 52,000 = 6,240
Divide by original: 6,240 ÷ 52,000 = 0.12
Multiply by 100: 0.12 × 100 = 12
✓ Maya received a 12% pay increase
Example 3 — Test Score Improvement
Percentage improvement between two test scores
A student scored 64 on their first practice test and 80 on the second. What was the percentage improvement?
Difference: 80 − 64 = 16
Divide by original: 16 ÷ 64 = 0.25
Multiply by 100: 0.25 × 100 = 25
✓ The test score improved by 25%
How to Calculate Percentage Decrease
The process mirrors percentage increase, with one change in Step 1: subtract the new value from the original, so the difference stays positive before dividing.
- 1Find the difference. Subtract the new value from the original: Original − New. Keeping this positive makes the final answer easier to interpret.
- 2Divide by the original. Divide the difference by the original (starting) value.
- 3Multiply by 100. Convert to a percentage.
- 4Interpret the result. This is the percentage decrease. Alternatively, use the unified formula — the output will be negative, confirming the direction of change.
Example 4 — Utility Bill Reduction
Percentage reduction in a monthly electricity bill
An electricity bill fell from $140 per month to $119 per month after switching to LED lighting. What was the percentage reduction?
Difference: 140 − 119 = 21
Divide by original: 21 ÷ 140 = 0.15
Multiply by 100: 0.15 × 100 = 15
✓ The bill decreased by 15%
Example 5 — Stock Price Drop
Percentage fall in a stock price over one week
A stock was priced at $240 on Monday. By Friday it had fallen to $192. What was the percentage decrease?
Difference: 240 − 192 = 48
Divide by original: 48 ÷ 240 = 0.2
Multiply by 100: 0.2 × 100 = 20
✓ The stock price decreased by 20%
Find the Original Value (Reverse Calculation)
Sometimes you know the new value and the percentage change, but need to work backward to the original. A jacket is marked down to $68 — that is 15% off. What was the original price? This is the reverse calculation, and no competitor in this topic covers it.
Reverse formula after a percentage increase
r = the percentage increase (e.g. 25 for 25%)
Worked Example — House Price
A house sold for $437,500 after a 25% price increase. What was the original asking price?
Answer: $350,000
Reverse formula after a percentage decrease
r = the percentage decrease (e.g. 15 for 15%)
Worked Example — Sale Price
A jacket is marked down to $68 — that is 15% off. What was the original price?
Answer: $80.00
Always check a reverse calculation by applying the percentage change forward. If $80 decreased by 15%: (80 − 68) ÷ 80 × 100 = 15%. Confirmed.
Percentage Change with Negative Numbers
When the original value is negative — a bank overdraft, a temperature below zero, a business operating at a loss — the formula still works, but use the absolute value of the original as the denominator to prevent sign errors.
|Old| = absolute value of the original (always positive)
Example 6 — Business Loss Reduction
Percentage change between two negative values
A company's quarterly profit went from −$50,000 (a loss) to −$20,000 (a smaller loss). What was the percentage change?
Difference: −20,000 − (−50,000) = +30,000
Divide by |original|: 30,000 ÷ 50,000 = 0.6
Multiply by 100: 0.6 × 100 = 60
✓ A 60% improvement — the loss shrank by 60%
Sequential (Compound) Percentage Changes
If a price increases by 20%, then decreases by 20%, are you back where you started? Most people say yes. The answer is no — and understanding this matters for finance, data analysis, and exam questions.
Starting with $100: a 20% increase gives $100 × 1.20 = $120. Then a 20% decrease applies to $120, not $100: $120 × 0.80 = $96. The result is $96, not $100. Each percentage change applies to a different base value, so they do not cancel.
Worked example — Bonus pool
Two successive percentage changes on a sales bonus pool
A sales manager's performance bonus pool was $80,000 in Q1. It increased by 15% in Q2, then decreased by 10% in Q3. What is the final Q3 pool?
After Q2: $80,000 × 1.15 = $92,000
After Q3: $92,000 × 0.90 = $82,800
Net effect: (82,800 − 80,000) ÷ 80,000 × 100 = +3.5%
✓ Final pool: $82,800. Net change: +3.5% from the original — not 15% − 10% = 5%
Each percentage applies to a different base. 20% up on $100 is $20; but 20% down on $120 is $24 — a larger absolute fall. Consecutive equal increases and decreases always leave you below your starting point because the base grows larger before the equal-sized drop.
Percentage Change vs. Percentage Difference vs. Percentage Points
These three terms describe related but distinct ideas. Mixing them up — common in news reporting and business presentations — produces numbers that can mislead by an order of magnitude. For a deeper look at how these measures are used in context, the statistical interpretation guide goes through real cases.
Directional comparison
Compares a starting value to an ending value. Divides by the original.
(New − Old) ÷ Old × 100
4% → 5%: (5−4) ÷ 4 × 100 = 25% increase
Symmetric comparison
Compares two values with no fixed "start." Divides by their average.
|V₁ − V₂| ÷ ((V₁+V₂)/2) × 100
4% vs 5%: 1 ÷ 4.5 × 100 = 22.2%
Arithmetic difference
Simple subtraction between two percentages. No division involved.
New% − Old%
5% − 4% = 1 percentage point
When a headline says "interest rates rose 25%" and another says "rates rose 1 percentage point," both can be mathematically correct about the same event (4% to 5%). Understanding which measure a source uses — and why — is a core statistical literacy skill covered in the statistical interpretation guide.
Common Mistakes to Avoid
Wrong: (120 − 100) ÷ 120 × 100 = 16.7% | Right: (120 − 100) ÷ 100 × 100 = 20%. Always divide by the original (starting) value.
If a test score goes from 70% to 84%, the percentage change is 20% — not 14%. The 14-point difference is the percentage point change. These are different quantities.
A 20% increase followed by a 20% decrease does not return to the starting value. The net result is a 4% decrease (see Compound Changes above). The base shifts after each step.
A percentage change of −35% means a 35% decrease. The negative sign indicates direction. It is not "−35% decrease" — that double-negates. Write either "a 35% decrease" or "a percentage change of −35%."
Practice Problems
Four problems with fully worked solutions. Click "Show solution" to reveal the working — ungated, no sign-up required.
A coffee shop charges $4.50 for a latte in January and $5.13 in December. What is the percentage increase in price?
A car's value depreciates from $22,000 to $14,300 after three years. What is the percentage decrease in value?
A population grew from 125,000 to 141,250. What was the percentage growth? The following year it decreased by 8%. What is the population after both changes?
A hoodie is on sale for $51 after a 15% discount. What was the original price?
Frequently Asked Questions
Percentage increase = ((New Value − Original Value) ÷ Original Value) × 100. Subtract the original from the new value, divide by the original, then multiply by 100. Example: if a price rises from $80 to $100, the increase is (100 − 80) ÷ 80 × 100 = 25%.
Percentage decrease = ((Original Value − New Value) ÷ Original Value) × 100. Subtract the new value from the original, divide by the original, then multiply by 100. Example: if a price falls from $100 to $80, the decrease is (100 − 80) ÷ 100 × 100 = 20%.
Percentage change is directional — it compares a starting value to an ending value using the original as the denominator. Percentage difference is symmetric — it uses the average of both values as the denominator. Going from 4% to 5% is a 25% percentage change, but only a 22.2% percentage difference.
Percentage points are the arithmetic difference between two percentages (5% − 4% = 1 percentage point). Percentage change measures how large that difference is relative to the starting value ((5 − 4) ÷ 4 × 100 = 25%). These describe very different magnitudes and are often misused in news reporting.
Yes. If a value doubles, it has increased by 100%. If it triples, it has increased by 200%. If sales rise from $10,000 to $35,000, the percentage increase is (35,000 − 10,000) ÷ 10,000 × 100 = 250%. There is no upper limit on how large a percentage increase can be.
Use the reverse formula: Original = New Value ÷ (1 + Rate/100). Example: if a product now costs $138 after a 15% price increase, the original price was 138 ÷ 1.15 = $120. For a decrease, use: Original = New Value ÷ (1 − Rate/100).
They do not simply add up. Each change applies to a different base value. For example, increasing by 20% then decreasing by 20% gives 96% of the original — a 4% net decrease, not 0%. To find the final result: Final = Original × (1 + r₁/100) × (1 + r₂/100), where negative changes use negative r values.
Use the standard formula: ((End Value − Start Value) ÷ Start Value) × 100. The start and end values are the first and last points of the period you are measuring. For compound growth across multiple periods, use: Total % change = ((Final ÷ Initial) − 1) × 100. The z-score guide at statisticsfundamentals.com/z-score/ covers how change relates to distributional position.
Key Takeaways
One formula covers both: ((New − Original) ÷ Original) × 100. Positive = increase; negative = decrease.
Always divide by the original value. Dividing by the new value is the most common mistake.
Reverse calculation: Original = New ÷ (1 + r/100) for an increase; Original = New ÷ (1 − r/100) for a decrease.
When the original value is negative, use its absolute value as the denominator: % change = (New − Old) ÷ |Old| × 100.
Sequential changes don't add. A 20% increase then 20% decrease leaves you 4% below start — not back to zero.
Percentage change ≠ percentage points. A rate rising from 4% to 5% is a 25% increase but a 1 percentage-point increase.
Percentage change ≠ percentage difference. Change uses the original as denominator; difference uses the average of both values.
A negative result from the unified formula means the value decreased. It is not an error — the sign indicates direction.
Common Core Math Standard 7.RP.3 — Ratios and Proportional Relationships | Freedman, Pisani & Purves — Statistics (4th ed.) | For related tools: percentage change calculator, percentage calculator, mean vs. median vs. mode.