What Is Percentage Increase? Formula, Examples, and Common Uses
Understand percentage increase: the formula, how to calculate it step by step, and real-world examples in prices, salaries, and test scores. Includes common mistakes to avoid.
Related Calculators
- Percentage Change CalculatorCalculate directional percentage change between an old value and a new value.
- Percentage Decrease CalculatorCalculate the absolute decrease and percentage decrease from an original value to a lower value.
- Percentage Increase CalculatorCalculate the absolute increase and percentage increase from an original value to a higher value.
- Percentage Difference CalculatorCalculate the symmetric percentage difference between two nonnegative values.
- Reverse Percentage CalculatorFind the original value before a discount, reduction, markup, tax, or percentage increase was applied.
- What Percentage Is X of Y CalculatorFind what percentage one value represents of another value.
What Percentage Increase Means
A percentage increase describes how much a value has grown relative to its original value, expressed as a percentage of that original.
Formula: Percentage Increase = ((New Value − Original Value) ÷ Original Value) × 100
It answers the question: "By what percentage did this value grow?"
Step-by-Step Calculation
Example 1: Price increase A product costs $80 and the new price is $100. - Change = $100 − $80 = $20 - Percentage Increase = ($20 ÷ $80) × 100 = 25% increase
Example 2: Salary raise Salary goes from $65,000 to $70,000. - Change = $70,000 − $65,000 = $5,000 - Percentage Increase = ($5,000 ÷ $65,000) × 100 = 7.69% increase
Example 3: Test score improvement Score improves from 72 to 89. - Change = 89 − 72 = 17 - Percentage Increase = (17 ÷ 72) × 100 = 23.6% increase
Common Mistakes
Mistake 1: Dividing by the new value instead of original Many people mistakenly calculate (change ÷ new value) × 100, which gives a different and incorrect result. - Wrong: ($20 ÷ $100) × 100 = 20% (this is the % of new value, not the increase) - Correct: ($20 ÷ $80) × 100 = 25%
Mistake 2: Confusing percentage increase with percentage points If a tax rate rises from 15% to 20%, the increase is: - 5 percentage points (absolute difference) - 33.3% increase in the tax rate (relative change: 5 ÷ 15 × 100)
These are different things. Financial and political contexts often exploit this ambiguity.
Reverse Calculation: Finding the Original Value
If you know the final value and percentage increase, you can find the original:
Original Value = New Value ÷ (1 + Percentage Increase/100)
Example: After a 20% increase, a product costs $120. What was the original price? - Original = $120 ÷ 1.20 = $100
Percentage Increase vs. Percentage Change
"Percentage change" is the general term; it can be positive (increase) or negative (decrease). "Percentage increase" specifically refers to upward changes.
When a value decreases, the formula gives a negative result — this is a percentage decrease, not a percentage increase.
Real-World Applications
- Retail: "30% off" means a 30% decrease from original price
- Finance: Investment returns expressed as percentage increase/decrease
- Salary: Raises quoted as percentage of current salary
- Inflation: CPI measures percentage increase in price basket over time
- Population: Growth rate expressed as annual percentage increase
Related Guides
- How Percentages Work: Complete Guide with ExamplesUnderstand percentages from the ground up. Covers what percent means, basic percentage calculations, percentage increase and decrease, and common real-world uses.
- How to Calculate Percentages Without a Calculator: Mental Math MethodsLearn to calculate percentages in your head using simple strategies: the 10% shortcut, doubling/halving, and breaking percentages into parts. Works for tips, discounts, and sales.
- Percentage Difference vs. Percentage Change: What's the Difference?Percentage difference and percentage change are not the same thing. Learn when to use each, how to calculate both, and why the distinction matters in data analysis and everyday math.
- Reverse Percentage Explained: Find the Original Value Before a % ChangeLearn how to calculate the original value before a percentage increase or decrease. Covers the reverse percentage formula with worked examples in prices, discounts, and taxes.
- Comment calculer une racine carréeLearn how to use the Racine Carrée Calculator, understand its assumptions and interpret the estimate.
Frequently Asked Questions
- What is the formula for percentage increase?
- Percentage Increase = ((New Value − Original Value) ÷ Original Value) × 100. Always divide the change by the ORIGINAL value, not the new value. Example: from 50 to 75 is a (25 ÷ 50) × 100 = 50% increase, not (25 ÷ 75) × 100 = 33.3%.
- Is 100% increase the same as doubling?
- Yes — a 100% increase means the value increased by an amount equal to its original value, which exactly doubles it. Going from 50 to 100 is a 100% increase. Going from 50 to 150 would be a 200% increase.
- What is the difference between percentage increase and percentage points?
- Percentage points measure the arithmetic difference between two percentages. Percentage increase measures the relative change. Example: interest rate rising from 2% to 3% is a 1 percentage point increase, but a 50% percentage increase (1 ÷ 2 × 100 = 50%). These are two different facts about the same change.
- How do I find the original price after a percentage increase?
- Divide the current price by (1 + percentage/100). After a 25% increase, if the price is $125: original = $125 ÷ 1.25 = $100. Don't subtract the percentage — that only works for simple numbers and won't give the right answer in most cases.
Last updated 7/28/2026