Increase and Decrease Percentage Formula Explained
Learn how to apply percentage increases and decreases to any value with confidence
Try Increase/Decrease CalculatorWhy Understanding This Formula Matters
Whether you're calculating price markups, salary raises, discounts, or budget cuts, the ability to increase or decrease a value by a percentage is a fundamental skill. This formula appears everywhere: retail pricing, financial planning, business reporting, and personal budgeting.
The increase and decrease percentage formula tells you what a value becomes after applying a percentage change. It's different from calculating the percentage change between two values—instead, you start with one value and a percentage, then find the result.
This guide breaks down both formulas, shows you exactly when to use each, and provides direct access to AnyPercent's increase/decrease calculator so you can verify your work instantly and save time.
Understanding the Increase Formula
When you increase a value by a percentage, you're adding a portion of that value to itself. The percentage increase formula combines the original value and the increase into one calculation.
The Formula Explained
The percentage increase formula is:
New Value = Original Value × (1 + (Percentage ÷ 100))
Where:
- Original Value: The starting amount
- Percentage: The percentage increase (e.g., 15 for a 15% increase)
- New Value: The result after the increase
For example, if a product costs $200 and you increase the price by 15%, the new price is $200 × (1 + (15 ÷ 100)) = $200 × 1.15 = $230.
The factor 1.15 represents "the original 100% plus an additional 15%." You can verify this calculation using the increase/decrease calculator.
Understanding the Decrease Formula
When you decrease a value by a percentage, you're removing a portion of that value. The percentage decrease formula works similarly to the increase formula, but subtracts instead of adds.
The Formula Explained
The percentage decrease formula is:
New Value = Original Value × (1 − (Percentage ÷ 100))
Where:
- Original Value: The starting amount
- Percentage: The percentage decrease (e.g., 20 for a 20% decrease)
- New Value: The result after the decrease
For example, if a budget of $50,000 is cut by 20%, the new budget is $50,000 × (1 − (20 ÷ 100)) = $50,000 × 0.80 = $40,000.
The factor 0.80 represents "80% of the original," which is what remains after removing 20%. You can calculate this instantly at AnyPercent.
Step-by-Step Calculation Workflow
Follow these steps to apply percentage increases or decreases accurately.
For Percentage Increase:
- Identify your original value (starting amount)
- Identify the percentage increase
- Divide the percentage by 100 to convert it to a decimal
- Add 1 to the decimal (e.g., 0.15 becomes 1.15)
- Multiply the original value by this factor
For Percentage Decrease:
- Identify your original value (starting amount)
- Identify the percentage decrease
- Divide the percentage by 100 to convert it to a decimal
- Subtract the decimal from 1 (e.g., 1 − 0.20 = 0.80)
- Multiply the original value by this factor
These workflows apply to any scenario where you need to adjust a value by a percentage. For more context on related calculations, see our guide on percentage change vs percentage difference.
Real-World Examples
Example 1: Salary Raise (Percentage Increase)
An employee earns $60,000 per year and receives a 5% raise. What is the new salary?
Formula: New Salary = $60,000 × (1 + (5 ÷ 100))
Calculation: $60,000 × 1.05 = $63,000
Interpretation: The new salary is $63,000 after a 5% increase.
Example 2: Discount Pricing (Percentage Decrease)
A laptop costs $1,200 and is on sale for 25% off. What is the sale price?
Formula: Sale Price = $1,200 × (1 − (25 ÷ 100))
Calculation: $1,200 × 0.75 = $900
Interpretation: The sale price is $900 after a 25% discount.
Both of these calculations can be verified instantly with AnyPercent's calculator, which also shows the step-by-step breakdown and the amount of increase or decrease.
Worked Examples Table
| Scenario | Original Value | Percentage | Formula Setup | Result |
|---|---|---|---|---|
| Price increase | $500 | +10% | $500 × 1.10 | $550 |
| Budget cut | $80,000 | −15% | $80,000 × 0.85 | $68,000 |
| Investment growth | $10,000 | +8% | $10,000 × 1.08 | $10,800 |
| Sales decline | $250,000 | −12% | $250,000 × 0.88 | $220,000 |
Each scenario shows how the formula adapts to different contexts. For a complete tutorial on calculating percentage change from two known values, check out our guide on how to calculate percentage increase and decrease.
Common Mistakes and How to Avoid Them
| Mistake | Why It Happens | How to Fix It |
|---|---|---|
| Forgetting to add or subtract 1 | Multiplying by the decimal directly (e.g., 0.15 instead of 1.15) | Remember: 1 represents the original 100%, then add or subtract the change |
| Using the wrong sign (+ vs −) | Confusing increase with decrease | Increase = add to 1 (1.15); Decrease = subtract from 1 (0.85) |
| Entering percentage as decimal without dividing by 100 | Treating 15% as 15 instead of 0.15 | Always divide the percentage by 100 before adding or subtracting from 1 |
| Applying multiple percentage changes incorrectly | Adding percentages instead of compounding | Apply each percentage change sequentially to the new value, not the original |
Using AnyPercent for Increase/Decrease Calculations
AnyPercent's increase/decrease calculator handles both formulas automatically and shows you the full breakdown:
- Enter your original value and percentage
- Select "Increase" or "Decrease"
- Get instant results with step-by-step formulas
- See both the new value and the amount of change
- Copy Excel-compatible formulas for spreadsheet integration
You can also explore related tools:
- Percentage Change Calculator: Calculate the percentage change between two known values
- Percentage Difference Calculator: Compare two values symmetrically
- Discount Calculator: Specialized tool for retail pricing and discounts
Spreadsheet Formulas
If you're working in Excel or Google Sheets, you can use these formulas directly in your spreadsheets:
For Percentage Increase:
=A1*(1+(B1/100))
Where A1 is the original value and B1 is the percentage increase.
For Percentage Decrease:
=A1*(1-(B1/100))
Where A1 is the original value and B1 is the percentage decrease.
These formulas match exactly what AnyPercent uses, ensuring consistency between manual calculations and automated workflows.
Conclusion
The increase and decrease percentage formulas are essential tools for applying percentage changes to values in business, finance, and everyday life. Remember that both formulas multiply the original value by a factor: (1 + percentage/100) for increases and (1 − percentage/100) for decreases.
By understanding these formulas and using tools like AnyPercent's calculator, you can handle pricing adjustments, budget changes, and financial projections with confidence and accuracy.
For more percentage calculation guides, explore our complete article library, or learn about the reverse process in our percentage change calculation guide.