Free Percentage Calculator - Calculate Increases & Decreases
Calculate percentages, increases, decreases, and differences instantly with detailed step-by-step solutions for any calculation
Calculate what percentage of a number is another number
Result
Percentage (%)
20%
Of Number
100
Result
20.00
X% of Y
Get your numbers ready
Turn the percentage into a 'usable number': "20% means '20 out of 100'"
Multiply to find your 'piece' of the number
Complete Formula
Visual Guide:
Visual representation of 20% of 100
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Understanding Percentages
A Comprehensive Guide to Percentage Calculations
Percentages are a fundamental concept in mathematics and everyday life. Whether you're calculating discounts, growth rates, or analyzing data, understanding percentages is essential. This guide will help you master percentage calculations.
X% of Y
Find what percentage one number is of another. For example, what percentage is 25 of 100?
Percentage Change
Calculate the percentage change between two values. Useful for tracking growth or decline.
Reverse Percentage
Find the original value before a percentage increase. Essential for understanding pre-discount prices.
Chain Calculations
Calculate multiple percentage changes in sequence. Useful for complex financial scenarios.
Percentage Increase
Calculate how much a value has increased by a certain percentage. Useful for price increases and growth rates.
Percentage Decrease
Calculate how much a value has decreased by a certain percentage. Essential for discounts and depreciation.
Understand Percentage Calculations with Real Examples
Learn step-by-step how to solve percentage problems with practical examples from everyday life
1. Calculating a Percentage of a Number
A. To find what percent one number is of another:
Percentage = (Part ÷ Whole) × 100
Example: What percentage is 85 out of 100? → (85 ÷ 100) × 100 = 85%
B. To find a portion (like 20% of 80):
Portion = Percentage × Total
Example: What is 20% of 80? → 0.20 × 80 = 16
What it does:
Finds a specific portion of a total amount.
“What is 20% of 80?”
Why it's useful:
Used for tips, discounts, commissions, and taxes.
How it works:
1. Convert the percent to a decimal → 20% = 0.20
2. Multiply the decimal by the total number → 0.20 × 80
Result:
20% of 80 = 16
Example:
“You want to leave a 20% tip on an €80 meal. The tip is €16.”
2. Calculating a Percentage Increase
New Value = Original Value × (1 + Percentage ÷ 100)
This formula helps you calculate a value after it has been increased by a percentage.
€50,000 × (1 + 20 ÷ 100) = €60,000
If your salary increases by 20% from €50,000, this is how you calculate your new salary.
What it does:
Calculates the new value after increasing by a percentage.
“What is €100 increased by 25%?”
Why it's useful:
Used for salary raises, price increases, population growth, and investment returns.
How it works:
1. Convert percentage to decimal → 25% = 0.25
2. Add 1 to the decimal → 1 + 0.25 = 1.25
3. Multiply by original value → €100 × 1.25
Result:
€100 + 25% = €125
Example:
“Your salary increases from €40,000 to €50,000. That's a 25% increase.”
3. Calculating a Percentage Decrease
New Value = Original Value × (1 - Percentage ÷ 100)
This formula helps you calculate a value after it has been decreased by a percentage.
€100 × (1 - 25 ÷ 100) = €75
If a €100 item is discounted by 25%, this is how you calculate the sale price.
What it does:
Calculates the new value after decreasing by a percentage.
“What is €100 decreased by 20%?”
Why it's useful:
Used for discounts, depreciation, budget cuts, and loss calculations.
How it works:
1. Convert percentage to decimal → 20% = 0.20
2. Subtract decimal from 1 → 1 - 0.20 = 0.80
3. Multiply by original value → €100 × 0.80
Result:
€100 - 20% = €80
Example:
“A €500 TV is on sale with a 20% discount. The sale price is €400.”
4. Finding Percentage Change
Percentage Change = ((New Value - Original Value) ÷ Original Value) × 100
This formula helps you find the percentage change between two values.
((150 - 100) ÷ 100) × 100 = 50%
If a value increases from 100 to 150, this is how you calculate the percentage change.
What it does:
Calculates the percentage difference between two values.
“What is the percentage change from 50 to 75?”
Why it's useful:
Used for analyzing trends, measuring growth rates, and comparing changes over time.
How it works:
1. Subtract old value from new value → 75 - 50 = 25
2. Divide by old value → 25 ÷ 50 = 0.5
3. Multiply by 100 → 0.5 × 100 = 50%
Result:
Change from 50 to 75 = +50% increase
Example:
“A company's revenue grew from €2M to €3M. That's a 50% increase.”
5. Reverse Percentage Calculation
Original Value = Final Value ÷ (1 + Percentage ÷ 100)
This formula helps you find the original value before a percentage increase.
€120 ÷ (1 + 20 ÷ 100) = €100
If an item costs €120 after a 20% markup, this is how you calculate its original price.
What it does:
Finds the original value before a percentage change.
“What was the original price if €120 is after a 20% increase?”
Why it's useful:
Used for finding original prices, pre-tax amounts, and initial values before changes.
How it works:
1. Convert percentage to decimal → 20% = 0.20
2. Add 1 to decimal → 1 + 0.20 = 1.20
3. Divide final amount by result → €120 ÷ 1.20
Result:
Original value = €100
Example:
“If a product costs €120 after a 20% markup, its original cost was €100.”
6. Chain Percentage Calculations
Result = Original × (1 + P1 ÷ 100) × (1 + P2 ÷ 100) × ...
This formula helps you calculate multiple percentage changes in sequence.
€100 × (1 + 20 ÷ 100) × (1 - 10 ÷ 100) = €108
If €100 increases by 20% and then decreases by 10%, this is how you calculate the final amount.
What it does:
Calculates multiple percentage changes in sequence.
“What is €100 after a 20% increase followed by a 10% decrease?”
Why it's useful:
Used for compound interest, multiple discounts, and sequential changes over time.
How it works:
1. First change: €100 × (1 + 0.20) = €120
2. Second change: €120 × (1 - 0.10) = €108
3. Each change is applied to the previous result
Result:
Final value = €108
Example:
“An investment of €1000 grows 8% in year 1, then 12% in year 2, reaching €1209.60.”
Tips & Best Practices for Percentage Calculations
25% = 0.25 × Original Value
Always convert percentages to decimals before multiplying. For example, 25% becomes 0.25.
New Value = Original × (1 ± Percentage ÷ 100)
Use brackets when doing percentage increases or decreases — the brackets ensure correct order of operations.
Essential Tips:
- • Double-check if you're increasing or decreasing (adds vs. subtracts)
- • Use percentage change for comparisons over time
- • Reverse percentage is useful when working backward
- • Chain percentages are not additive
- • When in doubt, use a calculator!
Best Practices:
- • Practice with real-life scenarios (tips, discounts, taxes)
- • Use rounding wisely - only at the final step
- • Know your context (finance, health, business)
- • Keep calculations accurate throughout
- • Consider the impact of small mistakes
Real-Life Applications:
- • Tips at restaurants
- • Sales discounts
- • Interest rates
- • Salary raises
- • Tax calculations
Watch Out For:
- • Forgetting to convert to decimals
- • Missing brackets in formulas
- • Confusing increase vs. decrease
- • Adding chain percentages
- • Rounding too early