Percentage Calculator
Calculate percentages, increases, decreases, and differences
Calculation Type
Calculate the result after increasing a value by a percentage
Quick Examples
Complete Percentage Guide
Understanding Percentages
The word "percent" comes from the Latin "per centum," meaning "per hundred." A percentage is simply a way to express a number as a fraction of 100. For example, 25% means 25 out of 100, or one quarter. Percentages are used in virtually every aspect of daily life — from calculating sales tax and tips to understanding interest rates and statistical data.
Core Formulas
- Find X% of Y: Result = Y × (X / 100)
- % Increase: New Value = Original × (1 + Rate / 100)
- % Decrease: New Value = Original × (1 − Rate / 100)
- % Difference: |A − B| / ((A + B) / 2) × 100
Real-World Applications
- Shopping discounts: A $80 item at 30% off costs $80 × 0.70 = $56
- Sales tax: A $100 purchase with 8.5% tax totals $108.50
- Restaurant tips: A 20% tip on a $65 bill is $13
- Pay raises: A 5% raise on a $50,000 salary adds $2,500
- Investment returns: A 7% annual return on $10,000 yields $700 in year one
Converting Between Formats
- Percentage to decimal: Divide by 100 → 45% = 0.45
- Decimal to percentage: Multiply by 100 → 0.125 = 12.5%
- Fraction to percentage: Divide then × 100 → 3/8 = 37.5%
- Percentage to fraction: Put over 100 and simplify → 75% = 3/4
Common Percentage Mistakes to Avoid
Successive percentage changes are not additive
A 50% increase followed by a 50% decrease does NOT return to the original value. If $100 increases by 50% to $150, then decreases by 50%, it becomes $75 — a net loss of 25%.
Percentage points vs. percentages
If an interest rate goes from 4% to 5%, that's a 1 percentage point increase, but a 25% relative increase. These are different concepts and confusing them can lead to costly misunderstandings.
Reversing a percentage
If you paid $108 including 8% tax, the original price is $108 / 1.08 = $100, NOT $108 − 8% of $108 = $99.36.
Frequently Asked Questions
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. For example: if your rent went from $1,200 to $1,350, the increase is (1350 − 1200) / 1200 × 100 = 12.5%.
What is the difference between margin and markup?
Markup is the percentage added to cost to get the selling price (based on cost). Margin is the percentage of the selling price that is profit (based on selling price). A 50% markup results in a 33.3% margin.
How do I find what percentage one number is of another?
Divide the part by the whole, then multiply by 100. For example: 35 is what percent of 200? Answer: 35 / 200 × 100 = 17.5%.
Can percentages be greater than 100%?
Yes. A percentage over 100% indicates a value greater than the reference. For instance, if sales grew from $1M to $2.5M, that's a 150% increase, meaning the growth itself is 1.5 times the original.
Complete Percentage Guide
Understanding Percentages
The word "percent" comes from the Latin "per centum," meaning "per hundred." A percentage is simply a way to express a number as a fraction of 100. For example, 25% means 25 out of 100, or one quarter. Percentages are used in virtually every aspect of daily life — from calculating sales tax and tips to understanding interest rates and statistical data.
Core Formulas
- Find X% of Y: Result = Y × (X / 100)
- % Increase: New Value = Original × (1 + Rate / 100)
- % Decrease: New Value = Original × (1 − Rate / 100)
- % Difference: |A − B| / ((A + B) / 2) × 100
Real-World Applications
- Shopping discounts: A $80 item at 30% off costs $80 × 0.70 = $56
- Sales tax: A $100 purchase with 8.5% tax totals $108.50
- Restaurant tips: A 20% tip on a $65 bill is $13
- Pay raises: A 5% raise on a $50,000 salary adds $2,500
- Investment returns: A 7% annual return on $10,000 yields $700 in year one
Converting Between Formats
- Percentage to decimal: Divide by 100 → 45% = 0.45
- Decimal to percentage: Multiply by 100 → 0.125 = 12.5%
- Fraction to percentage: Divide then × 100 → 3/8 = 37.5%
- Percentage to fraction: Put over 100 and simplify → 75% = 3/4
Common Percentage Mistakes to Avoid
Successive percentage changes are not additive
A 50% increase followed by a 50% decrease does NOT return to the original value. If $100 increases by 50% to $150, then decreases by 50%, it becomes $75 — a net loss of 25%.
Percentage points vs. percentages
If an interest rate goes from 4% to 5%, that's a 1 percentage point increase, but a 25% relative increase. These are different concepts and confusing them can lead to costly misunderstandings.
Reversing a percentage
If you paid $108 including 8% tax, the original price is $108 / 1.08 = $100, NOT $108 − 8% of $108 = $99.36.
Frequently Asked Questions
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. For example: if your rent went from $1,200 to $1,350, the increase is (1350 − 1200) / 1200 × 100 = 12.5%.
What is the difference between margin and markup?
Markup is the percentage added to cost to get the selling price (based on cost). Margin is the percentage of the selling price that is profit (based on selling price). A 50% markup results in a 33.3% margin.
How do I find what percentage one number is of another?
Divide the part by the whole, then multiply by 100. For example: 35 is what percent of 200? Answer: 35 / 200 × 100 = 17.5%.
Can percentages be greater than 100%?
Yes. A percentage over 100% indicates a value greater than the reference. For instance, if sales grew from $1M to $2.5M, that's a 150% increase, meaning the growth itself is 1.5 times the original.