Math Tools
Percentage
Calculator
Six types of percentage calculations in one place — find percent of a number, percent change, reverse percentage, percent difference, tips, and more.
% of Number
X% of Y = ?
What %?
X is what % of Y?
% Change
From X to Y
Reverse %
Original before %
% Difference
Between two values
Tip Calculator
Bill + tip split
Percentage of a Number
Result = (X / 100) × Y
% of
Result
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💡 Real-World Percentage Uses
Discount Savings
20% off $120 = $24 saved → $96
Investment Return
$1,000 → $1,250 = 25% gain
Sales Tax
$50 + 8% tax = $4 tax = $54 total
Exam Score
45 out of 60 = (45/60)×100 = 75%
Weight Loss
From 90kg to 81kg = 10% loss
Interest Rate
$5,000 × 4.5% = $225/year
How to Calculate Percentages
A percentage is a number expressed as a fraction of 100. The word comes from the Latin per centum meaning "by the hundred." Percentages are used to compare proportions, express change, and describe ratios in everyday life.
The 6 Percentage Formulas
1. % of Number: Result = (X / 100) × Y
2. What %: Result = (X / Y) × 100
3. % Change: Result = ((New − Old) / |Old|) × 100
4. Reverse %: Original = Final / (1 ± Percent/100)
5. % Difference: Result = (|V1 − V2| / ((V1+V2)/2)) × 100
6. Tip: Tip = Bill × (Tip%/100); Each = (Bill+Tip)/N
What is the difference between percent change and percent difference?
Percent change measures the change from an old value to a new value: ((New−Old)/Old)×100. It has direction (positive = increase, negative = decrease). Percent difference measures the relative difference between two values with no "direction": (|V1−V2|/average)×100. Use percent change for before/after comparisons and percent difference when there's no clear baseline.
How do I add two percentages together?
You cannot simply add percentages unless they are of the same base. For example, a 10% increase followed by a 10% decrease does NOT give 0% — it gives: 100 × 1.10 × 0.90 = 99, which is a 1% net loss. To correctly combine percentage changes, multiply the factors: (1 + p1/100) × (1 + p2/100) − 1 = combined rate.
How do I calculate percentage increase from a sale price to original price?
Use the reverse percentage formula: Original = Final / (1 − Discount%). For example, if a sale price is $60 after a 25% discount: Original = 60 / (1 − 0.25) = 60 / 0.75 = $80. Many people incorrectly add the percentage back: 60 + 25% of 60 = 75 (wrong). The reverse formula gives the correct original price.