Percentage Calculator
Calculate percentages easily with our free online tool – solve percentage problems with step-by-step solutions
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About Percentages
What is a Percentage?
A percentage is a way to express a number as a part of a whole. The word “percent” means “per hundred” – so when we say 25%, we mean 25 out of 100.
Percentages are useful for comparing different quantities. For example, if you score 80 out of 100 on a test, you can say you got 80%.
History of Percentages
The concept of percentages dates back to ancient times. The Romans used a system similar to percentages for calculating taxes.
The modern percent symbol (%) evolved from the Italian term “per cento” meaning “for a hundred”. It became widely used in the 20th century for business and statistics.
How to Calculate Percentages
To calculate a percentage, divide the part by the whole and multiply by 100.
For example, to find what percentage 25 is of 50: (25 ÷ 50) × 100 = 50%.
To find a percentage of a number, convert the percentage to a decimal and multiply. For example, 20% of 50 is 0.20 × 50 = 10.
Real-World Applications
Percentages are used in many areas of life:
- Calculating discounts during sales
- Determining interest rates on loans
- Analyzing statistics in sports
- Calculating tips at restaurants
- Measuring battery life on devices
Frequently Asked Questions
To calculate a percentage, divide the part by the whole and multiply by 100. For example, if you have 20 apples out of 50, the percentage is (20/50) × 100 = 40%.
To add a percentage to a number, multiply the number by (1 + percentage/100). For example, to add 15% to 100: 100 × (1 + 15/100) = 100 × 1.15 = 115.
To subtract a percentage from a number, multiply the number by (1 – percentage/100). For example, to subtract 15% from 100: 100 × (1 – 15/100) = 100 × 0.85 = 85.
A percentage point is the absolute difference between two percentages. For example, if an interest rate increases from 5% to 7%, it has increased by 2 percentage points, which is a 40% increase.
Reverse percentages help you find the original value when you know the percentage change. For example, if you have a number that is 15% greater than the original and equals 115, the original is 115 ÷ 1.15 = 100.