What is the formula for calculating discounts?

To find the discount amount, multiply the original price by the discount percentage (as a decimal). Subtract that amount from the original price to find the final sale price.

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Understanding Percentages

The word "percentage" comes from the Latin phrase per centum, which literally translates to "by the hundred." Therefore, a percentage is simply a specific fraction out of exactly 100.

For example, if you scored an 85% on a math test, it means that if the test had exactly 100 points, you would have earned 85 of them. Mathematically, 85% is exactly the same as the fraction 85/100, or the decimal number 0.85.

Core Percentage Formulas

You can solve almost any percentage problem manually using these three primary formulas:

Finding the Percentage of a Number:
Formula: (Percentage / 100) Ã— Total Value
Example: What is 20% of 50? -> (20 / 100) Ã— 50 = 10.
Finding What Percentage One Number is of Another:
Formula: (Part / Whole) Ã— 100
Example: 15 is what percent of 75? -> (15 / 75) Ã— 100 = 20%.
Percentage Change (Increase/Decrease):
Formula: ((New Value - Old Value) / |Old Value|) Ã— 100
Example: Price changed from $40 to $50. -> ((50 - 40) / 40) Ã— 100 = 25% Increase.

Real World Use Cases

Percentages are one of the most frequently used mathematical concepts in daily adult life. You utilize them constantly in:

Scenario	Application
Shopping & Discounts	Calculating the final price of an item that is "30% off" during a sale.
Taxes & Tipping	Adding a 7% sales tax to a purchase, or calculating a 20% tip at a restaurant.
Finances & Careers	Asking for a 10% raise at work, or calculating the 5% APY interest on a savings account.
Business Metrics	A company reporting that "revenue increased by 22% year-over-year."

How Do I Calculate Percentages In My Head?

Mental math with percentages is easy once you understand the "10% rule." To find 10% of any number, simply move the decimal point one place to the left.

For instance, to find a 20% tip on a $45.00 restaurant bill:
1. Move the decimal point one place left to find 10% -> $4.50
2. Multiply that number by 2 to get 20% -> $4.50 Ã— 2 = $9.00
You should leave a $9.00 tip.

To find 5% of a number in your head, simply find 10% and cut it in half!

Frequently Asked Questions

How do you calculate a percentage?

To calculate a percentage, divide the part by the whole and multiply by 100. For example, if you have 20 apples out of 50 total apples, the percentage is (20 Ã· 50) Ã— 100 = 40%.

How do I calculate a percentage increase?

Subtract the original number from the new number, then divide that difference by the original number. Finally, multiply the result by 100. If the result is positive, it's an increase.

Why does removing 50% not reverse adding 50%?

Because the starting base numbers are different. If a $100 stock goes up 50%, it's now worth $150. If the stock then drops 50% from its new $150 high, it drops $75, making it worth only $75. (Not the original $100).