Percentage Formulas Guide

Master percentage calculations with our comprehensive formula guide and examples

Percentage Increase

Calculate how much a value has increased as a percentage of the original value.

Formula:

((New Value - Old Value) ÷ Old Value) × 100

Example:

From 100 to 120: ((120 - 100) ÷ 100) × 100 = 20%

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Percentage Decrease

Calculate how much a value has decreased as a percentage of the original value.

Formula:

((Old Value - New Value) ÷ Old Value) × 100

Example:

From 200 to 150: ((200 - 150) ÷ 200) × 100 = 25%

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Percent Change

Calculate the percentage change between two values (can be positive or negative).

Formula:

((To Value - From Value) ÷ From Value) × 100

Example:

From 50 to 65: ((65 - 50) ÷ 50) × 100 = 30%

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What Percent is A of B

Find what percentage one number represents of another number.

Formula:

(A ÷ B) × 100

Example:

25 of 100: (25 ÷ 100) × 100 = 25%

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Percentage Of

Calculate a specific percentage of a given number.

Formula:

(Percentage ÷ 100) × Number

Example:

20% of 150: (20 ÷ 100) × 150 = 30

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Reverse Percentage

Find the original value before a percentage change was applied.

Formula:

Final Value ÷ (1 ± Percentage ÷ 100)

Example:

80 after 20% discount: 80 ÷ (1 - 20 ÷ 100) = 100

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Understanding Percentages

Percentages are one of the most practical mathematical concepts we use in everyday life. From calculating tips and taxes to understanding interest rates and discounts, percentages help us make sense of proportional relationships.

The word "percent" comes from the Latin "per centum," meaning "by the hundred." When we say something is 25%, we mean 25 out of every 100, or 25/100, or 0.25 as a decimal.

Understanding these formulas empowers you to verify calculations, catch errors, and build confidence in working with percentages in any context.