Percentage Formulas

1. Basic Percentage Formula

$P=\frac{\mathrm{Part}}{\mathrm{Whole}}\times 100$

To find the percentage of a part out of a whole.

2. Percentage Increase/Decrease

$\mathrm{Percentage\; Increase}=\frac{\mathrm{New\; Value}–\mathrm{Old\; Value}}{\mathrm{Old\; Value}}\times 100$

$\mathrm{Percentage\; Decrease}=\frac{\mathrm{Old\; Value}–\mathrm{New\; Value}}{\mathrm{Old\; Value}}\times 100$

To calculate the percentage increase or decrease between two values.

3. Finding the Part (Given Percentage)

$\mathrm{Part}=\frac{\mathrm{Percentage}}{100}\times \mathrm{Whole}$

To find the part when the percentage is given.

4. Finding the Whole (Given Percentage)

$\mathrm{Whole}=\frac{\mathrm{Part}\times 100}{\mathrm{Percentage}}$

To find the whole quantity when you know the part and the percentage.

5. Percentage of a Number

$\mathrm{Percentage\; of\; a\; Number}=\frac{\mathrm{Percentage}}{100}\times \mathrm{Number}$

To calculate a certain percentage of a given number.

6. Percentage Change

$\mathrm{Percentage\; Change}=\frac{\mathrm{New\; Value}–\mathrm{Old\; Value}}{\mathrm{Old\; Value}}\times 100$

To calculate the percentage change from an old value to a new value.

7. Successive Percentage Changes

$\mathrm{Successive\; Percentage\; Change}=(1+\frac{\mathrm{P1}}{100})\times (1+\frac{\mathrm{P2}}{100})–1$

To calculate the overall percentage change when multiple percentage changes are applied sequentially.

8. Finding Discount Percentage

$\mathrm{Discount\; Percentage}=\frac{\mathrm{Discount}}{\mathrm{Marked\; Price}}\times 100$

To find the percentage discount based on the marked price.

9. Finding Marked Price After Discount

$\mathrm{Marked\; Price}=\frac{\mathrm{Discounted\; Price}}{(1–\frac{\mathrm{Discount\; Percentage}}{100})}$

To find the marked price after applying a percentage discount.

10. Successive Discount Formula

$\mathrm{Final\; Price}=\mathrm{Original\; Price}\times (1–\frac{\mathrm{d1}}{100})\times (1–\frac{\mathrm{d2}}{100})$

When successive discounts are given, multiply each discount factor (1 – discount percentage) in sequence to find the final price.

11. Percentage Profit or Loss

$\mathrm{Profit\; Percentage}=\frac{\mathrm{Profit}}{\mathrm{Cost\; Price}}\times 100$

$\mathrm{Loss\; Percentage}=\frac{\mathrm{Loss}}{\mathrm{Cost\; Price}}\times 100$

To calculate the percentage profit or loss based on the cost price.

12. Finding the Original Price After Profit or Loss Percentage

$\mathrm{Original\; Price}=\frac{\mathrm{Selling\; Price}}{(1+\frac{\mathrm{Profit\; Percentage}}{100})}$

$\mathrm{Original\; Price}=\frac{\mathrm{Selling\; Price}}{(1–\frac{\mathrm{Loss\; Percentage}}{100})}$

To find the original price before profit or loss is added or subtracted.

13. Finding Percentage of Change in Value (Using Absolute Value)

$\mathrm{Percentage\; Change}=\frac{\mathrm{Absolute\; Change\; in\; Value}}{\mathrm{Original\; Value}}\times 100$

To determine the percentage change using the absolute difference between the original and new values.

14. Percentage Composition (of a mixture)

$\mathrm{Percentage\; Composition\; of\; Component}=\frac{\mathrm{Mass\; of\; Component}}{\mathrm{Total\; Mass}}\times 100$

To calculate the percentage of a component in a mixture or compound.

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