Formula Sheet • Percentages & Financial Maths

Percentage Formula Sheet

Every percentage formula you need — percentage of amounts, multipliers for increase and decrease, reverse percentages, simple and compound interest, depreciation, and business margins.

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Finding Percentages

Percentage of an Amount

\text{Value} = \frac{P}{100} \times X

P = percentage rate • X = total / base amount.

Worked Example

\displaystyle 35\% \text{ of } 80 = \frac{35}{100} \times 80 = 0.35 \times 80 = 28

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One Quantity as % of Another

\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\%

Expresses what portion a single value represents out of a whole total.

Worked Example

\displaystyle \frac{18}{60} \times 100\% = 0.30 \times 100\% = 30\%

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Find Whole from Known Part

\text{Whole} = \frac{\text{Part}}{P} \times 100

Used when a percentage share is known and you need the full 100% total.

Worked Example

\displaystyle 45 \text{ is } 30\% \implies \text{Total} = \frac{45}{30} \times 100 = 150

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Percentage Change & Multipliers

Percentage Increase

\text{New} = \text{Original} \times \left(1 + \frac{r}{100}\right)

r = percentage increase rate • Multiplier is always greater than 1.

Worked Example

\displaystyle 200 \text{ increased by } 15\%: 200 \times 1.15 = 230

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Percentage Decrease

\text{New} = \text{Original} \times \left(1 - \frac{r}{100}\right)

r = percentage decrease rate • Multiplier is always between 0 and 1.

Worked Example

\displaystyle 200 \text{ decreased by } 15\%: 200 \times 0.85 = 170

Percentage Change Calculator →

Percentage Change (%)

\Delta\% = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%

Positive result indicates an increase; negative result indicates a decrease.

Worked Example

\displaystyle \frac{100 - 80}{80} \times 100\% = \frac{20}{80} \times 100\% = +25\%

Percentage Change Calculator →

Reverse Percentages & Tax

Reverse Percentage (Original Value)

\text{Original} = \frac{\text{Final Amount}}{1 \pm \frac{r}{100}}

Use + after an increase; use − after a discount or decrease.

Worked Example

\displaystyle \text{Paid } 85\text{ after } 15\% \text{ off} \implies \frac{85}{0.85} = 100

Reverse Percentage Calculator →

Adding VAT / Sales Tax

\text{Gross} = \text{Net} \times \left(1 + \frac{\text{Tax}\%}{100}\right)

For standard 20% VAT, multiply net price by 1.20.

Worked Example

\displaystyle 50 + 20\% \text{ VAT} = 50 \times 1.20 = 60

Percentage Calculator →

Extracting VAT / Sales Tax

\text{Tax} = \text{Gross} - \frac{\text{Gross}}{1 + \frac{\text{Tax}\%}{100}}

Finds the exact tax paid inside a gross VAT-inclusive receipt total.

Worked Example

\displaystyle 60 \text{ gross} \implies \text{Net } \frac{60}{1.20} = 50 \implies \text{VAT} = 10

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Interest & Growth

Simple Interest

I = \frac{P \times r \times t}{100}

P = principal • r = annual interest rate (%) • t = time in years.

Worked Example

\displaystyle I = \frac{1000 \times 5 \times 3}{100} = 150 \implies \text{Total} = 1150

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Compound Interest

A = P\left(1 + \frac{r}{100}\right)^n

A = total accrued • P = principal • n = compounding periods.

Worked Example

\displaystyle A = 1000(1 + 0.05)^3 = 1000(1.157625) \approx 1157.63

Percentage Calculator →

Depreciation / Decay

V = P\left(1 - \frac{r}{100}\right)^n

Used for vehicle depreciation, equipment write-down, and radioactive decay.

Worked Example

\displaystyle V = 10\,000(1 - 0.20)^3 = 10\,000(0.8)^3 = 5120

Percentage Change Calculator →

Profit, Markup & Margins

Profit / Loss Percentage

\text{Profit \%} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\%

Profit equals Selling Price minus Cost Price; calculated relative to Cost.

Worked Example

\displaystyle \text{Cost } 40,\; \text{Sell } 50 \implies \frac{10}{40} \times 100\% = 25\%

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Markup Percentage

\text{Markup} = \frac{\text{Selling Price} - \text{Cost}}{\text{Cost}} \times 100\%

The percentage added onto the wholesale cost price to set the retail price.

Worked Example

\displaystyle \text{Cost } 80,\; \text{Sell } 120 \implies \frac{40}{80} \times 100\% = 50\%

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Profit Margin Percentage

\text{Margin} = \frac{\text{Selling Price} - \text{Cost}}{\text{Selling Price}} \times 100\%

The percentage of the total revenue that remains as profit after deducting cost.

Worked Example

\displaystyle \text{Cost } 80,\; \text{Sell } 120 \implies \frac{40}{120} \times 100\% \approx 33.3\%

Percentage Calculator →

Operation	Multiplier Calculation	Decimal Multiplier	Worked Example (Base = 200)
10% Increase	$\displaystyle 1 + \frac{10}{100}$	× 1.10	$\displaystyle 200 \times 1.10 = 220$
20% Increase (Standard VAT)	$\displaystyle 1 + \frac{20}{100}$	× 1.20	$\displaystyle 200 \times 1.20 = 240$
50% Increase	$\displaystyle 1 + \frac{50}{100}$	× 1.50	$\displaystyle 200 \times 1.50 = 300$
10% Decrease	$\displaystyle 1 - \frac{10}{100}$	× 0.90	$\displaystyle 200 \times 0.90 = 180$
20% Decrease	$\displaystyle 1 - \frac{20}{100}$	× 0.80	$\displaystyle 200 \times 0.80 = 160$
50% Decrease	$\displaystyle 1 - \frac{50}{100}$	× 0.50	$\displaystyle 200 \times 0.50 = 100$

Curriculum & Revision Note

About These Percentage Formulas

Percentages are one of the most practically useful areas of secondary school maths. This sheet brings together percentage multipliers, percentage change equations, reverse percentage formulas, simple and compound interest, annual depreciation, and commercial profit markup versus margin relationships.

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