Select Answer Mode | |
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Basic % | |

% Increase | |

% Decrease | |

Compound Values | |

Compound % |

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## User Guide

This tool will help you calculate percentage values using the various methods of changing a base value into a new one by a set percentage.

### Answer Modes

#### Basic Percent Value

Use this method to calculate either of the parameters involved in determining the proportion of a value equivalent to a defined percentage. e.g. 15% of 270 is 40.5. You can choose to calculate the percentage value, original value or the percent number.

#### Percentage Increase

This method is used to calculate either of the parameters involved in adding the proportion of a value to the original value. e.g. 15% increase on 270 is 310.5. This method is often used to calculate how much tax or interest should be added to a value, or how much to markup a price. You can choose to determine the final value, proportional amount of increase, starting value, or percent increase.

#### Percentage Decrease

This method is used to calculate either of the parameters involved in subtracting the proportion of a value from the original value. e.g. 15% decrease on 270 is 229.5. This method is often used to calculate how much the price of an item is discounted, or in reverse it can be used to set a selling price based on a required % profit margin. You can choose to determine the final value, proportional amount of decrease, starting value, or the percent decrease.

#### Compound Values

This calculation type is used to calculate any of the parameters that are involved in increasing an initial value multiple times by a fixed percentage rate. This compounding technique is often used in calculating how much bank loan interest will be charged, or bank savings interest will be paid over a long period of time. e.g. a bank loan at 15% per annum, for a loan of £270, paid back after 3 years, would cost £140.64. You can choose to select the final total, the amount of compounded increase, initial value, percentage rate or the number of times it will take to compound.

#### Compound Percentage

This method calculates the total amount of percentage increase after you have applied a given percentage a certain number of times to the resulting incremented percentage each time.

### Formulas

The formulas used by this percentage calculator to determine each individual parameter are as follows:

#### Basic

D = S · pc / 100

S = 100 · D / pc

pc = 100 · D / S

#### % Increase

E = S · (100 + pc) / 100

D = S · pc / 100

S = 100 · E / (100 + pc)

pc = (100 · E / S) – 100

#### % Decrease

E = S · (100 – pc) / 100

D = S · pc / 100

S = 100 · E / (100 – pc)

pc = 100 – (100 · E / S)

#### Compound Values

E = S · ((100 + pc)/100)ⁿ

D = S · ((100 + pc)/100)ⁿ – S

S = E / ((100 + pc)/100)ⁿ

n = ln(E / S) / ln((100 + pc) / 100)

pc = (E / S)^{1/n} · 100) – 100

#### Compound Percentage

pcn = (((100 + pc) / 100)ⁿ · 100) – 100

n = ln((100 + pcn) / 100) / ln((100 + pc) / 100)

pc = ((100 + pcn) / 100)^{1/n} · 100) – 100

#### Symbols

- S = Start value
- D = Difference between start and end value
- E = End value
- pc = percent value
- pcn = compounded percent value
- n = number of times to compound percentage increase

### Parameters

#### Start Value

This is the original value you start with before applying any percentage calculation

#### Percentage (%)

This is the proportion of something as a percentage, and 1 percent is equivalent to a fraction of 1/100th or 0.01.

In the context of this calculator, the percentage is the proportion to find of a value, to apply an increase or a decrease in a value, the rate to compound, or the effective percentage increase due to the compounding of a percentage rate, n times.

#### Number Of Times (n)

This is the number of times to compound a percentage rate, or how many times to increase a value by a set percentage rate. e.g. 3% compounded 3 times means 1.03 x 1.03 x 1.03 = 1.0927.

#### % Value

This is the difference between the start and end value, which also represents the proportion of the start value that corresponds to the required percentage.

#### End Value

This is the final value you are left with after applying the percentage calculation.