## Formula for Percent Change from one number to another

### The formula for Percent change

Percent Change = ((Final Value - Initial Value) / Initial Value) * 100%

This formula can be used to calculate the percent change of any two values, regardless of their units.

You can use it to calculate the percent change of a population, a stock price, or a temperature as per examples below:

Example for Percent Increase in Population Growth in the World

Population in 2021 = 788 crores

Population in 2022 = 800 crores

Percentage increase = 800-788 / 788 * 100 = + 1.52 % increase

Example for Percent decrease of a Company Growth after one year

Growth in starting year = 100

Growth after one year = 90

Percentage decrease = 90-100 / 100 * 100 = - 10 % decrease

Example for Percent Change from negative to positive

Previous value = -5

New value = 2

Percentage increase = 2 -- 5 / -5 * 100 = 140 % increase

Example for Percent Change for Fraction

Previous value = 1/4

New value = 1/2

Percentage increase = (1/2)-(1/4) / (1/4) * 100 = 100 % increase

Example for Percent change from 0 to 1, 0 to any number

Anything divided by 0 is undefined or infinity. In practical terms, it means 100% increase

Example to find new value using old value and percentage change

Previous score = 700

Percentage increase = 12%

new value = 700 + 700 * 12/100 = 784 increase

Example to find old value using new value and percentage change

new value = 100

percentage = 25

old value = 100 - (100 * 25 / 100) = 75

## Find Initial Value or Final Value given Percent Change

### Here are the generic formulas to find initial value or final value given percent change:

To find the initial value:

Initial Value = Final Value / (1 + (Percent Change / 100))

To find the final value:

Final Value = Initial Value * (1 + (Percent Change / 100))

In these formulas, Percent Change is the percent change expressed as a decimal. For example, if the percent change is 20%, then you would use 0.2 in the formula.

## Percent Change: The Math Behind the Change

- Finance: Percent change is used to track the performance of stocks, bonds, and other investments. It is also used to measure inflation, interest rates, and currency exchange rates.
- Economics: Percent change is used to analyze economic indicators such as GDP growth, unemployment rates, and consumer spending. It is also used to compare economic performance across countries and time periods.
- Science: Percent change is used to measure changes in scientific variables, such as temperature, pressure, and concentration. It is also used to interpret experimental results and make comparisons.
- Everyday Life: Percent change is used in everyday situations, such as comparing prices, tracking weight loss or gain, and calculating discounts.

## Percent Change vs Rate of Change

- The terms "percent change" and "rate of change" are often used interchangeably, but they have distinct meanings in statistics and mathematics.
- Percent change is a measure of the relative change in a value over a certain period. It is calculated as the difference between the final value and the initial value, divided by the initial value, and then multiplied by 100% to express the result as a percentage.
- Rate of change, on the other hand, is a measure of how quickly a value is changing over time. It is typically expressed in units per unit of time, such as kilometers per hour, dollars per year, or degrees Fahrenheit per minute.

Feature | Percent Change | Rate of Change |
---|---|---|

Definition | Relative change between two values | Speed at which something is changing |

Expression | Percentage | Units per unit of time |

Application | Comparing changes in different quantities | Understanding how quickly something is changing |

- Percent change: The population of a city increased by 20% from 2010 to 2020.
- Rate of change: The population of a city is increasing at a rate of 2% per year.
- Percent change: The price of a stock increased by 10% from yesterday.
- Rate of change: The price of a stock is increasing at a rate of $0.50 per day.
- Percent change: The temperature increased by 5% from yesterday.
- Rate of change: The temperature is increasing at a rate of 2 degrees Fahrenheit per hour.

- Use percent change when you want to compare relative changes in different quantities. For example, you can use percent change to compare the population growth of two countries, the price increase of two stocks, or the temperature change in two cities.
- Use rate of change when you want to understand how quickly something is changing over time. For example, you can use rate of change to determine the average speed of a car, the inflation rate of an economy, or the rate of population growth.

## Percent Change Table

Input | Percent Change (% change) |
---|---|

## Percent change from 1/4 to 1/2 | + 100% |

## Percent change from 2 to 1 | - 50% |

## Percent change from 0 to 1 | 100% or infinity increase |

## Percent change from 1 to 2 | + 100% |

## Percent change from 4 to 7 | + 75% |

## Percent change from 4 to 3 | - 25% |

## Percent change from 4 to 5 | + 25% |

## Percent change from 2 to 3 | + 50% |

## Percent change from 8 to 10 | + 25% |

## Percent change from 12 to 15 | + 25% |

## Percent change from 10 to 3 | - 70% |

## Percent change from 10 to 24 | + 140% |

## Percent change from 100 to 80 | - 20% |

## Percent change from 15 to 18 | + 20% |

## Percent change from 2/5 to 4/5 | + 100% |

## Percent change from 2 to 1.6 | - 20% |

## Percent change from 8 to 2 | - 75% |

## Percent change from 3/8 to 7/8 | + 133.333% |

## Percent change from 3 to 30 | + 900% |

## Percent change from 4/5 to 3/5 | - 25% |

## Percent change from 40 to 60 | + 50% |

## Percent change from 40 to 20 | - 50% |

## Percent change from 4 to 1 | - 75% |

## Percent change from 50 to 35 | - 30% |

## Percent change from 5 to 9 | + 80% |

## Percent change from 50 to 22 | - 56% |

## Percent change from 8 to 6 | - 25% |

## Percent change from 6 to 36 | + 500% |

## Percent change from 4 to 6 | + 50% |

## Percent change from 10 to 9 | - 10% |

## Percent change from 19 to 9 | - 52.6316% |

## Percent change from 6 to 9 | + 50% |

## Percent change from 10 to 8 | - 20% |

## Percent change from 5 to 8 | + 60% |

## Percent change from 4 to 7 | + 75% |

## Percent change from 5 to 7 | + 40% |

## Percent change from 2/7 to 4/7 | + 100% |

## Frequently Asked Questions on Percentage Change Calculator

Percentage change is calculated as the difference between 2 values divided by the old value and multiplied by 100.

Percentage change from 1 to 3 = (3-1 / 1) x 100 = 200% change

Not exactly. Rate of change is always with respect to time. Percent change is just change from old to new. The formula to compute the change from old to new is the same

Percent Change = + (New Value - Previous Value / Previous Value * 100)

Percent Change = - (New Value - Previous Value / Previous Value * 100)

+ 33.33333% increase

- 16.66667% decrease

new value = (previous value * 20 / 100) + previous value

previous value = new value - (new value * 10 / 100)

532

4,20,000