# What is my growth rate?

Finds the average growth rate per period between a start value and an end value: the compound rate, the linear (simple) rate, and the total change, with a growth curve.

- Page: https://www.acalculator.org/math/growth-rate-calculator
- JSON spec: https://www.acalculator.org/math/growth-rate-calculator.json
- Version: 3dfc62509555

## Default answer

Example with the default inputs (Start value 200, End value 300, Number of periods 5): From 200 to 300 over 5 periods is a compound growth rate of 8.4472% per period.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| from | Start value | The value at the beginning, more than 0. |
| to | End value | The value at the end, 0 or more. |
| n | Number of periods | How many periods (years, months, quarters) lie between the two values, more than 0. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| compound | Compound growth rate per period | The steady rate per period that turns the start value into the end value: (end ÷ start)^(1/n) − 1. |
| linear | Linear growth rate per period | The total change spread evenly over the periods, as a percent of the start value: (end − start) ÷ (start × n). |
| total | Total growth | The change from start to end as a percent of the start value. |
| change | Change | The end value minus the start value. |

## Method

Compound rate = (end ÷ start)^(1/n) − 1; linear rate = (end − start) ÷ (start × n); total growth = (end − start) ÷ start.

## Assumptions

- The start value is more than 0 and the end value is 0 or more; the number of periods is more than 0 and may be a fraction.
- The compound rate assumes steady growth by the same percent each period; the linear rate assumes the same amount each period.
- The total growth, linear rate and change are worked out exactly from the decimals typed.

## Worked examples

1. from = 200, to = 300, n = 5 gives compound = 8.447177%, linear = 10%, total = 50%, change = 100. Source: Compound rate formula as in https://en.wikipedia.org/wiki/Compound_annual_growth_rate.
2. from = 1,000, to = 1,210, n = 2 gives compound = 10%, linear = 10.5%, total = 21%.
3. from = 80, to = 60, n = 3 gives compound = -9.14397%, linear = -8.333333%, total = -25%, change = -20.
4. from = 0.1, to = 0.3, n = 1 gives compound = 200%, linear = 200%, total = 200%, change = 0.2.

## FAQ

### How do I calculate the growth rate?

For the total growth, subtract the start value from the end value and divide by the start value: from 200 to 300 is (300 − 200) ÷ 200 = 50%. For the average rate per period, use the compound growth rate formula (end ÷ start)^(1/n) − 1.

### What is the compound growth rate?

The steady percent per period that turns the start value into the end value: (end ÷ start)^(1/n) − 1. From 200 to 300 over 5 periods it is 1.5^(1/5) − 1 = 8.45% per period. Over years it is the same as the CAGR (compound annual growth rate).

### What is the linear growth rate?

The total growth divided evenly between the periods: (end − start) ÷ (start × n). From 200 to 300 over 5 periods it is 50% ÷ 5 = 10% per period. It assumes the same amount is added each period, not the same percent.

### Why is the compound rate lower than the linear rate?

Compound growth earns growth on growth, so a smaller percent each period reaches the same end value. 8.45% compounded for 5 periods turns 200 into 300, just as 10% of 200 (20) added 5 times does.

### Can the growth rate be negative?

Yes. When the end value is smaller than the start value, every rate is negative: from 80 to 60 over 3 periods is −25% in total, −8.33% a period linear, and −9.14% a period compound.

### What counts as a period?

Any equal step of time: a year, a quarter, a month, or a generation. The rates are per that step. Use a fraction for a part period, such as 2.5 years.

### How is this different from the exponential growth calculator?

This page starts from two values and finds the rate between them. The exponential growth calculator starts from a rate and finds where the value ends up, or any one of its four values from the other three.

## Sources

- OpenStax, College Algebra 2e, section 6.1 Exponential Functions (finding an exponential function from two points): https://openstax.org/books/college-algebra-2e/pages/6-1-exponential-functions
- Wikipedia, Compound annual growth rate (the compound rate formula and its linear counterpart): https://en.wikipedia.org/wiki/Compound_annual_growth_rate