What is my growth rate?
Type a start value, an end value, and the number of periods between them. You get the average growth rate per period, compound and linear, and the total growth.
- Compound growth rate per period
- 8.4472%
From 200 to 300 over 5 periods is a compound growth rate of 8.4472% per period.
- Linear growth rate per period
- 10%
- Total growth
- 50%
- Change
- 100
Compound growth rate per period: 8.4472%. From 200 to 300 over 5 periods is a compound growth rate of 8.4472% per period.
The value at a steady compound rate
How to calculate
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.
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.
Method: Compound rate = (end ÷ start)^(1/n) − 1; linear rate = (end − start) ÷ (start × n); total growth = (end − start) ÷ start.
- 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
Each example is checked against the calculator on every build.
- Start value 200, End value 300, Number of periods 5 gives Compound growth rate per period 8.447177%, Linear growth rate per period 10%, Total growth 50%, Change 100.Source: Compound rate formula as in https://en.wikipedia.org/wiki/Compound_annual_growth_rate
- Start value 1,000, End value 1,210, Number of periods 2 gives Compound growth rate per period 10%, Linear growth rate per period 10.5%, Total growth 21%.
- Start value 80, End value 60, Number of periods 3 gives Compound growth rate per period -9.14397%, Linear growth rate per period -8.333333%, Total growth -25%, Change -20.
- Start value 0.1, End value 0.3, Number of periods 1 gives Compound growth rate per period 200%, Linear growth rate per period 200%, Total growth 200%, Change 0.2.
How it works
With a start value A (more than 0), an end value B (0 or more), and n periods (more than 0, fractions allowed):
- Compound growth rate per period = ((B ÷ A)^(1/n) − 1) × 100%. It is the steady rate r with A × (1 + r)^n = B. When B is 0 it is −100%.
- Linear growth rate per period = (B − A) ÷ (A × n) × 100%: the total growth split evenly between the periods.
- Total growth = (B − A) ÷ A × 100%.
- Change = B − A.
The numbers are read as the exact decimals typed; the total growth, the linear rate and the change are worked out exactly and then shown as the nearest 64-bit float, and the compound rate is worked out in 64-bit floating point. Percents are shown to at most 4 decimal places and the change to at most 6. A result too large for a 64-bit float (a tiny start value or a tiny number of periods) has no answer.
The chart draws A × (B ÷ A)^(s ÷ n) for s from 0 to n, the value at the steady compound rate, with a marker at n.
Limits
- A is more than 0 and at most 10^15; B is from 0 to 10^15; n is more than 0 and at most 1,000.
Worked examples by hand
200 to 300 over 5 periods. B ÷ A = 1.5, and 1.5^(1/5) = 1.084472, so the compound rate is 8.447177% per period. The total growth is 100 ÷ 200 = 50%, and the linear rate 50% ÷ 5 = 10% per period. The change is 100.
1000 to 1210 over 2 periods. 1.21 = 1.1², so the compound rate is 10%. The total growth is 21%, and the linear rate is 10.5%.
80 to 60 over 3 periods. 0.75^(1/3) = 0.908560, so the compound rate is −9.143970%. The total growth is −20 ÷ 80 = −25%, and the linear rate is −8.333333%.
0.1 to 0.3 over 1 period. Exactly 0.3 − 0.1 = 0.2, and 0.2 ÷ 0.1 = 2, so every rate is 200% and the change is 0.2.
Other questions people ask
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.