Answer first
What this calculator tells you
Calculate the ending value, the doubling time and the total growth for a steady percentage change per period. Project a quantity that grows or shrinks by a fixed percent each period. Formula: End value = start × (1 + r)^t; doubling time = ln 2 ÷ ln(1 + r); total growth = (1 + r)^t − 1. At the worked-example inputs, the ending value is 2,158.9. Holding every other input steady, moving growth rate per period from 4.0% to 12.0% moves the result from 1,480.2 to 3,105.8.
Transparent method
The formula
Project a quantity that grows or shrinks by a fixed percent each period.
Worked example
Example inputs
How to interpret the result
Exponential growth adds a fixed percent of the current value each period. A value of 1,000 growing 8 percent a period is 2,158.92 after 10 periods, a rise of 115.9 percent. It doubles in about 9.01 periods, since the time to double depends on the rate and not on the starting value.
At the worked-example inputs the ending value is 2,158.9. It rises with growth rate per period, starting value and number of periods.
These are exact mathematical formulas; results are limited only by floating-point precision, not by real-world estimation. Confirm the convention (rounding rule, sign, base) your assignment or application expects.
Before you rely on it
What to check
Use the same period for the rate and the count. An 8 percent yearly rate over 10 years is 10 periods, and an 8 percent monthly rate over 10 years is 120.
The common error
Where people go wrong with exponential growth calculator
Treating a decline as a growth rate in reverse. Falling 20 percent and then rising 20 percent does not get you back, because the second change applies to the smaller number.
Sensitivity evidence
How growth rate per period changes the ending value
Holding every other input at the worked-example value, moving growth rate per period from 4.0% to 12.0% moves the ending value from 1,480.2 to 3,105.8: a spread of 1,625.6, or 75% of the worked-example result.
| Growth rate per period | Ending value | Periods to double | Total growth |
|---|---|---|---|
| 4.0% | 1,480.2 | 17.7 | 48.0% |
| 6.0% | 1,790.8 | 11.9 | 79.1% |
| 8.0%worked example | 2,158.9 | 9 | 115.9% |
| 10.0% | 2,593.7 | 7.3 | 159.4% |
| 12.0% | 3,105.8 | 6.1 | 210.6% |
Every input, tested
Which input moves the ending value most
Of the 3 inputs, growth rate per period moves the ending value most (802.9 across the range tested) and number of periods moves it least (332.6).
| Input | Tested from | To | Ending value at each end | Swing |
|---|---|---|---|---|
| Growth rate per period | 6.0% | 10.0% | 1,790.8 to 2,593.7 | 802.9 (37%) |
| Starting value | 900 | 1,100 | 1,943 to 2,374.8 | 431.8 (20%) |
| Number of periods | 9 | 11 | 1,999 to 2,331.6 | 332.6 (15%) |
Two variables at once
Ending value by growth rate per period and starting value
Across the grid the ending value runs from 1,184.2 to 3,727. Moving growth rate per period from 4.0% to 12.0% shifts it by 1,625.6 at the middle column, and moving starting value from 800 to 1,200 shifts it by 863.6 at the middle row, so growth rate per period is the bigger lever here.
| Growth rate per period \ Starting value | 800 | 1,000 | 1,200 |
|---|---|---|---|
| 4.0% | 1,184.2 | 1,480.2 | 1,776.3 |
| 6.0% | 1,432.7 | 1,790.8 | 2,149 |
| 8.0% | 1,727.1 | 2,158.9 | 2,590.7 |
| 10.0% | 2,075 | 2,593.7 | 3,112.5 |
| 12.0% | 2,484.7 | 3,105.8 | 3,727 |
The highlighted cell is the worked example: 2,158.9.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Starting value | 1,000 | Enter the starting value used in this calculation. |
| Growth rate per period | 8.0% | Use a negative rate for a decline. Doubling time applies only to a positive rate. |
| Number of periods | 10 | Enter the number of periods used in this calculation. |
| Ending value | 2,158.9 | |
| Periods to double | 9 | |
| Total growth | 115.9% | |
Inputs, definitions and assumptions
Starting value
Enter the starting value used in this calculation. The prefilled worked-example value is 1,000.
Growth rate per period
Use a negative rate for a decline. Doubling time applies only to a positive rate. The prefilled worked-example value is 8.0%.
Number of periods
Enter the number of periods used in this calculation. The prefilled worked-example value is 10.
How to use this calculator
- 1Verify the inputs. Gather starting value, growth rate per period and number of periods from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the ending value at 2,158.9. Store your own version of it as Scenario A.
- 3Test one change. Start with growth rate per period, the input with the biggest effect here: moving growth rate per period from 6.0% to 10.0% takes the ending value from 1,790.8 to 2,593.7, a swing of 37% of the worked-example figure.
- 4Check the extremes. At half the example growth rate per period (4.0%) the ending value is 1,480.2; at double (16.0%) it is 4,411.4.
People also ask
Frequently asked questions
How do you calculate exponential growth?
End value = start × (1 + r)^t; doubling time = ln 2 ÷ ln(1 + r); total growth = (1 + r)^t − 1. Enter growth rate per period in percent (8 means 8%). At the worked-example inputs the ending value is 2,158.9.
What does the exponential growth result mean?
Project a quantity that grows or shrinks by a fixed percent each period. At the worked-example inputs the ending value is 2,158.9. It rises with growth rate per period, starting value and number of periods.
How much does growth rate per period change the ending value?
Holding every other input at the worked-example value, moving growth rate per period from 4.0% to 12.0% moves the ending value from 1,480.2 to 3,105.8, a spread of 1,625.6.
What are the limits of this exponential growth calculator?
These are exact mathematical formulas; results are limited only by floating-point precision, not by real-world estimation. Confirm the convention (rounding rule, sign, base) your assignment or application expects. The tables on this page test growth rate per period only from 4.0% to 12.0%; a value outside that range is not tabulated here.
Which input moves the ending value most in the exponential growth calculator?
Ranked by how far each moves the ending value across the range tested: growth rate per period (802.9, 37%), starting value (431.8, 20%) and number of periods (332.6, 15%).
If I double growth rate per period in the exponential growth calculator, does the ending value double?
Doubling it from 8.0% to 16.0% takes the ending value from 2,158.9 to 4,411.4, which is 2.04 times the worked-example figure. So the result scales almost exactly in proportion. Halving it to 4.0% gives 1,480.2.
How much does starting value matter in the exponential growth calculator?
The worked example uses 1,000. Holding every other input at its worked-example value, moving starting value from 900 to 1,100 takes the ending value from 1,943 to 2,374.8, a swing of 20% of the worked-example figure.
How much does number of periods matter in the exponential growth calculator?
The worked example uses 10. Holding every other input at its worked-example value, moving number of periods from 9 to 11 takes the ending value from 1,999 to 2,331.6, a swing of 15% of the worked-example figure.
Which inputs change the periods to double in the exponential growth calculator?
At the worked-example inputs it is 9. Growth rate per period takes it from 11.9 to 7.3.
Which inputs change the total growth in the exponential growth calculator?
At the worked-example inputs it is 115.9%. Growth rate per period takes it from 79.1% to 159.4% and number of periods takes it from 99.9% to 133.2%.
Is rounding the same as truncating?
No. Rounding looks at the digit after the cutoff and rounds up or down to the nearest value. Truncating simply cuts off everything after the cutoff regardless of its value. Truncating 2.99 to one decimal gives 2.9. Rounding gives 3.0.
Sources and evidence
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