Free · Exponential models
Compound Growth Doubling Periods
Convert a constant positive percentage increase per period to doubling time, or solve the required growth rate, with a bounded compounding chart.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
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Formula and method
An increase of 100 percent per period doubles a positive quantity in one period.
t=ln(2)/ln(1+r/100); r=100*(2^(1/t)-1); A(n)=A(0)*(1+r/100)^n.
Worked example
Enter these known values and leave the other values blank.
- Increase
- 100 % per period
- Doubling time
- 1 periods
Assumptions and limitations
- The increase is a constant percentage per period. The numerical doubling time solves (1+r/100)^t=2 and is measured in those same periods. It is a discrete compounding rate, not a continuous-rate percentage.
- A finite future doubling time requires r>0 and t>0. Zero growth never doubles and negative growth describes decay, outside this model. Extreme values can exceed finite numerical resolution.
- The initial amount only scales the chart and does not change the doubling time. Positive amounts double in value; negative amounts double in magnitude; a zero amount stays zero and has no unique observed doubling event.
- The chart is retained only for 1≤t<100000. It samples consecutive integer-spaced periods through the first sample at or beyond fractional t, using five significant digits. The sampling step increases for longer times, with at most 992 points.
Common questions
Does the initial amount change doubling time?
The initial amount only scales the chart and does not change the doubling time. Positive amounts double in value; negative amounts double in magnitude; a zero amount stays zero and has no unique observed doubling event.
Why does the chart stop at a sampled period after the doubling time?
The chart is retained only for 1≤t<100000. It samples consecutive integer-spaced periods through the first sample at or beyond fractional t, using five significant digits. The sampling step increases for longer times, with at most 992 points.
References
- OpenStax: exponential growth models
- NIST DLMF: hyperbolic logarithm identities
- Calculation definition and unit reference
Use log1p-equivalent atanh and expm1-equivalent hyperbolic identities to retain tiny positive growth instead of adding/subtracting nearly equal unit values. Bind exact captured local chart sampling and explicit model domains, preserving original controls, callback sampling intervals, chart conditions and notes.