How this calculator works
Continuous growth applies an instantaneous rate through e^(rt). Discrete growth applies a percentage change once per period. Enter the length of one rate period so time units stay consistent; an annual rate needs a one-year period. Negative rates model decay. Values must stay positive, and recovering time requires a non-zero rate. Months and years follow the engine's fixed duration conversions rather than calendar dates.
Formula
Continuous: X = X0 e^(r t/P). Discrete: X = X0 (1+r)^(t/P). Here r is a fraction and P is the rate period in the same units as t.
Worked example
At a continuous rate ln(2), about 69.314718% per day, 100 becomes 200 after one day. A discrete rate of 10% per year turns 100 into 121 after two years.
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Frequently asked questions
Are continuous and discrete rates interchangeable?
No. A continuous rate r has a per-period multiplier e^r. A discrete rate r has multiplier 1+r.
Can this calculate decay?
Yes. Enter a negative continuous rate or a discrete rate between -100% and zero.
What does the main time result measure?
The scalar time result is in seconds, the engine base unit. The elapsed-time readout also offers hours, days and years.