How this calculator works
Two positive observations determine a continuous log growth rate. Time zero is the initial observation, and every entered time uses one consistent unit. The fitted model assumes the same proportional rate continues; it does not account for capacity limits, seasonality or random variation. A negative rate gives decay. Reversing the formula can find an initial value or a future target time.
Formula
y(t) = y0 exp(kt); k = ln(y1/y0)/Δt; t = ln(target/y0)/k; y0 = y(t)exp(-kt); doubling or halving time = ln(2)/|k|.
Worked example
A series rising from 100 to 200 in 10 days has k = ln(2)/10 per day. The model predicts 400 at day 20 and a 10-day doubling time.
Advertisement
Frequently asked questions
Is k the same as a percent change?
No. The effective change over one time unit is exp(k)-1.
Can I fit negative or zero observations?
No. This positive exponential model requires strictly positive values.
How reliable is a distant forecast?
It can be very sensitive to small rate errors. Check whether a constant proportional trend remains plausible.