Exponential Growth Calculator
Project how a quantity grows or shrinks at a steady percentage rate. Enter the starting value, the rate per period and the number of periods to get the final value, the total change, and the doubling time — or the half-life if the rate is negative.
- Total change
- 628.8946
- Total percent change
- 62.89%
- Growth factor per period
- 1.05 ×
- Doubling time
- 14.2067 periods
- Half-life
- —
Value period by period
| Period | Value | Change in period |
|---|
Saved setups
Save a set of inputs you reuse — your usual rate, your loan, your room sizes — and load it back in one tap.
Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Enter the starting value.
- Enter the growth rate per period as a percentage; use a negative number for decay.
- Enter the number of periods, in the same unit of time as the rate.
- Choose per-period or continuous growth and read the final value. The table lists every period.
Worked examples
1,000 growing 5% per period for 10 periods
- Final value
- 1,628.8946
- Total change
- 628.8946
- Total percent change
- 62.89%
- Doubling time
- 14.2067 periods
500 decaying 3% a year for 20 years
- Final value
- 271.8972
- Half-life
- 22.7566 periods
1,000 growing continuously at 2% for 35 periods
- Final value
- 2,013.7527
- Doubling time
- 34.6574 periods
Doubling time and the rule of 70
A quick estimate of doubling time is 70 divided by the percentage rate. At 5% that gives 14 periods; the exact figure is 14.21. The shortcut works well for rates up to about 10%.
For decay the same idea gives the half-life: something losing 3% a year halves in about 22.8 years.
Getting the inputs right
The rate and the number of periods must use the same unit — a monthly rate with a count of months, a yearly rate with years.
Per-period and continuous growth are close but not equal. A continuous rate of 5% is the same as 5.127% applied once per period, because e^0.05 = 1.05127.
Questions people ask
What is 1,000 growing at 5% for 10 periods?
1,628.89. That is 1,000 × 1.05¹⁰, a total increase of 62.89%.
How long does it take to double at 5% growth?
About 14.21 periods: ln 2 ÷ ln 1.05.
What is the difference between linear and exponential growth?
Linear growth adds the same amount each period; exponential growth multiplies by the same factor. Starting from 100, +10 per period reaches 200 after 10 periods, while +10% per period reaches 259.37.