Case 1
- Starting amount
- 1000
- Growth rate per period
- 0.05
- Number of periods
- 10
1,648.721271
Open with these valuesExponential Growth Calculator
Change any value to update the result.
1,648.721271same unit
Final amount: 1,648.721271 same unitExamples
How the result moves
Number of periods → Final amount (same unit)Your current valid inputs, with one value varied across the range.
How the result moves
Held fixed: Starting amount 1,000.00, Growth rate per period 0.0500.
| Number of periods | Final amount |
|---|---|
| 0.000 | 1,000.000000 |
| 5.000 | 1,284.025417 |
| 10.000Your value | 1,648.721271 |
| 15.000 | 2,117.000017 |
| 20.000 | 2,718.281828 |
Continuous growth multiplies the starting amount by e raised to rate times time: 1000 at a rate of 0.05 over 10 periods becomes 1648.72. Enter the rate as a decimal, and use a negative one for decay. This is the continuous model, so it grows a shade faster than yearly compounding.
Worked examples
Case 2
- Starting amount
- 500
- Growth rate per period
- 0.1
- Number of periods
- 5
824.360635
Open with these valuesCase 3
- Starting amount
- 2000
- Growth rate per period
- -0.03
- Number of periods
- 8
1,573.255722
Open with these valuesHow it's calculated
A = P × e^(r × t)
- StepEnter the starting amount in whatever unit you care about.Starting amount=1,000
- StepWrite the rate per period as a decimal — 5 % becomes 0.05.Growth rate per period=0.05
- ResultEnter how many periods run; a negative rate models decay.Growth rate per period=0.05·Number of periods=10→1,648.721271same unit
Reference table
| Start, rate, periods | What it models | Final amount |
|---|---|---|
| 1000, 0.05, 10 | Steady 5 % growth for ten periods | 1648.721271 |
| 500, 0.1, 5 | A brisk 10 % over five | 824.360635 |
| 10000, 0.07, 20 | Twenty periods at 7 % | 40551.999668 |
| 1000, 0, 10 | No growth at all | 1000.000000 |
| 2000, -0.03, 8 | A 3 % decline each period | 1573.255722 |
| 100, -0.5, 3 | Strong decay | 22.313016 |
Questions
How do I calculate exponential growth?
Use A = P × e^(r × t): multiply the starting amount by e, about 2.71828, raised to the rate times the time. A starting 1000 growing continuously at 0.05 for 10 periods becomes about 1648.72.
What is exponential growth?
It is growth by a constant proportion of the current value at every instant, so the amount added keeps getting bigger. That produces the steep, accelerating curve familiar from compound interest, population growth and viral spread.
Should the rate be a percentage or a decimal?
A decimal: 5 % per period is 0.05, and 12 % is 0.12. For decay use a negative rate — −0.03 is a 3 % decline each period.
What is the difference between continuous and discrete growth?
This calculator uses continuous growth, A = P × e^(r × t), where the quantity compounds at every instant. Discrete growth, A = P × (1 + r)^t, compounds once per period. For the same rate the continuous model ends slightly higher — 1648.72 against 1628.89 at 5 % over ten periods.
Can I use this for exponential decay?
Yes. Enter a negative rate and the same formula models decay — radioactive material, a drug clearing the bloodstream, a depreciating value. At −0.5 over 3 periods an initial 100 falls to about 22.31.
How does this relate to doubling time?
They are two views of the same curve. The doubling time is ln 2 ÷ r, so at a rate of 0.07 the amount doubles after 9.9021 periods — feed that back in here and you get exactly twice the start.