# Exponential Growth Calculator

URL: https://speedycalculator.com/calculators/math/exponential-growth/
Last updated: 2026-10-25

> The exponential growth calculator projects a quantity that grows or decays by a fixed percentage each period. It also gives the doubling time or half-life for the rate you enter.

## Inputs

- Initial value
- Growth rate per period (%)
- Number of periods

## Results

- Final value
- Doubling time (or half-life)

## Formula

```
x(t) = x₀ × (1 + r)^t
```

## Explanation

Populations, investments and viral spread often grow exponentially at first. Decay uses a negative rate.

### How to use the Exponential Growth Calculator

- **Initial value**
- **Growth rate per period**
- **Number of periods**
- Want to work backwards? Type a value into **Final value** and **Number of periods** is calculated for you.

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Multiply the starting value by one plus the rate, raised to the number of periods.

### Inputs explained

FieldWhat to enterInitial valueA numberGrowth rate per periodIn %Number of periodsA number

### What each result means

- **Final value** = [Initial value] × (1 + [Growth rate per period]÷100)^[Number of periods]
- **Doubling time (or half-life)** = abs(ln(2) ÷ ln(1 + [Growth rate per period]÷100))

### Example values

How the main result changes when **Number of periods** changes and everything else stays at the example values above:

Number of periodsFinal value51,402.55177.51,661.0333101,967.151412.52,329.6851152,759.0315203,869.6845

## Worked example

Inputs — Initial value: 1,000; Growth rate per period: 7 %; Number of periods: 10.

Results — **Final value = 1,967.1514**; Doubling time (or half-life) = 10.245 periods.

## FAQ

**How do I model decay?**
Use a negative rate, such as −5%.

**What is the difference from linear growth?**
Linear growth adds a fixed amount; exponential growth multiplies by a fixed factor.

**What formula does the Exponential Growth Calculator use?**
x(t) = x₀ × (1 + r)^t.

**Can I work backwards from the result?**
Yes. Type the result you want into Final value and the calculator finds the matching number of periods.