# Doubling Time Calculator

URL: https://speedycalculator.com/calculators/math/doubling-time/
Last updated: 2026-10-30

> The doubling time calculator works out how many periods it takes for a quantity growing at a constant percentage rate to double, compares it with the rule of 72, and shows when it would triple.

## Inputs

- Increase per period (%)
- Initial amount (optional)

## Results

- Doubling time
- Rule of 72 estimate
- Tripling time
- Amount after doubling
- Growth factor after 10 periods

## Formula

```
Doubling time = ln 2 ÷ ln(1 + r/100)
Rule of 72 estimate ≈ 72 ÷ r
```

## Explanation

Anything that grows by a fixed percentage each period – savings, a bacterial culture, a city's population or prices under inflation – doubles in a fixed number of periods. Knowing the doubling time turns an abstract rate such as 7% a year into something you can picture: money doubling roughly every ten years.

### How to use the Doubling Time Calculator

- **Increase per period**
- **Initial amount (optional)**
- Every result field is editable: type into **Doubling time** and **Increase per period** plus every other field update to match.

Results update as you type, and everything is calculated in your browser.

### How it works

With growth rate r per period, after t periods the amount is x₀(1 + r)ᵗ. Setting that equal to 2x₀ and taking logarithms gives t = ln 2 / ln(1 + r). The rule of 72 is a quick mental shortcut that is accurate for rates between about 4% and 12%.

### Inputs explained

FieldWhat to enterIncrease per periodIn %Initial amount (optional)A number

### What each result means

- **Doubling time** = ln(2)÷ln(1 + [Increase per period]÷100)
- **Rule of 72 estimate** = 72÷[Increase per period]
- **Tripling time** = ln(3)÷ln(1 + [Increase per period]÷100)
- **Amount after doubling** = 2×[Initial amount (optional)]
- **Growth factor after 10 periods** = (1 + [Increase per period]÷100)^10

### Example values

How the main result changes when **Increase per period** changes and everything else stays at the example values above:

Increase per period (%)Doubling time (periods)3.520.14885.2513.5464710.24488.758.263410.56.9422145.2901

## Worked example

Inputs — Increase per period: 7 %; Initial amount (optional): 1,000.

Results — **Doubling time = 10.2448 periods**; Rule of 72 estimate = 10.286 periods; Tripling time = 16.2376 periods; Amount after doubling = 2,000; Growth factor after 10 periods = 1.9672 ×.

## Key terms

- **Doubling time**: The time needed for a quantity growing exponentially to double.
- **Rule of 72**: The approximation t ≈ 72 / r for a percentage growth rate r.

## FAQ

**What is the rule of 72?**
Divide 72 by the percentage growth rate to estimate the doubling time. At 8% a year, money doubles in about 72 ÷ 8 = 9 years.

**Does the initial amount change the doubling time?**
No. Doubling time depends only on the growth rate; the starting amount just sets the scale.

**What happens with a negative rate?**
The quantity shrinks, and the result becomes a negative "doubling time" – its magnitude is exactly the time to halve (the half-life).

**Which period does the result use?**
The same period as the rate – a monthly rate gives a doubling time in months.


## Sources

- [OpenStax – College Algebra 2e](https://openstax.org/details/books/college-algebra-2e)
- [Wolfram MathWorld – Doubling time](https://mathworld.wolfram.com/DoublingTime.html)