# Doubling Time Calculator

Calculate how long it takes for a value to double at any growth rate. Uses the exact formula, Rule of 70, and Rule of 72. Free online doubling time tool.

## What this calculates

Find out how many periods it takes for a quantity to double at a given growth rate. This calculator gives you the exact result alongside the popular Rule of 70 and Rule of 72 approximations.

## Inputs

- **Growth Rate (%)** — The growth rate per period as a percentage. Must be greater than zero.
- **Compounding** — options: Continuous, Discrete (per period) — Choose continuous or discrete compounding.

## Outputs

- **Exact Doubling Time** — The precise doubling time using the exact formula.
- **Rule of 70 Estimate** — Quick approximation: 70 / growth rate.
- **Rule of 72 Estimate** — Quick approximation: 72 / growth rate.
- **Formula Used** — formatted as text — The exact formula applied for the calculation.

## Details

Doubling time tells you how long exponential growth takes to double a value. Whether you are tracking population, investments, bacteria, or inflation, the concept is the same.

**Exact Formulas:**

For continuous compounding:
t = ln(2) / r

For discrete compounding (once per period):
t = ln(2) / ln(1 + r)

Where r is the growth rate as a decimal (e.g., 7% = 0.07) and ln is the natural logarithm.

**The Rule of 70:**

A quick mental shortcut: Doubling Time is about 70 / (growth rate in percent). At 7% growth, something doubles in roughly 70 / 7 = 10 periods. This works best for rates between 2% and 10%.

**The Rule of 72:**

Similar to the Rule of 70 but uses 72 instead. It is slightly less accurate overall but easier to compute mentally because 72 has more factors (divisible by 2, 3, 4, 6, 8, 9, 12). At 6% growth: 72 / 6 = 12 periods.

**Real-World Examples:**

- A savings account at 3% interest doubles in about 23.4 years
- A population growing at 2% per year doubles in about 35 years
- An investment earning 10% annually doubles in roughly 7.3 years

## Frequently Asked Questions

**Q: What is the difference between the Rule of 70 and Rule of 72?**

A: Both are quick approximations for doubling time. The Rule of 70 (70 / rate) is more accurate for continuous compounding. The Rule of 72 (72 / rate) is more popular in finance because 72 is evenly divisible by 2, 3, 4, 6, 8, and 12, making mental math easier. The difference between them is small, typically less than 3%.

**Q: Does the doubling time formula work for decay or shrinkage?**

A: Not directly. Doubling time applies to growth (positive rates). For decay, you would calculate the half-life instead, using t = ln(2) / |r| where r is the magnitude of the decay rate. The math is the same, but the interpretation is that the quantity halves rather than doubles.

**Q: How accurate is the Rule of 70?**

A: The Rule of 70 is most accurate for growth rates between about 2% and 10%, where it is typically off by less than 1-2%. At very high rates (above 20%), the approximation becomes significantly less reliable, and you should use the exact formula ln(2) / ln(1 + r) instead.

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Source: https://vastcalc.com/calculators/math/doubling-time
Category: Math
Last updated: 2026-04-08