Math & Growth

Doubling Time Calculator

Calculate the exact time needed for an investment or population to double at a constant growth rate.

Growth

Doubling Time Calculator

Determine how many periods it takes for a quantity to double under constant exponential growth.

Doubling Time
10.24 periods
Rule of 72 Approximation 10.29 periods
Rule of 70 Approximation 10 periods
Time to Reach Target 23.79 periods

Growth Milestones

Projected value over progressive doubling intervals

Milestone Estimated Periods Projected Value
Initial (1x) 0 periods 1.000
2x 10.2 periods 2.000
4x 20.5 periods 4.000
8x 30.7 periods 8.000
16x 41 periods 16.000
32x 51.2 periods 32.000

Doubling Time Calculator & Growth Guide

The doubling time is the characteristic period of time required for a quantity to double in size or value, assuming constant exponential growth.

Mathematical Formulas

1. Exact Formula

Given a constant growth rate r per period (expressed as a decimal, e.g. 5% = 0.05):

Doubling Time (T) = ln(2) / ln(1 + r)

2. Rule of 72 Approximation

A mental math shortcut frequently used in finance:

T ≈ 72 / Rate (%)

For instance, an investment compounding at 8% doubles in approximately 72 / 8 = 9 years.

3. Rule of 70 Approximation

Often preferred in population biology and economics for lower growth rates:

T ≈ 70 / Rate (%)

4. Time to Reach an Arbitrary Multiple / Target

To grow from initial amount A₀ to target amount A:

Time to Target (T) = ln(A / A₀) / ln(1 + r)