What is the doubling time formula?

The exact formula is T = ln(2) / r, where r is the growth rate as a decimal (e.g., 2% → 0.02). This comes from solving the exponential growth equation P(t) = P0 × e^(rt) for the time when P(t) = 2P0.

What is the Rule of 70?

The Rule of 70 is a mental shortcut: T ≈ 70 / growth_rate_%. It slightly overestimates doubling time compared to the exact formula (which uses ln(2) ≈ 69.315). Both are shown so you can see the difference.

What happens with a zero or negative growth rate?

A growth rate of zero means the population never doubles (infinite doubling time). A negative rate means the population is shrinking — the calculator shows the half-life (time to halve) instead.

What are some real-world doubling time examples?

World population growth of ~1% per year gives a doubling time of about 69 years. E. coli bacteria can double every 20 minutes under ideal conditions. An investment growing at 7% per year doubles in roughly 10 years.

Is this calculator only for biological populations?

No. The same formula applies to anything growing exponentially — bacterial cultures, financial investments, radioactive decay (half-life is the inverse), and more.

Population Doubling Time Calculator

Name: Population Doubling Time Calculator
Availability: InStock
Author: Nham Vu

Enter a growth rate to instantly calculate how long a population takes to double, with a full projection table.

Growth Parameters

Annual Growth Rate (%)

Use a negative value for a shrinking population.

Starting Population (optional)

Quick examples

Exact Doubling Time

T = ln(2) / r

—

years

Rule of 70 Estimate

T ≈ 70 / rate%

—

years

Calculation Breakdown

Population Projection Table

Doubling #	Time Elapsed	Multiplier	Population

Enter a growth rate and click Calculate

Results and projection table will appear here

Summary

Enter a growth rate to instantly calculate how long a population takes to double, with a full projection table.

How it works

Enter the annual growth rate as a percentage (use a negative value for a shrinking population).
The exact doubling time is computed from the exponential model P(t) = P0 × e^(r·t): solving P(t) = 2·P0 gives T = ln(2) / r, where r is the rate as a decimal.
The Rule of 70 approximation (T ≈ 70 / growth_rate_%) is shown alongside so you can compare the shortcut to the exact result.
Optionally enter a starting population to generate a projection table at each doubling interval.

Use cases

Estimate how quickly a bacterial culture doubles during exponential growth.
Project human population growth for geography or economics coursework.
Model investment compound growth and compare to the Rule of 72.
Understand wildlife population dynamics in conservation biology.
Illustrate the power of exponential growth in biology and finance lectures.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu