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소개

Doubling Time Calculator — Doubling time from growth rate: ln(2)/r. Enter Growth rate (r, per unit time) to get an instant, accurate result.

공식

For exponential growth N(t) = N₀e^(rt), the doubling time is t₂ = ln(2) / r — the time required for the population to reach exactly twice its starting size.

단계별 안내

Enter the Growth rate (r, per unit time).
Click Calculate to see your result instantly.

실제 예시

Example: With Growth rate (r, per unit time) = 0.1, the Doubling Time Calculator gives Doubling Time: 6.9315.

자주 묻는 질문

Where does ln(2) come from?

Setting N(t)/N₀ = 2 in the exponential growth equation and solving for t gives t = ln(2)/r, since ln(2) ≈ 0.693 is the natural log of the doubling factor.

What units is the growth rate r in?

r should be expressed per the same time unit you want the doubling time reported in — e.g. a rate per hour gives a doubling time in hours.

What inputs does the Doubling Time Calculator need?

You'll need to provide: Growth rate (r, per unit time). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.

How accurate is the Doubling Time Calculator?

The Doubling Time Calculator applies the formula exactly as calculated — For exponential growth N(t) = N₀e^(rt), the doubling time is t₂ = ln(2) / r — the time required for the population to reach exactly twice its starting size. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.

Is the Doubling Time Calculator free to use?

Yes, the Doubling Time Calculator is completely free, requires no signup, and runs instantly in your browser.