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Doubling Time Calculator

Calculate doubling time online — free, step by step. From a growth rate get the time to double, exactly and via the rule of 70.

Quick answer
How do you calculate doubling time?
Doubling time is how long a quantity takes to double at a constant growth rate. Exactly: ln(2) ÷ ln(1 + r), where r is the growth rate per period. Quick estimate with the rule of 70: 70 ÷ percent rate. Example: at 7% growth ≈ 10.24 periods (rule of 70: 70 ÷ 7 = 10).
The tool

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Comma or dot as decimal separator, negative values allowed.
Step-by-step
Press Calculate to see every step.
HowTo

Doubling Time Calculator — step-by-step

How do you calculate doubling time?
  1. 1
    Step 1 of 4

    Set the growth rate per period

    Give the constant growth rate per period in percent. Example: 7% per year.

  2. 2
    Step 2 of 4

    Plug into the exact formula

    Doubling time = ln(2) ÷ ln(1 + r), with r = 7% = 0.07.

  3. 3
    Step 3 of 4

    Compute

    ln(2) ≈ 0.6931, ln(1.07) ≈ 0.0677 → 0.6931 ÷ 0.0677 ≈ 10.24 periods.

  4. 4
    Step 4 of 4

    Estimate with the rule of 70

    70 ÷ 7 = 10. The rule of thumb is close to the exact value.

Examples

Doubling Time Calculator — examples

Worked examples with full working
r = 7%
ln(2) ÷ ln(1.07)
≈ 10.24
r = 10%
ln(2) ÷ ln(1.10)
≈ 7.27
r = 2%
ln(2) ÷ ln(1.02)
≈ 35
r = 1%
ln(2) ÷ ln(1.01)
≈ 69.7
r = 5%
ln(2) ÷ ln(1.05)
≈ 14.2
r = 70%
70 ÷ 70 (rule)
≈ 1
Theory

What is doubling time?

Doubling time tells you how long, under exponential growth at a constant rate, a quantity takes to double. From (1 + r)ᵗ = 2, taking logarithms gives the exact formula t = ln(2) ÷ ln(1 + r). Because ln(1 + r) ≈ r for small r and ln(2) ≈ 0.693, you get the well-known rule of thumb: doubling time ≈ 70 ÷ percent rate (the rule of 70; 72 is often easier to divide). Doubling time is central to compound interest, population growth, inflation and exponential processes of all kinds. Its counterpart for decay is the half-life.

Pitfalls

Common mistakes

Rate not converted to decimal

In ln(1 + r), r must be a decimal (7% = 0.07), not 7.

Rule of 70 for large rates

The rule is only accurate for small rates; at 70% it deviates a lot.

Linear instead of exponential growth

The formula only holds for a constant percentage (exponential) growth rate.
FAQ

Frequently asked questions

Glossary

Glossary — key terms explained simply

Whole (base)
The reference value that equals 100%.
Part (value)
The amount that belongs to a percentage.
Rate
The percentage (per hundred).
Difference
The result of a subtraction (new − old).
Relative
Expressed against a reference, dimensionless.
Absolute
In the unit of the quantity, without reference.
Factor
Number you multiply by (e.g. 1.25 for +25%).
Percentage point
Absolute difference between two percentages.