What it does
The Drake equation multiplies seven factors to estimate N, the number of civilisations in our galaxy whose signals we could detect now:
N = R* × fp × ne × fl × fi × fc × L
- R*: new stars formed in the galaxy per year
- fp: share of stars that have planets
- ne: planets per planetary system where life could exist
- fl: share of those where life actually starts
- fi: share of life that becomes intelligent
- fc: share of intelligent species that send detectable signals
- L: how many years such a civilisation keeps signalling
Nobody knows most of these, some not even to within a factor of a million. So instead of one number per factor, this page takes a low and a high value for each, draws every factor at random between them many times, and shows the whole distribution of N.
How to use it
- Start from one of three made-up presets (very uncertain, hopeful, cautious), or type your own. They are illustrations for learning, not anyone’s published estimates.
- For each factor type a low and high value. Fractions (fp, fl, fi, fc) must be between 0 and 1; type tiny numbers as 1e-9. Set low = high to fix a factor.
- Random draws and seed: more draws give a smoother histogram; the same seed always gives the same draws.
Each draw is log-uniform: every factor of ten between low and high is equally likely. That suits factors whose order of magnitude is unknown. The page also gives exact values (from the sum of uniform variables on the log scale) next to the Monte Carlo ones, so you can see the random error.
What you get
- The middle estimate (each factor at the middle of its range on a log scale), the median N, the range covering 90 % of draws, the chance N is below 1 and the chance it is at least 1,000.
- A histogram of log₁₀ N, and a table showing each factor’s share of the spread.
- Downloads: the factor table, summary and histogram (CSV), and a report as image, PDF or Word.
Worked example
With the made-up very uncertain preset, 100,000 draws and seed 1, the median is N = 0.0044, and 90 % of draws fall between 1.6 × 10⁻⁷ and 130. The chance of fewer than one civilisation is 79.9 % (exact: 80 %), and the chance of 1,000 or more is 2.11 % (exact: 2.09 %). The mean of log₁₀ N is −2.348 against the exact −2.349. The factor table shows that fl (where life starts, ranging over six factors of ten) causes 42 % of the spread and L 29 %.
Switch to the hopeful preset and the median rises to about 1,000, with N below 1 in only 0.023 % of draws.
Tips
- The middle estimate and the median can differ a lot from the plain average of N, which is dominated by the rare huge draws. That is why the page works on the log scale.
- To see how much a factor matters, fix it (low = high) and watch the spread shrink.
- A wide range on a single factor, such as fl, can make “we are alone” likely even when the other factors look hopeful.
FAQ
Are these real estimates? No. The presets are invented to show how the maths behaves. Use your own ranges, and look up current research for real values.
Why log-uniform? When you do not know whether a factor is 0.001 or 0.1, treating each factor of ten as equally likely is a common, simple choice. A plain uniform range would put almost all draws near the top value.
Is anything sent anywhere? No. Everything runs in your browser.
Where the numbers come from
- The equation: F. Drake (1961), as described in many textbooks. Treating each factor as log-uniform over a range follows the general approach of A. Sandberg, E. Drexler and T. Ord (2018), arXiv:1806.02404 (method only; none of their numbers are used). Exact distribution of a sum of independent uniform variables for log₁₀ N. Formulas only; no tables are copied.
- Checked in the tests against NumPy: the distribution of log₁₀ N by numerical convolution of the seven uniform densities and by a 2-million-draw Monte Carlo, for all three starting presets.
- The three starting presets (very uncertain, hopeful, cautious) are made up for illustration. They are not taken from any published estimate.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.