Drake Equation Explorer (Monte Carlo)

What it is for

Frank Drake wrote his equation in 1961 as an agenda for a meeting, not as a measurement: N = R* · fp · ne · fl · fi · fc · L. N is the number of civilisations in our galaxy whose signals we could detect now. The first three factors have since been measured. The last four are still pure guesses.

This tool keeps that difference visible. Each factor takes a single value or a range written as "low - high". The defaults for R*, fp and ne come from published measurements: Milky Way star formation (Robitaille & Whitney 2010; Licquia & Newman 2015), microlensing planet counts (Cassan et al. 2012) and Kepler's habitable-zone rocky planets (Bryson et al. 2021). For fl, fi, fc and L the defaults are wide assumption ranges and are labelled as such.

The tool then draws 100,000 random combinations from the ranges (log-uniform by default, so each factor of ten is equally likely) and reports the median, the 5–95 % range, the share of outcomes with N < 1 and how much each factor contributes to the spread. The same engine runs in the Drake explorer of the Proofline Sim Gallery.

Worked example

With the defaults, the median N is 4.14 civilisations and the central estimate (the product of the geometric means) is 4.27. But 90 % of draws lie between 0.00101 and 17,100, and 40 % give N < 1, which means we would probably be alone. The full possible range runs from 1.26e-7 to 145 million.

The spread table shows why. L alone causes 61.7 % of the variance of log₁₀ N, fl and fi 15.4 % each and fc 6.9 %. The three measured factors together contribute less than 1 %. Better telescopes could narrow R*, fp and ne further, but that would hardly change the answer.

Now set every factor to 1 and L to 10000. All draws give exactly N = 10,000, as the formula says. If you instead assume that life is very rare, with fl 1e-10 to 1e-3 and fi 1e-6 to 0.01, the median falls to 1.27e-7 and 99.4 % of draws give N < 1.

How to read the result

The histogram shows the distribution of N on a logarithmic axis, with N = 1 and the median marked. Share of draws with N < 1 is the chance, under your ranges, that we are the only detectable civilisation. The sensitivity bars split the variance of log₁₀ N between the factors; with independent log-uniform factors the shares are exact up to sampling noise.

Mean N is dominated by a few huge outcomes and is usually far above the median, so the median says more.

Tips and common mistakes

• Write ranges with a spaced dash, 0.001 - 1. A single number fixes the factor.
• Every factor must be above zero, and fractions can be at most 1. ne may exceed 1, and L is in years.
• Sampling of the ranges set to uniform gives far larger medians for wide ranges, because most of a uniform range from 0.001 to 1 lies above 0.1. That is a choice, not a finding.
• Random seed makes runs repeatable; change it to see the sampling noise.

FAQ

Is the answer evidence that aliens exist?

No. The result only restates your assumptions about fl, fi, fc and L, and the tool warns about this on every run.

Why does fp default to 0.5 - 1?

Microlensing surveys find on average at least one bound planet per star. The lower bound leaves room for stars without planets.

What is the central estimate?

The product of the geometric mean of each range, which is close to the median for log-uniform draws.

Can I save a scenario?

In Proofline, add the explorer to the notebook and use variants to compare scenarios side by side.