Drake Equation Explorer

What you are seeing: the Drake equation $N = R_\star \cdot f_p \cdot n_e \cdot f_l \cdot f_i \cdot f_c \cdot L$ visualized as a multiplicative chain of probabilities and a Monte Carlo histogram over their uncertain ranges. Each slider sets the log-range of one factor; 2000 trials draw log-uniformly from those ranges and the histogram shows the distribution of $N$ across 20 decades.

The Carroll-Ostlie reference values give $N \approx 30$ (lots of civilizations); pessimistic intelligence and signal-lifetime factors collapse $N$ below 1. The Fermi paradox is the gap between the optimistic central value and our observed lack of detections.

Figure 1. Drake-equation Monte Carlo: log-uniform sampling over the uncertain factors.

log10 R_star0.18

log10 f_l-0.30

log10 f_i-1.00

log10 L (yr)4.00

WHAT TO TRY

Widen the f_i slider (fraction that become intelligent), the least-known factor: the Monte Carlo histogram of log N smears across many orders of magnitude. The width of your answer is set by your least-constrained factor.
Pull L (civilization lifetime) up: the whole distribution shifts right, since N scales linearly with L. A long-lived civilization is worth more than a generous birth rate.
Compare the point estimate (product of midpoints) against the MC median: they disagree because multiplying log-uniform ranges is not the same as multiplying their centers.