Drake Equation Calculator Formula

Understand the math behind the drake equation calculator. Each variable explained with a worked example.

Use the Drake Equation Calculator

Formulas Used

Detectable Civilisations (N)

n_civilisations = r_star * f_planet * n_earth * f_life * f_intel * f_comm * l_years

Variables

VariableDescriptionDefault
r_starStar Formation Rate (R*)(/yr)1.5
f_planetFraction with Planets (fp)1
n_earthHabitable Planets per Star (ne)0.2
f_lifeFraction Developing Life (fl)0.13
f_intelFraction with Intelligence (fi)0.01
f_commFraction Communicating (fc)0.01
l_yearsCivilisation Lifetime (L)(yr)10000

How It Works

The Drake Equation

N = R* × fp × ne × fl × fi × fc × L

  • R* = rate of suitable star formation (stars/year)
  • fp = fraction with planetary systems
  • ne = habitable planets per system
  • fl = fraction where life develops
  • fi = fraction developing intelligence
  • fc = fraction developing detectable technology
  • L = years a civilisation remains detectable

    • Formulated by Frank Drake in 1961, this is a framework for thinking about extraterrestrial intelligence, not a precise prediction. Estimates of N range from less than 1 to millions.

    Worked Example

    Moderate estimates for each parameter.

    r_star = 1.5f_planet = 1n_earth = 0.2f_life = 0.13f_intel = 0.01f_comm = 0.01l_years = 10000
    1. 01N = 1.5 × 1.0 × 0.2 × 0.13 × 0.01 × 0.01 × 10000
    2. 02= 1.5 × 0.2 × 0.13 × 0.01 × 0.01 × 10000
    3. 03= 1.5 × 0.2 × 0.13 × 1 = 0.039
    4. 04N ≈ 0.039 (suggests we may be alone in the Galaxy with these values)
    5. 05Adjusting L to 1 000 000 years gives N ≈ 3.9

    Ready to run the numbers?

    Open Drake Equation Calculator