The radiometer equation made interactive. Pick a transmitter, a distance, and a telescope, and the tool tells you whether the signal is detectable. Use it to answer the symmetric Fermi question: could a civilisation around Omega Centauri hear us?
For a steady signal of bandwidth B_sig observed by a receiver with effective area A_eff, system temperature T_sys, and integration time τ, the minimum detectable flux density (in W/m²/Hz) at signal-to-noise ratio SNR is
S_min(per Hz) = SNR · k_B · T_sys / A_eff · √(B_obs / (n_pol · τ))
where k_B is Boltzmann's constant, n_pol = 2 polarisations, and B_obs is the matched filter bandwidth (≈ B_sig for a narrowband signal). Integrating this across the signal bandwidth and multiplying by the area of a sphere at distance d gives the minimum EIRP:
EIRP_min = S_min(per Hz) · B_sig · 4π d²
The leverage is in the √τ — every quadrupling of integration time gives you 2× sensitivity. Aperture A_eff and T_sys are linear, so the gain from going from MeerKAT to SKA-1 (~50× A_eff) is much larger than the gain from staring for a week instead of an hour.
In December 2025, Breakthrough Listen used MeerKAT to observe the interstellar object 3I/ATLAS less than 24 hours before its closest approach to Earth. They reported a 0.17 W EIRP detection limit — the most sensitive radio-technosignature search ever performed, capable of detecting a transmitter as weak as a typical mobile phone handset at that distance. The published result is the calibration check for this tool: plug in MeerKAT's effective area (~6,300 m²), T_sys (~20 K), a 1 Hz channel, 1 hour integration, and the actual 3I/ATLAS distance (~0.3 AU at closest approach), and you should recover an EIRP_min in the 0.1–0.2 W range.
Now move the distance slider to OC's 17,000 light-year preset. The 4π d² term increases by roughly 18–20 orders of magnitude relative to nearby SETI targets. The minimum detectable EIRP for typical parameters is ~10¹³–10¹⁵ W — meaning a civilisation around OC could only be detected if it were emitting well above Earth's radio leakage levels in narrowband at the right frequency for the right amount of time. Earth's commercial radio leakage (~10⁷ W EIRP at best) is utterly undetectable at OC distance. This is the symmetry argument: our radio silence at OC's distance does not constrain Earth-equivalent civilisations there, only civilisations broadcasting at K-I levels or above.
Interstellar medium dispersion / scattering (NE2001 model), RFI rejection, beam-pattern losses, source acquisition / pointing errors, frequency drift compensation, and the doppler-search penalty for civ-modulated signals. Real Breakthrough Listen sensitivities include a 10× factor over the bare radiometer equation to account for these effects. The headline figure here is the theoretical floor — actual surveys do somewhat worse.
The MTH says civilisations stop emitting in the radio because they're compressed into ergospheres (see Tool 4 and Tool 1). This tool quantifies the prior question — could we have heard them if they were still emitting? The answer for OC at typical "leakage" power levels is no, which means radio silence at OC is consistent with both "they're all gone / never were" (Fermi) and "they're there but not emitting at K-II" (MTH or simply civilisational reticence). The two hypotheses are observationally degenerate at OC distance unless we get to SKA-2 sensitivity or better — which the slider lets you check.
HS: "could Voyager's 23 W radio be detected from Alpha Centauri?" (answer: with Arecibo or larger, yes, in narrowband, with a 1-hour stare). Undergrad: derive the radiometer equation by combining the antenna gain, system noise, and SNR threshold; reproduce the Breakthrough Listen MeerKAT 3I/ATLAS limit. Project seed: compare the EIRP sensitivity floor of every major SETI survey from Ozma (1960) to SKA-2 (~2030s) as a single time series.
The first SETI experiment was Frank Drake's Project Ozma (1960), pointing the Green Bank 26-m at Tau Ceti and Epsilon Eridani for 200 hours total. Modern: Breakthrough Listen (2015–present, ~$100M Yuri Milner endowment) is the largest SETI effort to date — surveying ~1 million nearby stars + ~100 nearby galaxies + the galactic plane using GBT, Parkes, MeerKAT, and ATA. SKA-Mid (first light expected ~2028) will offer ~100× the sensitivity of current arrays for narrowband searches.
Wow! Signal 1977: 72-second narrowband signal at 1420.4 MHz from Big Ear; never recurred despite repeated re-observations. BLC1 (Breakthrough Listen Candidate 1, 2020): 982.002 MHz signal from Proxima Centauri direction; subsequently identified as terrestrial RFI. Boyajian's Star / KIC 8462852 ("Tabby's Star", 2015–present): irregular dimming events initially proposed as Dyson-sphere construction; consensus explanation is uneven dust clumps. The all-time absence of confirmed signals over ~60 years of intermittent searches is the "Great Silence" data point that feeds the Fermi paradox.
For a narrowband (~1 Hz) signal from distance d, the minimum detectable EIRP (effective isotropically radiated power) scales as d². Anchors: Arecibo 1974 message at 25 ly (M13): 10¹³ W EIRP. Earth's strongest radars (military planetary radar, ballistic missile defence): ~10¹³ W EIRP. Kardashev Type II beacon: 10²⁶ W could be detected across the entire Milky Way with current technology. The 2025 Garrett et al. analysis (A&ARv 33:5) summarises current Breakthrough-Listen sensitivity limits as a function of distance and EIRP.