A Kardashev-II civilisation needs to build something to capture a star's output. This tool computes how much asteroid-belt material that "something" actually requires — and how loud its waste-heat signature would be to a G-HAT-style survey looking for it from light-years away.
Dyson's 1960 Science note pointed out that if you wanted to capture significantly more than the ~10⁻¹⁰ fraction of the Sun's output that hits Earth, the only way (at any technology level) was to put a lot of collector area in orbit. Disassembling Jupiter to do this is a thought experiment, not a serious engineering proposal — the point was that the bookkeeping of stellar energy is straightforward, and that a civilisation that wanted star-scale power would visibly alter the host star's IR spectrum. That last clause is the basis of every megastructure search since.
Captured power P = f · L_☉ where L_☉ = 3.83×10²⁶ W. Local solar flux S(d) = 1361/d² W/m² for d in AU. Required panel area A = P/(S(d)·η). Panel mass = A·ρ. Stefan-Boltzmann tells us how much radiator surface you need to dump the captured energy as waste heat at temperature T_rad: A_rad = P/(σ·ε·T_rad⁴) with ε = 0.9 (greybody approximation). Peak emission wavelength from Wien's displacement law: λ_max = 2.898×10⁻³/T_rad metres.
A 100% swarm at 1 AU with typical panels (η=0.30, ρ=5 kg/m²) needs about 9×10²³ m² of collector — roughly 5×10²⁴ kg of panel material. That's ~15× the mass of Mercury, ~65× the mass of all asteroid belt + Moon combined. Even a 1% swarm needs about half a Moon mass. The standard MTH counter-argument is: if your goal is computation rather than energy capture per se, going to an ergosphere where the gravitational field is the substrate bypasses this mass scaling entirely. See BZ/Kardashev Tool 1: the same Kardashev-II power output can in principle come from an IMBH ergosphere with zero panel material at all (and an entirely different set of problems).
If a civilisation intercepts fraction f of the star's output and re-emits it as waste heat at radiator temperature T_rad, the host star's bolometric luminosity is unchanged (energy is conserved), but the spectrum shifts. The IR excess relative to a bare main-sequence spectrum is essentially f — i.e. if f = 0.10, the star has ~10% IR excess in the band where T_rad peaks. G-HAT's WISE-based survey rules out any K-III civilisation in ~10⁵ galaxies (Wright et al. 2014), and surveys for K-II Dyson swarms have placed limits at f ≳ ~0.1 around individual stars. So a 100% K-II Dyson swarm around a sun-like star within ~1 kpc would already have been ruled out. This is one of the strongest empirical Fermi constraints we have.
The "panel mass" line assumes flat solar collectors. Other architectures (statite light sails, gravitational lenses, mirror swarms feeding central absorbers) shift the bookkeeping; the mass-vs-coverage relation has the same shape but the prefactors change. The waste-heat argument is robust independent of architecture — the only way to avoid the IR signature is to either not actually capture the energy, or to engineer ways to do useful work that leak less waste heat than thermodynamics permits, which is impossible if the work is irreversible (see aestivation calculator).
Dyson 1960 (Science 131:1667, "Search for Artificial Stellar Sources of Infrared Radiation") proposed not a literal solid shell but a swarm of habitats orbiting the Sun, intercepting most of its 3.83×10²⁶ W output. Dyson noted the construction would require ~10²³ kg of material — comparable to the mass of all planetesimals and inner-system asteroids combined. A "complete" Dyson sphere intercepting 100% of L☉ would have radius ~1 AU and area ~2.83×10²³ m². A 10⁻⁴ fractional swarm (intercepting 0.01% of L☉) would only need to be ~10¹⁹ kg — well within the asteroid-belt budget (~3×10²¹ kg total).
Several searches have looked for the infrared excess that a partial Dyson swarm would produce. G-HAT survey (Wright et al. 2014 ApJ 792:26; Griffith et al. 2015) examined ~100,000 galaxies in WISE infrared data, finding no candidates with > 85% Type-III re-radiation. Carrigan 2009 examined IRAS individual-star data with similar null results. "Project Hephaistos II" (Suazo et al. 2024, MNRAS 531:695) reported 7 candidate M-dwarfs with anomalous IR excess from Gaia + 2MASS + WISE crossmatching — likely circumstellar dust but not yet conclusively excluded as partial swarms.
Inner Solar System material budget: asteroid belt ~3×10²¹ kg; Vesta + Ceres alone ~1.2×10²¹ kg; Mercury (whole) 3.3×10²³ kg; Earth (whole) 6×10²⁴ kg; Sun's metal content ~2×10²⁸ kg (most locked in stellar interior). A 10⁻⁴ Dyson swarm at ~10¹⁹ kg is achievable from asteroid disassembly; a 10⁻² swarm (~10²¹ kg) requires Vesta+Ceres-scale mining; a "full" Dyson at ~10²⁴ kg would require disassembling Mercury or a substantial fraction of Earth. The Vera Rubin LSST (first light 2026) will catalog the asteroid belt at ~mag 24, providing the most complete inventory of Solar System material yet.