How much thinking can a civilisation do? Kardashev's (1964) typology ranks civilisations by total power: planetary (Type I, ~10^16 W), stellar (Type II, ~10^26 W), galactic (Type III). This paper builds an analogous Cognitive Kardashev Scale: how much sustained AI-grade computation each tier could support. Four ingredients enter the calculation: total power P (watts), the share f of it devoted to cognition, the efficiency $η$ at which energy becomes compute (operations per joule), and the brain's own processing rate $C_{\mathrm{brain}}$ as a reference unit. Anchoring on 2024-2026 hardware (El Capitan, NVIDIA Blackwell, Vera Rubin) gives $η_{2026} = 10^{12}$ FLOP/J. Contemporary humanity sits at $K \approx 0.73$, three-quarters of the way to Type I. At Type I and $f = 1\%$, available compute is, within an order of magnitude, one personal AI's worth of cognition per human inhabitant; at Type II it is essentially incomprehensible. Three trajectories for frontier compute through 2035 are reported as conditional projections, not predictions. Whether the long-run binding constraint is energy or efficiency depends on engineering choices not yet made; the political economy of who has access may matter more than either.