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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 $\\eta$ 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 $\\eta_{2026} = 10^{12}$ 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. 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