The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)-traceable and self-calibrated method for measuring a microwave electric field strength based on electromagnetically induced absorption (EIA) in cold Rydberg atoms. Comparing with the method of electromagnetically induced transparency, we show that the equivalence relation between microwave Rabi frequency and Autler-Townes splitting is more valid and is even more robust against the experimental parameters in the EIAs linear region. Furthermore, a narrower linewidth of cold Rydberg EIA enables us to realize a direct SI-traceable microwave-electric-field measurement as small as $sim$100 $mumathrm{!V} mathrm{cm}^{!-!1}$.
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