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The bond length of a carbon-carbon sp$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$-sp$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ $\sigma $-bond without the perturbing effects of $\pi $-electroninteractionshasbeenestimatedbyhigh-levelabinitiocalculations[CCSD(T)/cc-pVNQwithCBSextrapolation]ontwoprototypicalsystems:a90$^{irc}$-twisted form of butadiene and the tub conformer of cyclooctatetraene. The butadiene system yields a value of 1.4818 \AA, considerably longer than previous estimates. The corresponding bond length in cyclooctatetraene is slightly shorter due to some $\pi $-electron delocalization. Ab initio results for related equilibrium structures of other rotamers/transition states of butadiene along the internal rotation coordinate (C-C bond) will be reported and compared with an experimental potential function.}