We develop a first-principles framework for evaluating the fundamental length scales of superconductivity, namely the coherence length ${\xi }_0$ and the magnetic penetration depth ${\lambda }_{\mathrm{L}}$, within superconducting density functional theory. By incorporating finite-momentum Cooper pairs, we formulate a microscopic scheme that enables a consistent and parameter-free determination of ${\xi }_0$, ${\lambda }_{\mathrm{L}}$, and the superconducting transition temperature $T_{\mathrm{c}}$ on the same theoretical footing. Applying the method to representative elemental superconductors, the A15 compound ${\mathrm{V}}_3\mathrm{Si}$, and ${\mathrm{H}}_3\mathrm{S}$ under high pressure, we obtain results in good agreement with available experimental data and reproduce the type-I or type-II classification across all materials studied. The unified access to ${\xi }_0$ and ${\lambda }_{\mathrm{L}}$ further allows us to construct the Uemura plot entirely from first principles, showing that higher-$T_{\mathrm{c}}$ systems are characterized by the simultaneous realization of strong pairing and large phase stiffness. Our results establish a predictive first-principles route to superconducting length scales and provide a microscopic interpretation of empirical correlations in superconductivity.

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• Coherence length
• Penetration depth
• Superconductivity
• Density functional theory
• First-principles calculations
• Landau-Ginzburg theory
• Methods in superconductivity