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We present a fine-structure entanglement classification under stochastic local operation and classical communication (SLOCC) for multiqubit pure states. To this end, we employ specific algebraic-geometry tools that are SLOCC invariants, secant varieties, to show that for n-qubit systems there are ⌈2^{n}/n+1⌉ entanglement families. By using another invariant, ℓ-multilinear ranks, each family can be further split into a finite number of subfamilies. Not only does this method facilitate the classification of multipartite entanglement but it also turns out to be operationally meaningful as it quantifies entanglement as a resource.