Enter your set elements as comma-separated values (e.g. 1, 2, 3) and the Subset Calculator generates every possible subset of that set. You'll see the total count of subsets, the number of proper subsets, and a full listing of all subsets including the empty set — up to 10 elements. Also try the Implied Probability Calculator.
Total Subsets (2ⁿ)
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Proper Subsets (2ⁿ − 1)
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Number of Elements (n)
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All Subsets
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A subset is a set whose elements are all contained within another set. If every element of set A also belongs to set B, then A is a subset of B, written A ⊆ B. Every set is a subset of itself, and the empty set ∅ is a subset of every set. See also our Coin Flip Probability Calculator.
A proper subset is a subset that is not equal to the original set — it must contain fewer elements. If A ⊆ B and A ≠ B, then A is a proper subset of B, written A ⊂ B. A set with n elements has 2ⁿ − 1 proper subsets.
The total number of subsets of a set with n elements is 2ⁿ. This includes the empty set and the set itself. For example, a set with 3 elements has 2³ = 8 subsets total.
Yes. The empty set ∅ (also written {}) is considered a subset of every set. Since it contains no elements, there is nothing in it that could violate the subset condition, so it trivially satisfies A ⊆ B for any set B. You might also find our Venn Diagram Generator (3 Sets) useful.
The power set of a set A is the collection of all subsets of A, including the empty set and A itself. If A = {1, 2}, then the power set P(A) = {∅, {1}, {2}, {1, 2}}. The power set of a set with n elements always contains exactly 2ⁿ elements.
An improper subset of a set is the set itself. Every set A is an improper subset of A because A ⊆ A. There is exactly one improper subset for any set — the set itself.
A set with 5 elements has 2⁵ = 32 total subsets and 2⁵ − 1 = 31 proper subsets. The subsets range from the empty set (size 0) up to the full set (size 5), with C(5,k) subsets of each size k.
Yes. You can enter any comma-separated values — numbers, letters, or words — and the calculator will generate all subsets. Elements are treated as distinct labels, so {a, b, c} works just as well as {1, 2, 3}.