Power Set & Subsets Calculator
Count every subset of a finite set: the power set has 2^n members, with 2^n−1 proper and 2^n−1 non-empty subsets.
Subsets of a set with 4 elements
- 1
Each element has 2 choices (in or out)
2^4 = 16Each of the n elements is independently included or excluded. - 2
Power set size = 2ⁿ
2^4 = 16
How does this calculator work?
A set with n elements has 2^n subsets in total, since each element is either in or out of a subset. Of these, 2^n − 1 are proper subsets (excluding the set itself) and 2^n − 1 are non-empty subsets (excluding the empty set). Subsets of size k number C(n, k).
Formula
How this is calculated
Enter n, the number of elements in your set (a non-negative integer). The power set is the collection of all possible subsets, including the empty set and the set itself. Each element can either be in or out of a given subset, so there are 2 choices per element and 2^n distinct subsets in total.
A proper subset is any subset that is not equal to the original set, so we subtract 1 to exclude the full set: 2^n − 1. Likewise, a non-empty subset excludes the empty set, also giving 2^n − 1. The number of subsets containing exactly k elements is the binomial coefficient C(n, k), and these sum to 2^n across all k.
Growth is exponential: adding a single element doubles the count. The chart plots 2^k for k = 0..n to show this doubling. For very large n the totals exceed standard number precision, so results are most meaningful for modest n; n must be a whole number and cannot be negative.
Frequently asked questions
Exactly 2^n, because each element is independently either included or excluded from a subset.
A proper subset excludes the set itself (2^n − 1); a non-empty subset excludes the empty set (also 2^n − 1). Both happen to equal 2^n − 1.
Yes. The power set contains both the empty set and the original set, which is why the total is 2^n rather than 2^n − 2.
Also known as
TG we-Calculate Editorial Team. (2026). Power Set & Subsets Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/subsets-power-set-calculator
TG we-Calculate Editorial Team. "Power Set & Subsets Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/subsets-power-set-calculator.
TG we-Calculate Editorial Team, "Power Set & Subsets Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/subsets-power-set-calculator
@misc{wecalculate_subsets_power_set_calculator, title = {Power Set & Subsets Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/subsets-power-set-calculator}}, year = {2026}, note = {TG we-Calculate} }
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