Understand the subject
What is a power set?
A power set contains every subset of a finite set, including the empty set and the full set. Each item independently has two membership choices.
Use it for small finite sets when you need to inspect or count all possible subsets.
See the structure
Every item is either out or in
start↙ ↓ ↘A: out/inB: out/inC: out/in2³ = 8
Worked example
Check the rule with a small case
A three-item set has 2³ = 8 subsets, including {} and the full set.
Interpret with care
Choose the right counting model
Generated subsets are capped for readability; the exact count remains valid beyond the display cap.
Use the Permutation & Combination Generator when a small case needs to be inspected rather than only counted.
Quick guide
How to use this calculator
- Enter distinct item labels.
- Read the exact number of subsets.
- Open the generated list to inspect the empty set and subsets of every size.
Calculation method
Give every item two membership choices
Each of n distinct items is either included or excluded, so a finite set has 2^n subsets.
Worked example
Power set of three items
Three items produce eight subsets, including the empty set and the full set.
2³ = 8
Supported inputs
Precision and limits
Discrete domain
Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.
Exact integers
Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.
Generation
Up to 12 distinct labels are accepted and at most 500 subsets are displayed.
