📐 Power Set Calculator
Calculate the power set of a set
Set with n elements
Enter the number of elements in your set (0-10 for full display)
How to Use This Calculator
Enter Set Size
Type the number of elements (n) in your set. For 0-5 elements, you'll see all subsets listed.
Click Calculate
See the power set size and all subsets if n ≤ 5.
Review Results
See the complete power set size and elements.
Formula
Power Set Size = 2n
Example 1: Set A = {a, b}
Power Set P(A) = {∅, {a}, {b}, {a,b}}
Size: 2² = 4 subsets
Example 2: Set B = {a, b, c}
Power Set P(B) = {∅, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}}
Size: 2³ = 8 subsets
About Power Set Calculator
The Power Set Calculator calculates the power set of a given set. The power set is the set of all possible subsets, including the empty set and the original set itself. The power set is denoted P(A) or 2A, and its size is always 2n where n is the size of the original set.
When to Use This Calculator
- Set Theory: Calculate power set size
- Combinatorics: Count all possible combinations
- Computer Science: Analyze subset enumeration
Why Use Our Calculator?
- ✅ Shows Size: Power set size instantly
- ✅ Lists Subsets: For small sets (n ≤ 5)
- ✅ Educational: Learn power set concept
- ✅ Free Tool: No registration
Key Properties
- Power set always includes empty set ∅
- Power set always includes the original set
- Size grows exponentially: 2n
- Power set is important in topology and measure theory
Tips
- For display purposes, n limited to 10
- Size calculation works for any n
- Power set is always larger than original set
Frequently Asked Questions
What is a power set?
The power set is the set of all possible subsets of a given set, including the empty set and the set itself.
Why is the size 2n?
Each element can be either included or excluded from a subset. With n elements, there are 2^n possible combinations.
Does the power set include the original set?
Yes! Every set is a subset of itself, so the power set always includes the original set.