📐 Subset Calculator
Calculate subsets of a set
Set with n elements
Enter the number of elements in your set (0-20)
How to Use This Calculator
Enter Set Size
Type the number of elements (n) in your set. For example, a set with 3 elements.
Click Calculate
Press "Calculate Subsets" to find all subset information.
Review Results
See total subsets, proper subsets, and breakdown by size.
Formula
Total subsets = 2n
Proper subsets = 2n - 1
Subsets of size k: C(n,k) = n!/(k!(n-k)!)
Example 1: Set with 3 elements {a, b, c}
Subsets: ∅, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}
Total: 2³ = 8 subsets
Proper: 8 - 1 = 7 subsets (excluding the set itself)
Example 2: Set with 4 elements
Total subsets: 2⁴ = 16
By size: 1 of size 0, 4 of size 1, 6 of size 2, 4 of size 3, 1 of size 4
This follows Pascal's Triangle!
About Subset Calculator
The Subset Calculator calculates the number of all possible subsets of a set with n elements. A subset is a collection of elements from the original set, including the empty set and the set itself. This is fundamental in set theory and combinatorics.
When to Use This Calculator
- Set Theory: Calculate power set size
- Combinatorics: Count all possible combinations
- Problem Solving: Count subsets in optimization problems
- Computer Science: Analyze algorithm complexity
Why Use Our Calculator?
- ✅ Total & Proper: Shows both counts
- ✅ Breakdown by Size: See subsets of each size
- ✅ Quick Calculation: Instant results
- ✅ Free Tool: No registration
Key Concepts
- Every set has 2n total subsets (power set size)
- Proper subsets exclude the set itself: 2n - 1
- Number of subsets of size k is C(n,k)
- The empty set ∅ is always a subset
Tips
- Remember: every element can be "in" or "out" of each subset
- That's why total = 2n
- Subset counts follow Pascal's Triangle
Frequently Asked Questions
What is a subset?
A subset contains zero or more elements from the original set. The empty set and the set itself are both subsets.
What is a proper subset?
proper subset is any subset except the original set itself. For a set of 3 elements, there are 7 proper subsets.
Why is the number 2n?
Each element can either be included or excluded from a subset. With n elements, there are 2n possible combinations.