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Power Set Calculator

Work out power set instantly with clear inputs, formula shown and shareable results.

About Power Set Calculator

The power set contains every subset, including the empty set and the whole set. Each element is either in or out of a given subset, so there are 2ⁿ subsets in total.

Formulas

Power set size

|P(A)| = 2^|A|

Subsets of size k

C(n, k)

Worked example

With the default values below, Power Set Calculator returns Size of the power set of 8. Change any input above and every figure here is recalculated in your browser.

Inputs used

Set elements
1, 2, 3
Also count subsets of exactly this sizeaccepts 0–20
2

Results

Size of the power set
8
The subsets
{} {1} {2} {1,2} {3} {1,3} {2,3} {1,2,3}
Elements in the set
3
Subsets of the chosen size
3

Step by step

  1. 1Values used
  2. 2Power set size
  3. 3Subsets of size k
  4. 4Size of the power set= 8
  5. 5The subsets= {} {1} {2} {1,2} {3} {1,3} {2,3} {1,2,3}
  6. 6Elements in the set= 3
  7. 7Subsets of the chosen size= 3

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How many subsets does a 3-element set have?

2³ = 8, of which C(3,2) = 3 have exactly two elements.

Is the empty set a subset of everything?

Yes, vacuously — there is no element of it that fails to be in the other set.

Related Calculators

Power Set Calculator – Calculate Size of the power set