Hasse Diagram Generator

Build posets and visualize order relationships clearly. Export diagrams and relation tables fast. Make your structure easier to teach.

Calculator Inputs

Enter a set of elements and a strict partial order relation. The tool derives the cover relation and draws the Hasse diagram.

Separate with spaces or commas.
Loads sample data into the form.
One per line. Allowed: a<b, a <= b, or a b.

Example Data Table

A classic example uses divisibility on {1,2,3,6}. Here are the direct (not implied) relations you can paste.

ElementsRelations (direct)Meaning
1, 2, 3, 6 1<2
1<3
2<6
3<6		 Divisibility: a divides b
∅, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} ∅<{1}
∅<{2}
∅<{3}
{1}<{1,2}
{1}<{1,3}
{2}<{1,2}
{2}<{2,3}
{3}<{1,3}
{3}<{2,3}
{1,2}<{1,2,3}
{1,3}<{1,2,3}
{2,3}<{1,2,3}		 Subset order: A ⊂ B
Note: Use plain element tokens (avoid commas inside tokens).

Formula Used

A Hasse diagram represents a finite partially ordered set (poset) using only cover relations.

  • Transitive closure: if a<b and b<c, then a<c is implied.
  • Cover relation: a ≺ b iff a<b and no c satisfies a<c<b.
  • Diagram edges: draw an edge only for covers, upward by level.
This tool computes closure, then filters to covers for a clean diagram.

How to Use

  1. List all elements as unique tokens.
  2. Enter direct relations a<b, one per line.
  3. Press Generate Diagram.
  4. Review covers, levels, and the diagram.
  5. Export CSV for tables or PDF for sharing.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.