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Topological sort calculator

Order the vertices of a directed graph so every arc points forward. Enter directed arcs ("A -> B") and the tool runs Kahn's algorithm with lexicographic tie-breaking and a DFS post-order, returning both valid orderings. If the graph contains a cycle it is not a DAG — the tool detects it and shows the offending cycle.

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Topological sort calculator works straight from this page — free, instant, nothing to install. It sits under Discrete maths & graphs in our catalogue, alongside Bitwise Calculator and Delaunay triangulation generator.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Topological sort calculator do?

Order the vertices of a directed graph so every arc points forward. Enter directed arcs ("A -> B") and the tool runs Kahn's algorithm with lexicographic tie-breaking and a DFS post-order, returning both valid orderings. If the graph contains a cycle it is not a DAG — the tool detects it and shows the offending cycle.

What does a concrete case look like?

A→B, A→C, B→D, C→D → A, B, C, D — the tool shows every step in between, not just the final figure.

When would I actually use this?

Anything modelled as points and connections: a shortest route, a network's capacity, a schedule with dependencies, or a circuit reduced to its logic.

What is the most common mistake?

Assuming a shortest path stays shortest when a weight changes sign. Negative edges break the greedy argument Dijkstra rests on, and the algorithm returns a confident wrong answer rather than an error.

What else is filed next to it?

Bitwise Calculator, Delaunay triangulation generator and Dijkstra shortest path calculator share its section. They are not variants of it — being filed together is not the same as being alike — but that is where to look if this turned out not to be the tool you wanted.

Where do the figures come from?

The algorithms are the textbook ones and their results are exact for the graph you enter. What varies is cost: several of these problems have no known efficient solution, so large inputs are answered by heuristic and the tool says when that is the case.

Further reading

All guides →
ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.