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Minimum spanning tree calculator

The cheapest way to connect every node of a weighted graph with no cycles — the classic problem behind laying cable, roads or pipes. List the edges as “A B weight” and Kruskal's algorithm finds the minimum spanning tree, its total weight, and draws it, highlighting the chosen edges.

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Open Minimum spanning tree calculator and you get an answer straight away, with no account to create. You will find it under Discrete maths & graphs, with Find minimum and maximum and Bitwise Calculator for the neighbouring cases.

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 Minimum spanning tree calculator do?

The cheapest way to connect every node of a weighted graph with no cycles — the classic problem behind laying cable, roads or pipes. List the edges as “A B weight” and Kruskal's algorithm finds the minimum spanning tree, its total weight, and draws it, highlighting the chosen edges.

What does a concrete case look like?

A–B 1, B–C 2, A–C 3 → A–B–C, Σ = 3 — 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.

How is Minimum spanning tree calculator different from Find minimum and maximum?

They sit next to each other but answer different questions. Find minimum and maximum: paste a list of numbers and get the smallest, the largest, the range between them, and how many values there are. Handles negatives and decimals. Pick whichever matches what you're starting from — both are free.

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 →
ExplainerMinus Seventeen Modulo Five Has Two Different Answers17 mod 5 is 2 everywhere. −17 mod 5 is −2 in JavaScript, C and Java, and 3 in Python, Ruby and a spreadsheet. Both are right, and the difference is a real bug.ExplainerThe Pigeonhole Principle Proves a Thing Exists Without Finding ItTen items in three containers force four into one of them. 367 people force a shared birthday. Neither statement tells you which container or which pair.ExplainerA Cone Is Exactly One Third of Its CylinderRadius 5, height 10: the cone holds 261.8 and the cylinder around it holds 785.4. The ratio is exactly a third, and it holds for any base shape at all.ExplainerOne Formula That Is Also a Rectangle and Also a TriangleParallel sides of 8 and 5 with a height of 4 give an area of 26 — the average width times the height. Make the two sides equal and it is a rectangle; shrink one to nothing and it is a triangle.ExplainerTwice as Wide Holds Four Times as Much; Twice as Tall Holds TwiceA cylinder of radius 5 and height 10 holds 785.4 units of volume. Double the radius and it holds 3,141.6; double the height instead and it holds 1,570.8.ExplainerForty Out and Sixty Back Averages Forty-EightThe harmonic mean of 40 and 60 is 48, not 50, because the slower leg takes longer and therefore counts for more. For 1, 2 and 4 it is 1.714 against an arithmetic mean of 2.33.