Shortest Path Calculator

Calculator

Graph type

Undirected adds a reverse edge for each entry.

Weight source

Euclidean uses coordinates to compute each edge weight.

Decimals

Controls formatting for distances.

Start node

Node labels can be letters, names, or IDs.

End node

Choose a different node than start.

Options

Skip edges with missing weights

Show Dijkstra step summary

Skipping can disconnect the graph.

Edge list (CSV lines)

Format: from,to,weight. For Euclidean mode, weight is optional (uses coordinates).

Node coordinates (optional)

Format: node,x,y or node,x,y,z. Used for Euclidean weights.

Example data table

From	To	Weight	Note
A	B	7	Edge list weight
A	C	9	Edge list weight
C	F	2	Short shortcut edge
F	E	9	Connects to destination

With the default dataset (undirected), the shortest A → E path is typically A → C → F → E.

Formula used

Dijkstra relaxation: For each edge (u,v) with weight w, update

dist[v] = min(dist[v], dist[u] + w)

This repeats by permanently selecting the unvisited node with the smallest current distance. It requires non-negative weights.

Euclidean weight (optional): If coordinates are provided,

w = √((x2-x1)² + (y2-y1)²) or √((x2-x1)² + (y2-y1)² + (z2-z1)²).

How to use this calculator

Enter your edges as CSV lines: from,to,weight.
Choose Directed if direction matters for your system.
Select Provided weights or Euclidean weights from coordinates.
Set the start and end node labels exactly as written.
Press Calculate Shortest Path to see results above the form.
Use Download CSV or Download PDF from the results panel.

Professional article

1) Shortest path as a physics modeling tool

In applied physics, "shortest" often means "least cumulative cost," not only least distance. A cost can represent travel time, energy, attenuation, pressure drop, or any scalar you can add along a route. This calculator maps that cost onto a weighted graph and returns an optimal route between two nodes.

2) Turning a physical layout into a graph

Model each junction, station, component, or waypoint as a node and each allowed transition as an edge. Examples include lab floor plans, robot waypoint maps, waveguide connections, and transport networks. Your edge list becomes a compact model you can revise when the setup changes.

3) Meaning of edge weights and units

Edge weights are the quantities that get summed along a path. If you use meters, the result is in meters; if you use seconds, it becomes minimum travel time. Keep units consistent and non-negative so the output remains physically meaningful and numerically stable.

4) Coordinate-driven distances for geometry-based problems

With coordinates, Euclidean mode computes edge weights from node positions in 2D or 3D. It works well for map-like layouts where distance approximates time or traversal cost. Coordinates do not create connections by themselves; edges still define which pairs are allowed to link.

5) Directed versus undirected behavior

Undirected graphs assume motion is symmetric: if A connects to B, then B connects to A with the same cost. Directed graphs represent one-way movement, asymmetric resistances, or constraint-driven routing. Direction can change reachability and can produce different optimal routes even when weights look similar.

6) Algorithm used and practical performance

The calculator uses Dijkstra relaxation, repeatedly settling the unvisited node with the smallest known distance and updating neighbors using dist[v] = min(dist[v], dist[u] + w). For typical lab and classroom networks, this approach is fast and easy to interpret.

7) Data quality checks and common pitfalls

Negative weights are rejected because they break Dijkstra assumptions. Missing weights can be skipped, but skipping may disconnect the graph and eliminate valid routes. In Euclidean mode, ensure endpoints have coordinates or provide fallback weights in the edge list.

8) Interpreting outputs and exporting results

The Results panel shows the shortest distance, the chosen path, and a distance table for all nodes. Infinity means unreachable under the current settings and skipped edges. Use CSV for spreadsheet analysis and PDF for sharing results in reports.

FAQs

1) What is the difference between provided and Euclidean weights?

Provided weights use the numeric values in your edge list. Euclidean weights compute each edge cost from node coordinates. Connectivity still comes from the edge list in both cases.

2) Can I use negative weights?

No. Dijkstra requires non-negative weights. If you need negative edges, switch to a method like Bellman-Ford in a different tool, or transform the model so all costs are non-negative.

3) What does infinity (in the distance table) mean?

Infinity indicates a node is unreachable from the selected start node given your direction setting and the edges you provided or skipped.

4) How do I represent one-way motion or constraints?

Choose Directed and list only the allowed direction, such as A,B,5. If the reverse is allowed with a different cost, add B,A,7 as a separate edge.

5) Some edges have no weights. What should I do?

Either add weights to every edge, or enable the option to skip missing weights. In Euclidean mode, missing weights are fine only when both endpoint coordinates are present.

6) Can I use 3D coordinates?

Yes. Provide node,x,y,z in the coordinate list. The calculator will use the 3D Euclidean distance for edges whose endpoints both include z values.

7) Does the calculator return all shortest paths?

It returns one shortest path based on the relaxation order. If multiple paths tie exactly, the reported path may differ depending on node labels and edge ordering, while the shortest distance remains correct.