Nodal Analysis Calculator

Formula Used

• x contains node voltages and voltage-source currents.
• Resistors contribute conductances: g = 1/R.
• Current sources add to the right-hand vector z.
• Voltage sources add extra equations (supernodes) using V(from) − V(to) = value.

How to Use This Calculator

1. Set the number of nodes excluding ground (node 0).
2. Add each component row with Type, From node, To node, and Value.
3. Use base units: Ω, A, and V for consistent results.
4. Press Solve Circuit to compute node voltages.
5. Review currents and power, then download CSV or PDF.

Why nodal analysis is efficient for DC networks

Nodal methods scale well because unknowns are node voltages, not branch currents. For an N‑node design, the core system contains N equations, and only voltage sources add extra variables. This calculator builds the conductance matrix directly from entered components, so large resistor networks solve consistently and repeatably.

Component stamping and matrix construction details

Each resistor contributes a conductance g = 1/R to the diagonal of connected nodes, and −g to the off‑diagonals when two non‑ground nodes share a branch. Current sources inject or remove current at nodes, updating the right‑hand vector. Voltage sources create a supernode constraint using V(from) − V(to) = value and introduce a source current unknown for accurate KCL balance.

Interpreting voltages, currents, and power results

Reported node voltages are relative to ground (node 0). For each element, the calculator also reports V(from) − V(to) and I(from→to). Resistor power is always dissipative using I²R. Source power uses passive sign convention, so a negative value typically indicates the source is delivering power to the network under the chosen polarity.

Data quality checks that prevent misleading outputs

Engineering inputs often fail due to floating nodes, duplicate node entries, or zero/invalid resistance values. This tool validates node ranges, prevents same‑node connections per row, and detects singular or ill‑conditioned matrices during solving. If the solver reports a singular system, add a reference path to ground or review source placement to restore a unique operating point.

Practical workflows for documentation and review

Use the example loader to benchmark your understanding, then replace rows with project values. After solving, export CSV for peer review, version control, or spreadsheet checks. Generate a PDF to attach results to design notes, test plans, or client deliverables. Consistent naming of nodes across schematics and this table reduces rework and makes audits faster.

FAQs

1) What circuit types does this calculator support?

It solves linear DC circuits using resistors plus independent current and voltage sources. Dependent sources, capacitors, inductors, and AC phasor analysis are not included in this version.

2) How do I choose node numbers correctly?

Assign node 0 to the reference ground. Number other unique connection points as 1..N. Every component row must connect two different nodes within that range.

3) Why am I getting a singular system message?

A singular matrix usually means the circuit is floating or lacks a reference path to ground. Add a resistor path to node 0, verify nodes are connected, and confirm sources are not conflicting.

4) How is current direction defined in the results?

Currents are reported from the “From” node to the “To” node. For resistors, the sign follows (Va − Vb)/R. For current sources, it matches the entered value and direction.

5) What does negative source power indicate?

With passive sign convention, negative power commonly means the source is delivering power to the circuit. Positive power means it is absorbing power, which can occur in loaded or opposing-source cases.

6) Can I export results without solving again?

Yes. After a successful solve, the latest results are stored for the session. You can download the CSV or generate the PDF again using the download buttons.

Example Data Table