Calculator Inputs
Use up to five unknown nodes. Leave a resistance blank to treat that branch as open.
Example Data Table
This sample matches the built-in example button. Positive current enters a node. Negative current leaves a node.
| Parameter | Value |
|---|---|
| Nodes | 3 |
| Node 1 to Ground | 100 Ω |
| Node 2 to Ground | 220 Ω |
| Node 3 to Ground | 150 Ω |
| R12 | 80 Ω |
| R13 | 120 Ω |
| R23 | 60 Ω |
| Injected Current at Node 1 | 2.4 A |
| Injected Current at Node 2 | 0.8 A |
| Injected Current at Node 3 | -0.5 A |
Formula Used
Node analysis applies Kirchhoff’s Current Law at each unknown node. The algebraic sum of currents leaving a node equals the injected current for that node.
For each resistor between node i and node j, branch current is:
Iij = (Vi - Vj) / Rij
For a resistor from node i to ground, ground current is:
Iig = Vi / Rig
The solver assembles these terms into the conductance matrix form:
[G][V] = [I]
Diagonal terms contain the sum of conductances connected to a node. Off-diagonal terms contain negative mutual conductance between connected nodes. The script then solves the linear system by Gaussian elimination with partial pivoting.
How to Use This Calculator
- Select the number of unknown nodes in the circuit.
- Enter any resistance from each node to ground.
- Enter resistor values between connected node pairs.
- Enter current injection for every node. Use negative values for currents leaving a node.
- Click Analyze Circuit to solve node voltages.
- Review the voltage summary, branch currents, KCL residuals, conductance matrix, and voltage chart.
- Use the export buttons after calculation to save CSV or PDF output.
FAQs
1. What does this calculator solve?
It solves unknown node voltages in grounded DC resistive networks, then calculates branch currents, ground currents, KCL residuals, and power values from the same solution.
2. What does positive injected current mean?
Positive current means a source pushes current into the node. Negative current means the current leaves that node toward the source or another reference direction.
3. Why do I get a singular matrix message?
That usually means the circuit floats without a proper ground path, has an isolated node, or does not contain enough resistive connections to define every voltage uniquely.
4. Can I leave some branches blank?
Yes. Any blank resistance is treated as an open branch, so no conductance is added between those two points.
5. Does this work for voltage sources directly?
Not directly. Standard node analysis with ideal voltage sources needs supernodes or source transformations before using this resistive conductance form.
6. What units should I use?
Use ohms for resistance, amperes for current, volts for calculated node voltage, and watts for power. Keep all values in consistent base units.
7. Why is KCL residual important?
KCL residual shows the numerical mismatch at each node after solving. Very small residuals confirm the matrix solution is internally consistent.
8. Can I export the results?
Yes. After calculation, the page provides CSV and PDF export actions so you can keep the node voltage report and supporting tables.