Calculator Input
Example Data Table
| Input Area | Example Rows | Meaning |
|---|---|---|
| Unknown nodes | A, B, C | A, B, and C are solved by nodal equations. |
| Known nodes | 0,0 and S,12 | Ground is zero volts. Source node S is 12 volts. |
| Resistor branches | A,S,2200 | A 2200 ohm branch connects node A to known node S. |
| Current sources | 0,A,0.002 | A 2 mA source flows from ground into node A. |
Formula Used
The calculator uses Kirchhoff current law at each unknown node. Current leaving and entering each node must balance.
G V = I
G is the conductance matrix. V is the unknown node voltage vector. I is the injected current vector.
For a resistor between node i and node j, conductance is:
g = 1 / R
The diagonal matrix term receives +g. A branch between two unknown nodes adds -g to the off diagonal terms. A resistor connected to a known voltage adds g × Vknown to the current vector.
For a current source flowing from node a to node b, the calculator subtracts current from node a and adds current to node b.
How to Use This Calculator
Enter unknown node names first. Use short labels, such as A, B, N1, or OUT.
Add known node voltages next. Ground is already treated as zero, but it is still useful to enter 0,0 for clarity.
Enter each resistor on its own line. Use the format from node, to node, and resistance in ohms.
Add independent current sources if the circuit has them. Use amps. Direction matters. A positive value flows from the first listed node to the second listed node.
Press the calculate button. The solved result appears above the form and below the header. Review voltages, branch currents, matrix terms, power, and residuals.
Use the CSV button for spreadsheet work. Use the PDF button for a printable engineering report.
Node Voltage Method Guide
What This Tool Solves
The node voltage method is a direct way to solve electrical networks. It is useful when a circuit has many branches. It reduces repeated current calculations. Each unknown node becomes one equation. The reference node is usually ground. This calculator builds those equations from your branch list. It then solves the matrix system and reports voltages.
Why Conductance Is Used
Nodal analysis works best with conductance. Conductance is the reciprocal of resistance. A resistor current can be written as conductance multiplied by voltage difference. This makes every branch fit into a matrix. The matrix diagonal shows all conductance connected to a node. Off diagonal values show conductance shared with another unknown node.
Known Voltage Nodes
Some nodes already have fixed voltage values. Ground is the most common case. A supply rail is another example. The calculator lets you list those nodes separately. When a resistor connects to a known node, its effect moves into the current vector. This keeps the unknown matrix smaller and cleaner.
Current Source Direction
Current source direction is important. A source from A to B removes current from A. It injects current into B. The calculator follows that rule. If your answer has the wrong sign, check the source direction first. A negative result often means the real direction is opposite your assumption.
Advanced Checks
The result includes residual current values. These show how closely the solved voltages satisfy Kirchhoff current law. Very small residuals mean the equations balance well. The tool also reports resistor power. This helps verify energy behavior and component loading.
Practical Accuracy
Use consistent units. Enter ohms, amps, and volts. Avoid mixing kilo-ohms with ohms unless you convert first. Very large and very small values in the same circuit may reduce numerical quality. The scaling hint warns when values are far apart.
Best Use Cases
This calculator is helpful for resistive bias networks, sensor dividers, loaded voltage dividers, source transformation checks, and circuit homework. It also supports quick design reviews. You can copy results into a report using the export buttons.
FAQs
What is the node voltage method?
It is a circuit analysis method. It finds unknown node voltages by applying Kirchhoff current law at each node. The final equations form a matrix system.
Which node should be ground?
Choose the most connected reference node when possible. Ground is normally zero volts. A good reference reduces equation complexity and improves readability.
Can I enter a supply voltage?
Yes. Add the supply node as a known node. For example, enter S,12 for a fixed 12 volt source node.
How do I enter current sources?
Use from node, to node, and current in amps. The current is treated as flowing from the first node to the second node.
Why is my matrix singular?
A singular matrix often means a floating node exists. It may also mean no ground reference is connected through the network.
What does residual mean?
Residual is the remaining KCL error after solving. Values near zero indicate a balanced and accurate solution.
Can this solve circuits with voltage sources between unknown nodes?
This version handles known voltage nodes directly. A voltage source between two unknown nodes needs a supernode method or modified nodal analysis.
Why are some currents negative?
A negative current means the actual current direction is opposite the listed branch direction. The magnitude is still useful.