Two Node Voltage Analysis
Node voltage analysis is a direct way to solve many circuits. It treats the reference conductor as zero volts. Every other node is written relative to that point. This calculator focuses on two unknown nodes, named v1 and v2. It supports resistors to ground, a resistor between nodes, current injection, and branches to known voltages.
Why this method helps
Nodal equations are compact. They work well when many parts share one reference. The method also reduces drawing mistakes. Instead of guessing loop currents, you balance current at each node. Each resistor contributes conductance. Each current source contributes to the right side of the equation. A known voltage branch becomes a conductance term plus a source term.
Practical electrical use
Use this tool during homework, lab checks, amplifier bias studies, sensor divider checks, and small network design. It is also useful when comparing hand calculations with simulation output. The result table shows the conductance matrix, determinant, node voltages, branch currents, and power estimates. These extra values help confirm signs and units.
Input accuracy matters
Resistance values must be positive. Leave optional branches blank or zero when they are not connected. Current source signs follow injection into the node. A source feeding the node is positive. A source leaving the node is negative. Known voltage branches can model Thevenin sources through series resistors. They can also represent bias rails connected through resistive paths.
Reading the result
The determinant must not be near zero. A very small determinant means the network is weakly defined or singular. Check for missing ground paths, open branches, or contradictory values. The two voltages are calculated from simultaneous equations. After solving, current through the between-node resistor is reported from v1 toward v2. Ground branch currents are reported from each node toward ground.
Best workflow
Start with a clean circuit sketch. Mark the ground node first. Label each branch. Convert all units carefully. Then enter the data and calculate. Export the CSV for spreadsheets. Use the PDF option for quick records. Compare the example table before testing your own circuit.
Advanced users can treat conductance values as modeling shortcuts. Large resistances approximate open circuits. Small resistances approximate strong connections. Always confirm ratings before building hardware.