Two Node Voltage Calculator

Solve v1 and v2 using nodal analysis. Use resistance branches, current sources, and known voltages. Download results, compare examples, and verify every circuit step.

Calculator

Formula used

The calculator uses nodal conductance equations.

G11 = 1/R1g + 1/R12 + 1/R1k
G22 = 1/R2g + 1/R12 + 1/R2k
G12 = G21 = -1/R12
B1 = I1 + Vk1/R1k
B2 = I2 + Vk2/R2k

D = G11G22 - G12G21
v1 = (B1G22 - G12B2) / D
v2 = (G11B2 - G21B1) / D

Blank or zero optional resistance branches are treated as open circuits.

How to use this calculator

Enter the resistor from v1 to ground. Enter the resistor from v2 to ground. Enter the resistor between both nodes. Add current sources as injected current into each node. Use negative current when the source leaves the node. Add optional known voltage branches when a node connects to a fixed voltage through resistance.

Select units before calculating. Press Calculate to show results above the form. Use CSV for spreadsheet work. Use PDF for a compact saved report.

Example data table

Case R1g R2g R12 I1 I2 Unit set Approx v1 Approx v2
Basic divider network 1000 2000 1500 5 2 ohm, mA, V 4.857 V 5.524 V
Weak second node 2200 4700 3300 3 1 ohm, mA, V 5.227 V 5.955 V
Bias branch added 1000 1000 2200 1 1 ohm, mA, V Depends on branch Depends on branch

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.

FAQs

What are v1 and v2?

They are two unknown node voltages measured against the reference node. The reference node is normally circuit ground.

What does positive current mean?

Positive current means current is injected into that node. Use a negative value when the source pulls current away from the node.

Can I leave a resistor field blank?

Yes. Blank or zero optional branches act like open circuits. Main branches may also be open, but the matrix must remain solvable.

Why is conductance used?

Nodal analysis works naturally with conductance. Conductance equals one divided by resistance. It makes current terms simple in KCL equations.

What causes a singular matrix?

A singular matrix often means the circuit has no valid reference path. Add a ground branch or check missing connections.

Can this model a Thevenin source?

Yes. Use the optional known voltage branch. Enter its series resistance and known voltage value for that node.

Does the PDF need an extra library?

No. This file creates a simple PDF directly. It is enough for text results and compact calculation records.

Are the results suitable for real circuits?

They are suitable for ideal resistor and source models. Always check component ratings, tolerances, and safety limits before building hardware.

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