Engineering Calc Tools

Circuits

Two-Loop Circuit Calculator (Mesh and Nodal Analysis)

Currents, node voltage and power in a two-source, three-resistor circuit by nodal and mesh analysis.

Tool no.
ECT-K07
Rev
1.0
Updated
Oct 2026
Method
Kirchhoff’s laws
How to use this calculator

Match your circuit to the sketch: a source and resistor on the left, a resistor in the middle shared by both loops, and a source and resistor on the right. Enter a source voltage as negative if its + terminal points down.

Formulas

Node voltage (KCL at a)Va = V1/R1 + V2/R21/R1 + 1/R2 + 1/R3
Mesh equations (KVL)(R1 + R3)Ia − R3Ib = V1  −R3Ia + (R2 + R3)Ib = −V2

Worked example

12 V with 2 Ω, 6 V with 4 Ω, 6 Ω in the middle (the default)

  1. Va = (12/2 + 6/4)/(1/2 + 1/4 + 1/6) = 7.5/0.9167 = 8.18 V.
  2. I1 = (12 − 8.18)/2 = 1.909 A; I2 = (6 − 8.18)/4 = −0.545 A; I3 = 8.18/6 = 1.364 A.
  3. The 6 V source is being charged: current flows into its + terminal.

Frequently asked questions

Mesh or nodal analysis?

Nodal analysis needs one equation per node (here just one); mesh analysis needs one per loop (here two). Both give the same currents.

What does a negative current mean?

Only that it flows the other way from the arrow you assumed.