Kirchhoff Loop Solver
Free kirchhoff loop solver — step-by-step solution, worked examples, instant answers.
Two-loop Kirchhoff circuit solver (shared middle branch).
About Kirchhoff Loop Solver
The Kirchhoff Loop Solver solves two meshes: V₁ = I₁R₁ + (I₁−I₂)R₃, −V₂ = I₂R₂ − (I₁−I₂)R₃ for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. The standard two-battery network that defeats series-parallel tricks — you MUST use Kirchhoff.
How to use Kirchhoff Loop Solver
- 1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
- 2The tool substitutes them into two meshes: V₁ = I₁R₁ + (I₁−I₂)R₃, −V₂ = I₂R₂ − (I₁−I₂)R₃ and recomputes live.
- 3Read the answer in the result box, then expand the step-by-step solution to see the full working.
- 4Copy the method into your notebook, or change inputs to explore how the result behaves.
Why use Kirchhoff Loop Solver?
- ✓Solves two meshes: V₁ = I₁R₁ + (I₁−I₂)R₃, −V₂ = I₂R₂ − (I₁−I₂)R₃ instantly as you type — no submit button, no waiting
- ✓Step-by-step solution shown for every calculation, not just the final answer
- ✓Realistic example values pre-loaded so you can see a worked example immediately
- ✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
- ✓Mobile-friendly and fast enough to use mid-homework or mid-lesson
Frequently asked questions
What formula does the Kirchhoff Loop Solver use?+
It uses two meshes: V₁ = I₁R₁ + (I₁−I₂)R₃, −V₂ = I₂R₂ − (I₁−I₂)R₃. The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.
What should I keep in mind when using this calculator?+
The standard two-battery network that defeats series-parallel tricks — you MUST use Kirchhoff. Method: assign loop currents, march around each loop summing voltage rises and drops, solve the simultaneous pair.
Is the Kirchhoff Loop Solver free to use?+
Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.
Can I use this for homework, teaching or exam prep?+
That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.
Embed Kirchhoff Loop Solver on your website
Want Kirchhoff Loop Solveron your own site? Paste this snippet into any HTML page — it's free, with no API key or sign-up. The tool loads in an iframe and keeps working exactly as it does here.
<iframe src="https://tooljolt.com/tools/kirchhoff-loop-solver" width="100%" height="640" style="border:1px solid #e5e7eb;border-radius:12px;max-width:680px" title="Kirchhoff Loop Solver — ToolJolt" loading="lazy"></iframe>Related Science tools
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