Free Circuit Analysis Tool for ECE Students
Draw any linear circuit in your browser and instantly get symbolic KVL, KCL, MNA equations and transfer functions in clean LaTeX. CircuitMath handles passive components, dependent sources, BJTs, and MOSFETs with automatic small-signal substitution — no installation, no account, no cost.
What is CircuitMath?
CircuitMath is a free, web-based circuit analysis tool designed for electrical and computer engineering students. You draw a schematic using the drag-and-drop editor, click Analyze, and CircuitMath returns the exact symbolic equations that describe the circuit's behavior — written in LaTeX and ready to paste into your homework, lab report, or thesis.
Undergraduate circuit courses spend enormous effort teaching students how to apply Kirchhoff's laws, set up nodal and mesh analysis systems, and derive voltage gains for small-signal transistor circuits. The algebra is mechanical but error-prone: a dropped sign, a mislabeled node, or an inverted dependent source can break the entire derivation. CircuitMath performs this mechanical step for you so you can focus on interpreting the results and understanding the physics.
The tool is not a SPICE simulator. It does not compute numerical operating points or run transient sweeps. Instead, it extracts the symbolic equations that define the circuit, giving you exact closed-form expressions like H(s) = R₂ / (R₁ + R₂) or A_v = −g_m R_C / (1 + (1/r_π + g_m) R_E) — the same equations you would write by hand, but verified and instant.
Key Features
Drag-and-Drop Schematic Editor
Place resistors, capacitors, inductors, voltage and current sources, grounds, and transistors with a single click. Wire them together with orthogonal routing that automatically snaps to component terminals. Rotate, move, and delete components with familiar keyboard shortcuts.
KVL, KCL, and MNA Equations
Every analysis produces Kirchhoff's Voltage Law equations around each mesh, Kirchhoff's Current Law equations at each node, and the full Modified Nodal Analysis matrix equation A·x = z. See the exact mathematical system that governs your circuit.
Transfer Function Extraction
Automatically computes the voltage transfer function H(s) = V_out / V_in by symbolically solving the MNA system. Works for resistive networks, reactive circuits in the Laplace domain, and small-signal transistor amplifiers. Get both expanded and factored forms.
BJT and MOSFET Small-Signal Models
Place NPN, PNP, NMOS, and PMOS transistors directly from the palette. CircuitMath automatically kills DC bias sources and substitutes each transistor with its hybrid-π small-signal equivalent (r_π, g_m·v_be, r_o) before running analysis.
Dependent Source Components
All four controlled-source types are available: voltage-controlled voltage source (VCVS), voltage-controlled current source (VCCS), current-controlled voltage source (CCVS), and current-controlled current source (CCCS). Build custom small-signal models by hand when you want full control.
LaTeX Export
Every equation — KVL, KCL, MNA matrix, transfer function — comes with a one-click copy button that puts properly formatted LaTeX on your clipboard. Paste directly into Overleaf, Microsoft Word with a LaTeX plugin, or any math-aware text editor.
Circuit Templates
Start from a library of common textbook circuits: voltage divider, current divider, RC and RLC filters, Wheatstone bridge, multi-loop networks, common-emitter and common-source amplifiers, cascode stages, and more. Adapt them to your specific problem.
100% Free, No Account
CircuitMath runs entirely in your browser. There is no paywall, no login, no trial limit, and no subscription. Your circuits are never sent to any account or saved server-side. Close the tab and the session ends.
How It Works
- Draw your circuit. Open the editor, drag components from the left palette onto the canvas, and connect them with wires. Double-click any component to set its symbolic value (
R_1,V_s,g_m, etc.) or a numeric value. - Click Analyze. CircuitMath validates your topology, converts the circuit to an Lcapy netlist, and runs Modified Nodal Analysis using SymPy under the hood. For circuits with transistors, the preprocessor first substitutes each device with its small-signal equivalent.
- Read the equations. The results panel shows KCL equations at every node, KVL equations for every mesh, the full MNA matrix, and — whenever possible — a closed-form transfer function
H(s) = V_out / V_in. - Copy to your document. Click the Copy LaTeX button next to any equation. Paste the LaTeX into your homework, lab report, or paper. The notation matches what textbooks use, with proper subscripts, fractions, and matrices.
Featured Tutorials
CircuitMath ships with a growing library of tutorials that explain the theory behind every analysis the tool performs. Each tutorial is a full-length article with step-by-step derivations, worked examples, and links back to the editor so you can verify the results yourself. Start with the fundamentals and work toward small-signal analysis.
Learn KVL from first principles: sign conventions, step-by-step mesh examples, common mistakes, and how CircuitMath automates loop equations.
Master KCL: conservation of charge, node equations, supernodes, and a step-by-step 4-node worked example.
Derive the voltage divider formula from KVL and Ohm's law, understand loading effects, and explore biasing and sensing applications.
A complete walkthrough: identifying nodes, writing KCL, handling voltage sources with supernodes, and solving the system.
CE configuration, small-signal equivalent circuit, deriving the voltage gain with and without emitter degeneration, and input/output impedance.
Circuit intuition, deriving H(s) = 1/(1 + sRC), cutoff frequency, Bode plot interpretation, and verifying with CircuitMath.
Who Uses CircuitMath?
Undergraduate ECE Students
The primary audience. If you are taking a first or second circuits course, CircuitMath helps you check your homework by giving you the exact symbolic answer. Work the problem by hand first, then verify using the tool. When your answer disagrees with CircuitMath, you learn exactly where your derivation went wrong — a more effective feedback loop than numeric SPICE results or the back of the textbook.
Graduate Students and Researchers
For courses in analog integrated circuit design, CircuitMath handles BJT and MOSFET small-signal analysis without requiring you to set up the hybrid-π model by hand. This is useful for quickly validating the gain expression of an amplifier topology before committing it to a SPICE simulation or layout.
Instructors and Teaching Assistants
Generating example problems for problem sets is tedious when every worked solution needs clean LaTeX. CircuitMath produces the symbolic solution directly in LaTeX, which can be pasted into lecture slides, handouts, or solution manuals. You can also use the template library as a starting point for canonical problems.
Self-Learners and Hobbyists
If you are working through a textbook on your own — Sedra & Smith, Razavi, Hambley, or similar — CircuitMath lets you explore what happens when you change component values or topologies. Swap a resistor for a capacitor, add emitter degeneration, or insert a cascode transistor, and watch the transfer function update immediately.
Frequently Asked Questions
- Is CircuitMath really free?
- Yes. There is no paywall, no subscription, no premium tier, and no free-trial timer. CircuitMath is supported by non-intrusive advertising. If you dislike ads, an ad blocker works normally — the tool functions identically.
- Do I need to create an account?
- No. CircuitMath has no login, no account system, and no way to save circuits server-side. Your circuit lives in your browser for the duration of the session.
- Does it handle transistor circuits?
- Yes. NPN BJT, PNP BJT, NMOS, and PMOS components are available in the component palette. When you analyze a circuit containing transistors, CircuitMath kills DC bias sources and substitutes each transistor with its hybrid-π small-signal equivalent before computing KCL/KVL/MNA equations. This is equivalent to what you would do by hand.
- Can I export the equations?
- Yes. Every equation displayed in the results panel has a Copy LaTeX button that copies properly-formatted LaTeX source to your clipboard. Paste into Overleaf, a Markdown file with KaTeX, or any LaTeX-aware editor.
- Does it support dependent sources?
- Yes. All four controlled-source types — VCVS (E), VCCS (G), CCVS (H), CCCS (F) — are available. Use them to build custom small-signal models or to analyze op-amp circuits and feedback networks.
- Is my circuit data saved?
- No circuit data is stored on any server. The analysis request is sent to a stateless backend that returns equations and then forgets the request. Your browser keeps the circuit in memory until you close the tab or click Clear All.
- What browsers are supported?
- Any modern browser with ES2020 support and SVG: Chrome, Edge, Firefox, Safari, Opera. Mobile browsers work for viewing but the drag-and-drop editor is designed for a mouse or trackpad on a desktop or laptop.
- Can I use CircuitMath offline?
- Not currently. The analysis engine runs on a server, so an internet connection is required to click Analyze. The editor itself will draw circuits offline, but equations are computed on request.
- How accurate are the equations?
- The equations are exact symbolic derivations, computed by the Lcapy library (which uses SymPy under the hood). They are the same equations a textbook would write, subject to the standard linear-circuit assumptions: ideal components, small-signal approximations for transistors, and the absence of noise and second-order effects.
- Is this a SPICE simulator?
- No. SPICE is a numerical simulator that computes operating points, transient responses, and frequency sweeps by solving the circuit equations for specific parameter values. CircuitMath is a symbolic tool that produces closed-form expressions in terms of the component symbols. Use SPICE when you need numbers; use CircuitMath when you need the formula.
- Can I cite CircuitMath in a paper or thesis?
- Yes. Cite the URL
https://circuitmath.comalong with the access date. The tool is provided for educational use.
Ready to try CircuitMath?
The editor is one click away. Draw your first circuit in under a minute.