Battery Equivalent Circuit Calculator

Example data table

Illustrative inputs and typical outputs for a Li-ion cell.

SOC (%)	I (A)	Model	R0 (Ω)	R1,C1	R2,C2	t (s)	Terminal V (V)
80	2.0	2RC	0.020	0.010, 2500	0.005, 8000	10	≈ 4.03
50	5.0	1RC	0.030	0.020, 1500	—	5	≈ 3.56
30	1.5	R0	0.040	—	—	0	≈ 3.42

Your results depend on your OCV method, temperature scaling, and RC time constants.

Formula used

The calculator uses a common Thevenin equivalent circuit.

OCV(SOC) = Vmin + (Vmax − Vmin)·SOC/100

R(T) = Rref·(1 + α·(T − Tref))

V(t) = OCV − I·R0 − Σ[I·Rk·(1 − e^(−t/(Rk·Ck)))]

Impedance for each RC branch (R in parallel with C):

Zk(jω) = Rk / (1 + jωRkCk)

Ztotal(jω) = R0 + Σ Zk(jω)

Use discharge direction for voltage drop under positive current. Choose charge direction to flip the sign for charging conditions.

How to use this calculator

Pick a chemistry preset, then keep or edit Vmin and Vmax.
Select an OCV method: from SOC or direct OCV input.
Enter current, direction, and a time for the step response.
Choose a model order: R0 only, 1RC, or 2RC.
Provide R and C values. Larger R·C means slower relaxation.
Optionally adjust temperature parameters to scale resistances.
Press Calculate to show results above this form instantly.
Use CSV or PDF buttons to export the computed table.

Professional notes

Why equivalent circuits matter

Equivalent circuit models compress cell physics into a few measurable parameters. By representing losses and storage with resistors and capacitors, engineers can predict voltage sag, recovery, and power capability without running full electrochemical simulations. This calculator uses a Thevenin structure that is widely applied in BMS estimators and pack sizing because it stays interpretable while remaining fast enough for scenario testing during early design reviews. The parameter set also supports documentation and auditing.

Open-circuit voltage baseline

Terminal voltage starts from open-circuit voltage, then dynamic drops are subtracted or added depending on current direction. You can enter OCV directly or approximate it from state of charge using a linear span between minimum and maximum values. Although real OCV curves are nonlinear, the linear option supports quick screening, design tradeoffs, and consistent comparisons across cells, batches, and temperature cases for reporting. It also prevents hidden curve assumptions when sharing results.

Ohmic loss and temperature scaling

The series resistance R0 captures immediate ohmic loss from current collectors, electrolyte, welds, and connectors. Under a step current, the instant change is I·R0, so it strongly influences peak power and heating. Because resistance typically rises in cold conditions and with aging, the calculator includes a temperature coefficient so you can scale R around a reference temperature and evaluate cold-start margin or thermal design targets. Use measured α values when you have characterization data.

Polarization dynamics with RC branches

RC branches represent slower polarization and diffusion effects that appear after the initial drop. Each branch contributes I·R·(1 − e^(−t/RC)) in the step response and is governed by its time constant τ = R·C. At t = τ, the branch reaches about 63% of its final value, which helps choose pulse durations, sampling windows, and interpret relaxation behavior in lab data. Multiple branches can mimic a broader distribution of relaxation processes.

Impedance interpretation for validation

For small-signal analysis, each RC branch produces a frequency-dependent impedance R/(1 + jωRC). At low frequency it behaves more resistive, while at high frequency its resistive component diminishes and the capacitive phase dominates. By changing frequency and exporting CSV or PDF, you can compare trends with EIS measurements, validate parameters, and create starting points for automated fitting routines and regression tests. Tracking changes over time helps quantify aging and degradation.

FAQs

1) Which model order should I choose?

Start with R0 for quick checks. Use 1RC when you see one clear relaxation in pulse data. Use 2RC when there are fast and slow recoveries that one branch cannot match.

2) What does the time constant mean?

Each RC branch has τ = R·C. After one τ, the branch reaches about 63% of its steady contribution in the step response. Larger τ values indicate slower voltage recovery.

3) Why does charging increase the voltage here?

Direction flips the sign of current in the model. Under charging, the ohmic and polarization terms add to OCV, producing a rise. This matches the convention used in many equivalent circuit formulations.

4) How should I pick Vmin and Vmax?

Choose values that bracket your usable SOC window at the same temperature. If you have an OCV curve, use it to estimate endpoints or switch to direct OCV input for point studies.

5) Is the impedance output a full EIS model?

No. It captures the selected R0 and parallel RC terms only. Inductive leads, Warburg diffusion tails, and nonlinear effects are not included. Treat it as a compact validation and fitting aid.

6) How can I calibrate parameters from test data?

Fit R0 from the immediate voltage step. Fit each RC pair from relaxation shape using τ and final drop magnitude. Then check frequency behavior by comparing the predicted |Z| and phase at measured points.