Battery Charge/Discharge: Voltage vs State-of-Charge (2D)

Load

C-rate 1.0C

Cell parameters

Internal resistance 40 mΩ

Capacity 2.5 Ah

Live Readout

State of charge

50%

Current

2.5 A

Open-circuit voltage

3.73 V

Terminal voltage

3.63 V

IR drop (|OCV − terminal|)

0.10 V

How it works

This is the 2D-native counterpart to the 3D lithium-ion cutaway simulator. Instead of orbiting a rendered cell showing ions and electrons in motion, it plots the two curves that actually describe a real charge/discharge cycle: the cell's open-circuit voltage (OCV) as a function of state of charge, and the terminal voltage you would actually measure once internal resistance is accounted for.

The open-circuit voltage follows the classic Li-ion shape — a steep rise near empty, a broad plateau in the middle, and a steep rise again near full:

OCV(soc) = 3.4 + 0.65·soc − 0.35·e^(−soc/0.04) + 0.15·e^(−(1−soc)/0.05)

Pushing current through the cell's internal resistance R adds or subtracts a voltage drop depending on direction — this is why a cell always reads higher than its OCV while charging and lower while discharging, and why that gap grows with current:

I = C-rate · Capacity (A)
V_terminal = OCV(soc) − I·R   (discharge)
V_terminal = OCV(soc) + I·R   (charge)

State of charge itself changes at a rate set only by C-rate — a 1C rate always empties or fills a cell in one simulated hour regardless of its capacity, because a bigger cell also draws a proportionally bigger current. Capacity and internal resistance instead control how far the terminal-voltage curve sags away from the OCV curve for a given C-rate: a larger cell (more amps at the same C-rate) or a higher-resistance cell pushes the terminal voltage down further under discharge, sometimes far enough to hit the low-voltage cutoff (3.0V) before the state of charge actually reaches zero — which is exactly why real high-drain applications can't simply push an arbitrary C-rate without losing usable capacity. The same effect caps how close to 4.2V a charging cell can get before hitting the high-voltage cutoff.