Battery Discharge-Rate Trade-off: Peukert's Law & Ragone Plot

Discharge Conditions

Discharge rate 1.0 C

Internal resistance (25°C) 60 mΩ

Peukert exponent k 1.10

Cell temperature 25 °C

Cell State

State of charge: 100%

Terminal voltage

4.20 V

Discharge current

3.40 A

Ohmic heat (I²R)

0.00 W

Power out

0.00 W

Usable capacity

3.40 Ah

Est. runtime now

60.0 min

How it works

Nameplate capacity (3.4 Ah here, an 18650-class Li-ion cell) is only delivered in full at a slow discharge. Drawing more current pulls Li⁺ out of the graphite anode faster than it can diffuse through the electrolyte and separator, so the cell yields less usable charge — Peukert's Law:

Q_eff = C_nom · (I₁C / I)^(k−1)
runtime ≈ Q_eff / I

At the same time, current through the cell's internal resistance R sags the terminal voltage below the open-circuit value and turns energy into heat:

V_term = V_oc(SoC) − I·R(T)
Heat   = I² · R(T)

Cold cells have higher internal resistance (sluggish electrolyte, slower ion transport), which is why the temperature slider scales R. The Ragone plot at the bottom of the stage traces energy density (Wh/kg) against power density (W/kg) as the discharge rate sweeps from 0.2C to 6C: pushing power up (right on the curve) always costs energy density (down) — you cannot have both a full tank and a fast fill at the same current path.

Discharge rate — how fast current is drawn, in multiples of the cell's 1C current (3.4 A).
Internal resistance — the cell's ohmic resistance at 25°C; higher values mean more voltage sag and heat per amp.
Peukert exponent k — how sharply usable capacity falls off at high current; k = 1 means no derating (ideal cell), real Li-ion cells sit around 1.05–1.15.
Temperature — cold cells (< 0°C) can lose most of their usable power; hot cells briefly perform better but age faster.

Real-world relevance: this trade-off is exactly why an EV or a power-tool battery pack quotes a different range/runtime at low draw than at full throttle, and why the same cell chemistry is marketed as either "high energy" or "high power" depending on how its electrodes and electrolyte are tuned.

Li⁺ ion flow (anode → cathode) Electron flow (external circuit)

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