Coulombic efficiency calculator: CE per cycle, average CE and capacity retention

CE = Q_out / Q_in    R_n = ICE × CEⁿ    CE_needed = (R / ICE)^1/n

Which capacity is “out”. CE is the charge recovered over the charge put in during one cycle. In a lithium||copper cell lithium is plated on copper and then stripped, and the average CE is the total stripping capacity over the deposited capacity (Nat Commun 2025, doi:10.1038/s41467-025-59955-0). For an anode half-cell the same holds with desodiation or delithiation over sodiation or lithiation: a hard carbon electrode with a first charge of 298 mAh g⁻¹ and discharge of 370 mAh g⁻¹ has an initial CE of 80.5 % (Chem Sci 2026, doi:10.1039/d6sc04167a). In a full cell (cathode against anode) it is discharge over charge: 99.94 / 117.35 mAh g⁻¹ = 85.16 % (iScience 2025, doi:10.1016/j.isci.2025.114581). The calculator applies discharge / charge to cathode half-cells and full cells and charge / discharge to anode and Li-metal half-cells, and reports the capacity lost in each cycle as Q_in − Q_out.

First cycle. The initial Coulombic efficiency (ICE) is low because active lithium or sodium is consumed in forming the interphase and trapped in the electrode; it sets the inventory left for every later cycle (Adv Sci 2026, doi:10.1002/advs.77874; Chem Sci 2026). Not all of a cathode’s first-cycle loss is permanent: in NCM/Li half-cells most of it was kinetic and recoverable with a constant-potential step at the end of discharge, and less than 10 mAh g⁻¹ was irreversible (PCCP 2016, doi:10.1039/c5cp07718d).

Average CE. The tool reports the arithmetic mean of the per-cycle CE over the range you choose, the way cycle-by-cycle Li||Cu data are summarised (Angew Chem 2026, doi:10.1002/anie.9595705), and the charge-weighted value Σ Q_out / Σ Q_in (Nat Commun 2025). Capacity retention is the out-capacity of a cycle divided by that of the reference cycle.

From CE to cycle life. When there is no reservoir, every inefficiency removes inventory for good, so the retention after n cycles is R = ICE × CEⁿ and the average CE needed for a target is (R / ICE)^1/n: for 80 % after 200 cycles, at least 99.89 % with ICE = 100 % and 99.94 % with ICE = 90 %; a cell averaging 99.7 % reaches 80 % after about 74 cycles, one averaging 99.9 % after about 223 (Adv Sci 2026). The calculator gives CEⁿ, the cycles to the target, n = ln(R / ICE) / ln CE, and the CE needed. In a graphite cell, an average CE of 99.00 % loses up to 60 % of the capacity in 100 cycles, and adding 0.01 % to the CE roughly doubles the cycle life (Angew Chem 2026).

Limits. CEⁿ is an upper bound for an anode-free cell: it assumes a constant CE, no loss on the cathode side and no reactivation of dead metal (Adv Sci 2026). In the other direction, lithium metal electrodes act as reservoirs that make up for lost lithium and mask parasitic reactions (Angew Chem 2026), and a half-cell with a nearly unlimited lithium supply does not show the capacity loss a cell with limited lithium suffers (Small Sci 2025, doi:10.1002/smsc.202500131). So a half-cell’s capacity usually fades more slowly than CEⁿ; the tool prints the measured retention next to the CEⁿ prediction for the same cycles so you can see the gap. CE values also depend on the protocol (current, capacity, substrate), so compare them only under the same conditions.

The built-in example is an illustrative cathode half-cell, not a measurement: 30 cycles in mAh g⁻¹, charge 228.4 and discharge 201.6 in cycle 1, falling to 193.1 and 192.7 in cycle 30. Cell type: cathode, so CE = discharge / charge.

1. First cycle. CE = 201.6 / 228.4 = 88.27 %; the first-cycle loss is 228.4 − 201.6 = 26.8 mAh g⁻¹, 11.7 % of the charge.
2. Average CE. Cycles 2 and 3 are still settling (98.09 % and 99.25 %), so average cycles 4–30: the mean of the 27 per-cycle values is 99.791 % (Σ discharge / Σ charge gives the same to four figures).
3. Retention. Against cycle 4 (199.4 mAh g⁻¹), cycle 30 keeps 192.7 / 199.4 = 96.64 %. CE²⁶ = 0.99791²⁶ predicts 94.70 %: the half-cell’s lithium counter electrode makes up part of the loss, so the capacity fades more slowly than CEⁿ.
4. Projection. If 99.791 % held, 500 more cycles would leave 0.99791⁵⁰⁰ = 35.08 % (67.6 mAh g⁻¹ from 192.7), and 80 % would be reached after ln 0.8 / ln 0.99791 = 106.5 cycles. Keeping 80 % for 500 cycles needs an average CE of 0.8^1/500 = 99.955 %, or 99.980 % if the 88.27 % first cycle also counts.

One cycle. The hard carbon half-cell in Chem Sci 2026 gave 370 mAh g⁻¹ on sodiation (discharge) and 298 mAh g⁻¹ on desodiation (charge): in One cycle mode, capacity in 370 and out 298 give CE = 80.54 %, the 80.5 % reported, and a first-cycle loss of 72 mAh g⁻¹.