Capacity fade
Capacity retention against cycle number, with the 80% end-of-life line.
Capacity retention against cycle number tells you how fast a cell is dying and when it will cross end-of-life. The knee, the cycle where fade stops being gradual and accelerates, is the number that matters, and it can be projected from the early trend.
What it measures
The plot is discharge capacity, normalized to the early-cycle baseline, against cycle number. The shape of that curve is diagnostic because different degradation physics produce different functional forms:
- Square-root fade, Q(n) = Q₀ − k·√n, the signature of SEI growth limited by diffusion through its own film. Fade decelerates as the film thickens.
- Linear fade, Q(n) = Q₀ − k·n, steady loss per cycle, typical of ongoing lithium inventory or active-material loss at a constant rate.
- Power-law and exponential forms: intermediate or accelerating regimes, often the handoff between mechanisms.
Two derived quantities carry the engineering decision: the knee point, the cycle where the curve departs from its early trend and fade accelerates (plating onset, electrolyte depletion, or pore clogging), and N80: the projected cycle number at 80% retention, the standard end-of-life definition.
How to read the output
A retention curve that tracks √n is a cell aging gracefully through SEI growth; the same data on a linear trend means something is being consumed at a constant rate and the cell will not slow down on its own. The knee is the alarm: once fade accelerates, the remaining life is far shorter than the pre-knee trend implies, so any projection fitted only to pre-knee data is an overestimate.
Read the projection together with its confidence interval. A N80 of 1,400 cycles with a 95% interval of ±80 cycles supports a warranty model; the same projection at ±600 cycles says the data does not yet constrain the answer, cycle longer before deciding.
A real use case
A cell team is qualifying two electrolyte formulations for a high-nickel NMC cell and cannot wait 2,000 cycles for the answer. Both lots are cycled to ~200 cycles. Formulation A tracks square-root fade with a projected N80 near 1,600 cycles; formulation B looks similar by eye at cycle 200, but its best fit is already linear and its projection lands near 900 cycles with a tight interval. The early curves differ by less than 2% retention, the model fit, not the raw number, separates them. B is cut from the next DOE round months before a full cycle-life test would have said so.
Common mistakes
- Extrapolating from too few cycles. Below ~50 cycles the model forms are barely distinguishable and any N80 number is noise dressed as a forecast.
- Fitting one model and trusting it. The honest answer compares linear, square-root, power-law, and exponential fits and reports which one the data actually prefers.
- Treating the knee as an outlier. A run of points dropping below the trend is the most important feature on the chart, not noise to be smoothed away.
- Comparing retention across cells tested at different temperatures or C-rates, fade constants are strongly condition-dependent.
- Normalizing to cycle 1 when the first cycles are formation. Formation losses are not cycling fade; baseline against the post-formation plateau.
Model competition, knee detection, and a bounded projection
Point Niobia at cycling data from any major cycler, Arbin, Neware, Maccor, BioLogic, Gamry, Digatron, Novonix, Basytec, LAND, and it computes the per-cycle capacity and efficiency summaries, fits the four fade models, and selects the best by fit quality. It detects the knee with the Kneedle algorithm and confirms it against the second derivative of the smoothed curve, then projects N80 (or N70) with a bootstrapped 95% confidence interval. Two guardrails are built in: it refuses to extrapolate from fewer than 50 cycles, and it always reports the model assumptions next to the number, so a projection never travels without its caveats.
Frequently asked
How many cycles do I need before a cycle-life projection is meaningful?
Niobia requires at least 50 cycles before it will extrapolate at all, and the confidence interval narrows substantially as more of the curve constrains the model. If the interval is still wide at your current cycle count, the right move is to keep cycling, not to trust the midpoint.
What physically causes the knee in a capacity fade curve?
Common drivers are the onset of lithium plating, electrolyte depletion, and pore clogging at the anode, mechanisms that feed on themselves once started. That self-acceleration is why pre-knee trends cannot be extrapolated through the knee.
Is 80% retention always the right end-of-life definition?
It is the standard convention for EV applications, but stationary storage often runs to 70% or below. Niobia projects to either threshold; what matters is quoting the threshold alongside the cycle number.