How much charge is left

Why can a device that measures its own battery constantly still be wrong about how long it will last?

The number on the screen looks like a reading. Sixty-one percent. It has the grammar of a measurement: a sensor looked at something and reported what it found.

But consider what would have to be sensed. The charge in a lithium-ion cell is lithium sitting in the layers of the graphite anode. No wire touches it, no gauge dips into it, and no instrument in the phone can count those atoms. So what exactly is being measured, and what is being inferred?

Start with what a battery actually exposes to the outside world. Three things: the voltage across its terminals, the current flowing in or out, and its temperature. That is the whole channel. Everything the device claims about charge must be reconstructed from those.

Take voltage first. A cell at rest does have a fairly reliable relationship between its open-circuit voltage and its state of charge — higher when full, lower when empty. So could we not just look it up?

Two problems appear at once. The first is that the relationship is steep only at the ends. Through the middle of a typical nickel-manganese-cobalt cell the resting voltage moves a few tens of millivolts across tens of percent of charge, and lithium-iron-phosphate is flatter still. A ten-millivolt error, which is nothing, becomes an error of many percent.

The second is worse: the lookup is only valid at rest. Draw current and the terminal voltage sags by the current times the cell's internal resistance, plus a slower polarisation effect that relaxes over minutes. A phone under load looks emptier than it is; a phone just unplugged looks fuller. And internal resistance rises with age and with cold, so the size of that distortion is itself unknown.

So try the other route. Integrate the current: count coulombs out and coulombs in, and you know how much charge has left the cell since you last knew where you stood. That is exact in principle — and it inherits two flaws that are structural rather than technical.

The first is drift. Any constant offset in the current sensor integrates linearly: half a milliamp of bias is invisible per second and appreciable after a week. Integration remembers every error and forgets nothing.

The second is the one that really matters, and it is worth stating slowly. A percentage is a ratio. Charge counting gives you the numerator — how much has come out. What is the denominator?

It is the cell's present full capacity: not the number printed on the pack, but what this particular cell, at this age, at this temperature, at this discharge rate, will actually deliver before its voltage falls below what the electronics can run on. That number is never observed directly either. It fades as the cell ages, it shrinks in the cold, and it shrinks again at high current because a harder pull drops the terminal voltage sooner and the cutoff arrives with usable lithium still in the anode.

So the gauge is estimating a fraction in which neither the numerator nor the denominator is measurable. That is the whole difficulty, and no better sensor removes it.

What does a real gauge do, then? It runs both estimators and reconciles them. Coulomb counting carries the short term, because it is smooth and responsive. When the device sits idle long enough for polarisation to relax, the gauge re-anchors on the resting voltage. And when it observes something close to a full charge or a deep discharge, it revises its estimate of full capacity — the denominator — and every percentage after that is computed against the new figure.

Now the odd behaviours stop being bugs. The gauge jumps because two disagreeing estimates were reconciled and the trusted one won. It re-learns after a few full cycles because those cycles are the only events that pin the denominator down. It shuts down at thirty percent in the cold because the cutoff is a voltage threshold, and a cold cell with raised internal resistance crosses that threshold while the model still thinks charge remains.

And the time estimate is a further layer of inference again, because it depends on future load, which no measurement can supply. Vendor algorithms are proprietary and I would not claim to know any specific one; the published families — voltage lookup, coulomb counting, impedance tracking, and Kalman-style filters that fuse them — are the general shape.

The tempting correction is that this is a precision problem: better sensors, tighter maths. It is not. State of charge is a hidden variable, and every observable quantity is a function of it together with confounders the device cannot separately measure — internal resistance, temperature, present capacity, cell-to-cell variation. The limit is identifiability, not resolution.

That reframing also explains why the folk advice about "calibrating" a battery by running it flat has a kernel of truth attached to bad advice. A full traverse does give the gauge two anchor points and a fresh capacity estimate, so the percentage genuinely gets more honest. But deep discharges are among the harder things you can do to a lithium-ion cell, so you are buying accuracy about the battery by spending some of the battery. Modern gauges are designed to re-learn opportunistically from partial cycles precisely to avoid asking for that trade.

One last distinction. The percentage and the runtime are different claims with different failure modes. A perfect state of charge still cannot tell you the hours remaining, because that depends on what you are about to do with the device. Runtime prediction is a forecast about the user, wearing the costume of a battery measurement.

• How impedance tracking uses the cell's measured resistance to estimate present capacity without needing a full cycle.
• Why cells in a series pack make this harder: the pack empties when the weakest cell does, not when the average does.
• The same shape elsewhere: any progress bar predicting an unobserved total.

Every term the collection defines is gathered in the glossary.