The Fractional Watt Problem: Eight Smart Plugs, One Calibrated Logger, and the Numbers in Between

Smart plugs that measure energy are now ordinary retail stock, sold in the same shops as extension leads. The promise is simple: put one between appliance and socket, and the app will tell you what the appliance costs. For a British household trying to understand a tariff, a heat pump's auxiliary load or a tumble dryer's real appetite, that is an attractive proposition. But a plug is not a meter in the fiscal sense. It is a small, cheap, thermally constrained device with a shunt, an analogue front end and a radio. Its arithmetic deserves the same scrutiny as its switching.

The bench, the logger and the loads

Eight 13 A smart plugs were bought at UK retail between spring and autumn 2026, spanning Wi-Fi, Zigbee and Matter models. Each was left on a bench supply at 230 V for an hour before testing, then checked against a calibrated power analyser with 0.1 W resolution and a stated accuracy of plus or minus 0.2% of reading plus 0.1 W. The reference was not a laboratory-owned artefact; it was a traceable logger hired for the exercise, which is the practical limit for a publication test.

Four load families were used. A 2.2 kW kettle represented a resistive load near the top of a domestic plug's range. A 40 W shaded-pole fan represented a small inductive load with a power factor well below unity. A group of standby loads — a television box, a games console in rest mode and a phone charger with no phone attached — covered the region below 5 W. A 700 W thermostatically controlled oil-filled radiator provided a cycling load whose duty cycle changed with room temperature.

Each plug was run for at least 30 minutes per load, with the reference and the plug's own app recorded at the start and end. For the cycling load, the run was extended to four hours. The plugs were not opened; the test was of the product as sold, including its firmware and cloud service.

Where the watts drift

At 2.2 kW, the eight plugs were reassuringly close. Seven reported within 1% of the reference; one read 1.6% high. For a kettle, that is unlikely to change a decision. At 40 W on the fan, the picture widened. The spread was from 2.8% low to 4.1% high, and the worst error was not on the cheapest plug. At 10 W, the absolute errors were small but the relative errors were not: one plug read 8.9 W, another 11.4 W.

Below 3 W, the behaviour changed by design. Three plugs reported zero watts for loads the reference could still see at 0.6 W to 1.2 W. Two others flickered between 0 W and 1 W. This is not necessarily a fault. A plug has to power its own radio and remain safe; a measurement floor is a reasonable engineering choice. The problem is that the floor is rarely stated in the app or the manual. A household using plug data to hunt standby waste may conclude that a device is off when it is merely beneath the plug's horizon.

The power-factor figures were the least trustworthy part of the dataset. On the resistive kettle, most plugs reported 1.00, which is correct. On the fan, the reference measured a power factor near 0.52; the plugs reported between 0.48 and 1.00. Two models appeared to assume unity whenever the current was small. One reported a plausible figure but with enough noise to make a single reading meaningless. Power factor is not a number most domestic users need, but it is increasingly surfaced in apps and exported to home-assistant dashboards. A confident wrong number is worse than an absent one.

The kilowatt-hour is a story, not a reading

The kWh figure is where plug-level monitoring becomes a decision tool. It is also where the arithmetic is most hidden. Internally, a plug accumulates energy from its own samples. Externally, the app usually shows a cloud-aggregated total, rounded to two decimal places, refreshed every minute or five minutes. The two are not the same object.

On the cycling radiator, the reference logged 2.84 kWh over four hours. The plugs' local totals ranged from 2.71 kWh to 2.93 kWh. Their app totals, read at the same moment, ranged from 2.70 kWh to 2.96 kWh. The differences are small in percentage terms, but they are not random: the app tended to smooth the duty cycle, understating short bursts and overstating the tail. For a load that switches every few minutes, a one-minute cloud sample is a poor integrator.

The rounding compounds the problem. A plug that reports 0.01 kWh resolution cannot distinguish a 0.004 kWh event from a 0.014 kWh one. Over a day, those fractions accumulate. Over a year, a 0.5 W bias becomes 4.4 kWh — not a large sum at current domestic rates, but enough to matter if the same bias is applied across a house full of plugs and then used to compare appliances.

What the app does with the error

Smart-plug apps are designed for reassurance, not metrology. Graphs are smoothed, labels are rounded and the unit of display is chosen for legibility. One app showed a live wattage to one decimal place but a daily total to two; another showed a daily total to three but updated it only when the app was opened. Neither is dishonest. Both make the underlying uncertainty harder to see.

The cloud layer adds a second source of drift. When a plug loses Wi-Fi, it may buffer readings and upload them later, or it may simply miss them. In a British home with a solid full-fibre connection, that matters less than in a stone-walled cottage with a weak access point. But the app rarely says which has happened. A flat line in the energy graph can mean zero load, a dropped connection or a firmware update. The user is left to infer.

What plug-level data can support

None of this makes smart plugs useless. For relative comparisons over days and weeks — does the old fridge use more than the new one, does the dehumidifier earn its place, is the television box really off — they are convenient and often good enough. For absolute billing, they are not. A plug is not a MID-certified meter, and its specification rarely states accuracy below 5 W or across power factors away from unity.

The practical rule is to use the plug for the shape of a load, not the last digit of its total. Cross-check anything that matters against a calibrated logger or, for whole-house questions, the smart meter's own display. Treat a reported 0.00 W as below the measurement floor, not as proof of disconnection. And when an app gives a power factor to two decimal places, ask what the plug actually measured before believing it.

The plug's own arithmetic is a useful instrument. It is not an audit. In a British home trying to make sense of 2026 tariffs and retrofit decisions, that distinction is the difference between evidence and a plausible number.