Why a Thermostat Lets the Temperature Swing

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Nothing is broken, and the reason the symptom is so confusing is that the thing you are adjusting is smaller than the thing you are standing inside. Every simple thermostat switches on below the setpoint and off above it, on purpose, and the gap between those two switching points is the deadband. The temperature then spends its entire life travelling from one edge of that gap to the other and back. So the swing you are complaining about is not an error around the setpoint. It is the deadband, seen from inside. And if the band is two degrees wide, moving the setpoint by one degree moves you from one part of the same swing to another part of the same swing, which is exactly the experience of raising it and getting hot, then lowering it and getting cold.

The useful part is that the band is almost always printed on the box, under a different name. It is the accuracy figure.

Why a controller refuses to switch at the setpoint

Imagine a controller with no band at all, switching the instant the measured temperature crosses the target. The moment it switches on, the temperature rises through the threshold and it switches off. The moment it switches off, the temperature falls back through and it switches on. Add any sensor noise at all and this happens many times a second. The output is a relay buzzing and an element flickering, and nothing in the system has a defined state.

So a band is added. Switch on at the setpoint minus some margin, switch off at the setpoint plus some margin, and in between do nothing. That single change turns an unstable oscillator into a predictable cycle, and it is the simplest possible controller: one comparison, two thresholds, no arithmetic. It is called bang bang control, and it is what is inside almost every temperature controller short of a laboratory instrument.

Three things follow immediately, and the third is the one that matters.

The swing is the band. Not approximately. The temperature settles into a sawtooth whose peak to peak amplitude is exactly the band width, and that amplitude does not depend on the wattage, the tank or room size, the ambient temperature, the insulation or the quality of the hardware. All of those change how long a cycle takes. None of them changes how far it travels. A more powerful heater in a smaller tank does not hold temperature more tightly; it arrives at the same two edges more often.

The duty cycle is set by the load, not the controller. The fraction of time the element runs settles at the steady heat loss divided by the element's capacity, all by itself, with no feedback loop needed. An oversized element runs briefly and often. An undersized one runs almost continuously and eventually cannot reach the upper edge at all, at which point the controller stops cycling and the system is simply at whatever temperature the loss allows.

And the period depends on everything the amplitude does not. The time to cross the band upward is the thermal capacity times the band, divided by the net heating power. The time to fall back is the capacity times the band divided by the heat loss. Add them and the whole period is the capacity times the band times the capacity over the product of the loss and the surplus, which is shortest when the element runs exactly half the time.

The correction: in water, the band is not protecting anything

The standard explanation for why the band exists, and the one I started this page believing, is that it protects the machine. Rapid on and off cycling is genuinely hard on a compressor, which has to start against a pressurised head, and hard on a relay, whose contacts erode a little on every make and break. Give the controller a band and the cycles get longer and fewer, and the equipment lasts.

That is correct, and it is correct about air. Put the numbers in water and it stops being the explanation.

Take the smallest heater we carry: 50 watts, in a 5 gallon tank. Five US gallons is 18.9 kilograms of water, and water takes 4,186 joules per kilogram per kelvin, so the tank is 79,240 joules per kelvin. A plus or minus 1 degree Fahrenheit band is 2 degrees wide, which is 1.111 kelvin. The shortest period the controller can produce, which happens at a 50 percent duty cycle, is four times the capacity times the band divided by the power: four times 79,240 times 1.111, divided by 50, which is 7,043 seconds. One hour and 57 minutes.

Now the largest: 800 watts in a 150 gallon tank. That is 568 kilograms of water, 2.38 million joules per kelvin, and the same arithmetic gives 13,208 seconds, or 3.67 hours.

So the fastest an aquarium heater can possibly cycle, at either end of the range we sell, is measured in hours. There is no compressor, there is no start load, and the relay will make and break perhaps a dozen times a day. Short cycling is not a risk that has been mitigated. It is not physically available.

The reason is one material property. Water holds about 4.19 megajoules per cubic metre per kelvin and air holds about 1,160 joules, a ratio of roughly 3,600. So the same two degree band that gives a six minute cycle in 300 square feet of air gives a two hour cycle in 5 gallons of water. Everything intuitive about thermostats comes from rooms, and water is a different regime.

Which leaves the question of what the band in a water heater is for, and the answer is less flattering: it is the measurement limit, wearing a control limit's clothes. A thermistor and a simple converter can resolve the water temperature to about a degree Fahrenheit, so the controller cannot switch on a tighter threshold than that without switching on noise. The band is the sensor. Which is exactly why the listings print it as an accuracy figure rather than as a control band, and why the two are the same number.

Two listings that publish the band as an accuracy

A SEAOURA 50W small aquarium heater with LED controller publishes, among its specifications, an accuracy of plus or minus 1 degree Fahrenheit, for tanks from 5 to 15 gallons, with an external LED controller, a switch between Celsius and Fahrenheit, and overheat and dry burn protection. Its record carries the accuracy figure in its own list of advantages, as accuracy stated at plus or minus 1 degree Fahrenheit, and is honest enough to add that the accuracy and wattage are maker stated.

Read that figure as a band and you have the whole behaviour of the product: the water will sit in a 2 degree Fahrenheit sawtooth, the element will run for about an hour and rest for about an hour, and the display will read whatever the probe happens to be seeing at that instant on the ramp. None of that is a defect. It is what the published number means. See our SEAOURA 50W heater with LED controller review.

An AZW 800W aquarium heater for 110 to 250 gallon tanks publishes the same stated accuracy of plus or minus 1 degree Fahrenheit at sixteen times the power, with a digital controller showing current and set temperature, double quartz glass and three safety cut offs. That is the figure that produces the 3.67 hour cycle above, and its record is appropriately careful, listing as drawbacks that the wattage and range are maker stated, that the accuracy claim is not independently verified, and that it needs full submersion and flow for accuracy. That last drawback is the subject of the next section and it is the most important sentence on the record. Details in our AZW 800W heater review.

Our own roundup of these is worth reading next to them, because it has the spread in one place. Our guide to aquarium heaters with a guard publishes a thermostat accuracy of plus or minus 1 degree on one pick, within plus or minus 2 degrees Fahrenheit on another, and plus or minus 1.8 degrees Fahrenheit on a third. Those are three different swing widths, from 2 to 4 degrees peak to peak, and the page presents them as three precision ratings rather than as three answers to the question of how far the water will drift. They are the latter.

The number that cannot mean what it says

And then the inconsistency, which is the find of this page and which exists because the same manufacturer splits the two halves of one specification across different listings.

A SEAOURA 50W small aquarium heater for 5 to 10 gallon tanks publishes an adjustment of 0.1 degree steps, a range of 63 to 94 Fahrenheit, an external dual LED controller and a memory function. It publishes no accuracy figure at all. Its stablemate above publishes an accuracy of plus or minus 1 degree and no adjustment step. Put the two together, which no single listing lets you do, and the setting resolution is twenty times finer than the interval the water actually occupies. Nineteen of the twenty available settings land inside one swing of the sawtooth, where the instrument reading the water cannot tell them apart.

To be clear about what is and is not wrong here. The 0.1 degree step is real: at 50 watts into 79,240 joules per kelvin, heating the water by 0.1 Fahrenheit takes 88 seconds, so the step is a physically achievable amount of heat. What it cannot be is a distinguishable setpoint, because the control band is 20 times wider than the step and the measurement that closes the loop is no better. A finer dial on a coarse measurement does not produce finer control. It produces more numbers.

The record for this one is also the best in the group on the thing that matters, listing as its main weakness that the probe must stay fully submerged to read correctly and as a drawback that the probe must be fully submerged to detect correctly. That is the right warning, and the next section is why. Full record in our SEAOURA 50W heater review.

The controller regulates at the sensor, and the sensor is in a gradient

A controller does not regulate the water. It regulates the one point where its probe is, and it has no way of knowing whether that point represents the rest of the tank. In a tank with a heater in it, it very often does not.

Work out how big the gradient is. Take the 300 watt heater, whose rod is 10.4 inches long. With the published cross section of about an inch by seven eighths, the wetted surface is roughly 0.020 square metres. Natural convection from a hot vertical surface into water runs somewhere between about 300 and 1,000 watts per square metre per kelvin depending on the temperature difference and the geometry, and no listing publishes it. Take the range at face value: 300 watts over 0.020 square metres needs a surface to bulk temperature difference somewhere between 15 and 50 kelvin.

So the glass of a running heater is tens of degrees above the water it is sitting in, and a plume of hot water is rising off it continuously. Against a control band of 1.111 kelvin, that gradient is between thirteen and forty five times the entire band. Which means a probe placed in the plume is not slightly wrong. It is reading a different system, and it will satisfy the controller and switch the element off while the far corner of the tank is still cold.

This is why every one of these listings carries a probe warning and why our own guide to aquarium heater wattage already has it right. That guide says to position the heater near good water movement so warmth spreads evenly, to keep the probe submerged and away from the heating element, and that poor flow creates hot and cold pockets that stress fish. All three of those are correct and this page is only adding the magnitude: the pocket a probe can sit in is tens of degrees deep, so flow is not a refinement on a good controller, it is the thing that makes the controller's reading mean anything at all. A small circulation pump does more for temperature stability than any accuracy figure on any box.

The two escapes, and both of them exist in our catalogue

There are exactly two ways out of a sawtooth and we carry one product for each, which is lucky because almost nothing else on the site exposes either.

The first is to stop switching fully on and off. A SEAOURA 300W aquarium heater for 50 to 60 gallon tanks publishes something none of the others do: adjustable power thermostat control that heats fast when the water is cold and then gently near the target. That is proportional control, and it is a different kind of controller rather than a better version of the same one. If the delivered power falls smoothly as the error shrinks, the system can approach the setpoint and stay there instead of crossing it, and the sawtooth collapses towards a line. It is the same idea as the proportional, integral and derivative control that our barbecue temperature controllers guide describes on pellet grills, where a variable speed fan replaces an on and off relay. The listing does not say how many power levels it has or over what error band it tapers, which is the specification that would tell you how much of the swing it removes, but the mechanism named is the right one. Record in our SEAOURA 300W heater review.

The second is to be given the band itself, and exactly one product in our catalogue does that. A SEAOURA aquarium chiller fan with timer and temperature control publishes fully customisable start and stop thresholds across a 60 to 104 Fahrenheit range. Start and stop as two separate numbers is the deadband, handed to the user as a setting, and it is the only place on this site where the quantity this whole page is about is adjustable at all.

Which makes the trade visible, so it is worth stating. Narrow the gap between your start and stop thresholds and the water holds closer to target, and the fan starts and stops more often. Widen it and the fan runs in long calm stretches and the water drifts further. For a fan that is an easy call and you should set it narrow, because a brushless fan has no start load worth protecting and the only cost of frequent cycling is the noise of it changing state. For a compressor it would be the opposite call. Our SEAOURA chiller fan review has the rest, and the separate reason that machine can only ever move the water 3 to 7 degrees is worked out in why an evaporative cooler runs out of degrees in humid air.

Problems in our own records

Three worth reporting.

The first is the split specification above. Two listings from the same brand, both 50 watts, one publishing a 0.1 degree adjustment step with no accuracy and the other publishing a plus or minus 1 degree accuracy with no step. Each number is harmless alone and together they are a contradiction, and the catalogue is arranged so that a buyer never sees them together.

The second is a sizing conflict between those same two 50 watt heaters. One is rated for 5 to 10 gallon tanks and the other for 5 to 15, with the same 50 watts and the same 63 to 94 Fahrenheit range. Wattage is what sets how much heat loss a heater can replace, so the same element cannot correctly serve a tank range 50 percent wider. One of the two ratings is optimistic and the listings give no way to tell which.

The third is a vocabulary problem across the whole site rather than a defect in any record. The phrase "plus or minus" appears in 33 of our published pages, almost always on a thermometer or a controller, and it is always introduced as accuracy. For an instrument that only reads, accuracy is the right word. For an instrument that reads and then switches, the same number is also the width of the interval the thing it controls will occupy, and those are different claims about different quantities. We have never drawn that distinction anywhere, and the result is 33 pages where a specification is reported at half its actual significance.

The honest limit, and the free technique that beats the purchase

The specification that would settle this is the deadband itself, stated as a band and separately from the sensor accuracy, and no product we carry publishes it that way. Several publish the number and call it accuracy, two publish a setting resolution instead, and one lets you set it without ever naming it. So you cannot shop for a tighter band. You can only read an accuracy figure as a band, which is the single most useful reading trick in this category, and it costs nothing.

Then two moves that beat buying a more accurate controller, and both follow from the arithmetic rather than from preference.

Fix the measurement, not the controller. The band cannot be tighter than the sensor can resolve, so a controller claiming a finer band than its probe can see is claiming nothing. But a probe in moving water, away from the element, placed where the organism or the food actually is, converts a reading from one corner of a gradient into a reading of the system. That is a placement decision and it is free, and against a gradient that can be tens of degrees deep it is worth more than any accuracy claim at any size. A second, independent thermometer at the far end of the tank is the simplest instrument you can add and the only way to find out whether the first one is telling the truth.

And add thermal mass or reduce loss rather than adding power. The swing is the band and the band does not move, so the only thing left to improve is how gently the system travels across it. More thermal mass and less heat loss both lengthen the cycle, which means fewer transitions and a gentler rate of change at every instant, which is what actually matters to anything living in the water. Insulating the back and sides of a tank, or keeping a lid on it, lowers the loss and therefore the duty cycle, and it does so without touching a single published figure. The temperature still travels the same two degrees. It just takes four hours to do it instead of two.