Resistance Heaters at the Wrong Voltage

Why this matters

A resistance element is the simplest load in the building: a fixed resistance that turns every watt it draws into heat. That simplicity is what makes it misbehave on the wrong voltage in a way people do not expect. Its power does not scale with voltage; it scales with voltage squared. A 4,500 W water heater element rated at 240 V makes about 3,380 W on a 208 V commercial or apartment service, roughly three quarters of its label, and the tank recovers a quarter slower for its whole life. The customer calls it a weak heater. The element is fine. The arithmetic below is how you show it, and how you catch the opposite case, where an element on too high a voltage burns itself out.

Safety before any reading

Measuring an element's resistance is done with the circuit off and proved dead, never on a live element. Open the disconnect or breaker, lock and tag it, then prove the element terminals dead with a tester checked on a known live source before and after, per NFPA 70E Article 120 (120.5 in the 2021 edition, renumbered in 2024), with work practices at 29 CFR 1910.333(b)(2). Lift one lead off the element before reading ohms, or the meter reads the element in parallel with whatever else is on the circuit. Opening a water heater's element cover exposes terminals that may share a compartment with a thermostat fed from the other leg, so the proving step covers every terminal in the compartment, not only the one you came for.

Work on the branch circuit itself (conductors, breakers, the service voltage) is an electrician's. If you are not qualified for it under your jurisdiction's licensing, recognize what you are seeing and call one.

Before power goes back on, the tank must be full: open a hot tap and run it until water flows steadily with no sputtering air. An element energized in air (a dry fire) can burn out in seconds. Close the element cover before the breaker closes, stand to the side of the panel as it closes, and confirm current on the element with a clamp meter once it is energized.

Why voltage squared

The element's resistance is set when it is made and changes only modestly with temperature for the alloys used in heating elements. Treat it as fixed. Then two forms of the power formula, both from Ohm's Law + Power Formula for Trades Reference, do all the work:

• Resistance from the rating: R = V squared / P
• Power at any other voltage: P = V squared / R

Because R is fixed, current falls when voltage falls (I = V / R), and power is voltage times that smaller current. Both drop together, so power drops by the square of the voltage ratio. The shortcut follows: new power = rated power x (new voltage / rated voltage) squared.

That squared is the whole point. Scaling the power by the voltage ratio alone, as if current stayed at the nameplate figure, overstates what the element makes.

The 4,500 W element on 208 V, line by line

ELEMENT RATED 4,500 W AT 240 V

resistance   R = 240 x 240 / 4,500
               = 57,600 / 4,500        = 12.8 ohms

at 240 V     I = 240 / 12.8            = 18.75 A
             P = 240 x 18.75           = 4,500 W

at 208 V     I = 208 / 12.8            = 16.25 A
             P = 208 x 16.25           = 3,380 W

shortcut     (208 / 240) squared       = 0.751
             4,500 x 0.751             = 3,380 W  (check)

share of label   3,380 / 4,500         = 75 percent
WRONG, linear    4,500 x 208 / 240     = 3,900 W

Two independent routes land on 3,380 W, which is the check. The linear version, 3,900 W, is what you get by assuming the current stays put while the voltage drops. It overstates the output by about 520 W, roughly 15 percent of the real figure, and it is the number people quote when they have not done the arithmetic.

A cold resistance reading on the bench will usually sit close to the calculated 12.8 ohms. If it reads open (infinite), the element is burned through. If it reads a small fraction of that, or there is any continuity from a terminal to the element's sheath or the tank, the element is shorted or grounded and is replaced, whatever its rating.

What 75 percent costs in recovery

Recovery is how many gallons an hour the tank can heat through a given rise. For a resistance element every watt goes into the water, so:

• Gallons per hour = (watts x 3.412 BTU/h per W) / (8.33 lb/gal x rise in F)

Take a 90 F rise, cold water at 50 F heated to 140 F (both illustrative):

• At 240 V: 4,500 x 3.412 = 15,354 BTU/h. 8.33 x 90 = 749.7 BTU per gallon. 15,354 / 749.7 = 20.5 gallons per hour.
• At 208 V: 3,380 x 3.412 = 11,533 BTU/h. 11,533 / 749.7 = 15.4 gallons per hour.
• Check: 15.4 / 20.5 = 0.75, the same ratio as the power. It has to be, because recovery is power divided by a constant.

Most residential electric tanks with two elements run only one at a time, so the 15.4 gallons per hour is the whole tank's recovery, not one element's share. A family that empties the tank on back-to-back showers now waits roughly a third longer for it to come back: 20.5 / 15.4 = 1.33. That is the complaint, and the fix is not a new element of the same rating.

Elements made for 208 V

The usual remedy is an element rated at the voltage actually present. Elements are sold with a 208 V rating, and many heaters list both voltages on their plate. Two cautions travel with that:

• A higher wattage at 208 V draws more current. Restoring the full 4,500 W at 208 V means 4,500 / 208 = 21.6 A, up from 16.25 A. Whether the branch circuit, its breaker and the heater's own wiring and thermostats are rated for that is a code and listing question for an electrician and the heater's manual, not something this card can answer.
• The heater's listing governs. Fitting an element of a wattage the heater's label does not list can void its listing and its warranty. Read the rating plate and the replacement chart in the manual before ordering.

The opposite direction: too much voltage

The square works the other way, and that direction burns things.

• 240 V element on 277 V (a common commercial voltage): (277 / 240) squared = 1.332. A 4,500 W element makes about 5,995 W and draws 277 / 12.8 = 21.6 A. A third more power than it was designed to shed into the water, and a sheath running hotter than its rating. Do not install it.
• 120 V element on 240 V: (240 / 120) squared = 4. Four times the rated power. It fails, often fast and with damage to the tank or the terminals.
• 240 V element on 120 V: a quarter of the rated power. Safe for the element, useless for the customer.

The 277 V case is worth remembering because both 240 and 277 V show up in commercial buildings, and the element's physical size gives no hint of which voltage it was built for. The stamp on the element and the plate on the heater are the only evidence.

The same arithmetic on other resistance loads

Baseboard heat. A 1,000 W, 240 V baseboard on a 208 V circuit makes 1,000 x 0.751 = 751 W. A room sized for four of them now gets 3,004 W where the plan assumed 4,000 W, and on the coldest days the thermostat cannot be satisfied. Baseboards are sold rated at 208 V for exactly this reason.

Electric strip heat in an air handler. A 10 kW strip kit rated at 240 V makes 7.5 kW on 208 V (10 x 0.751 = 7.51). Many kits print both outputs on their label; when the label gives a 208 V figure, use the label rather than the calculation, because it reflects the kit as tested. For the BTU and tons side of the same number, see Energy and Power Units: BTU, Kilowatts, Tons and Horsepower.

Where the rule does not apply. Motors, compressors, electronic loads and anything with a power supply do not behave as fixed resistances; their current can rise as voltage falls. The square law is for resistance heating only: water heater elements, baseboard, strip heat, duct heaters, and resistance wire in heat trace with a fixed resistance per foot. Self-regulating heat cable changes its resistance with temperature by design and follows its own data sheet.

Low voltage or a bad connection: the current tells you

With the element's cold resistance known, a running current reading separates two problems that both look like a weak heater. Divide the voltage at the supply by the current and compare the result with the element's resistance.

• The voltage really is low. Supply reads 206 V and the clamp reads 16.1 A. 206 / 16.1 = 12.8 ohms, the element's own resistance, so nothing else is in the circuit. The element is making 206 x 16.1 = 3,317 W, and the answer is the service voltage.
• Something else is in series. Supply reads 240 V but the clamp reads 18.2 A rather than the 18.75 A a healthy circuit would draw. 240 / 18.2 = 13.19 ohms, so 13.19 - 12.8 = 0.39 ohms sits somewhere outside the element. That small resistance is a loose or corroded terminal, and it is dissipating 18.2 x 18.2 x 0.39 = 129 W at one connection, which is a terminal block on its way to charring. The element itself is getting only 18.2 x 18.2 x 12.8 = 4,240 W.

The second case is the dangerous one, because the shortfall in heat is small and the heat at the connection is not. Discoloration, a brittle wire jacket or a melted terminal block at the element confirms it. The fix is the connection and whatever it has damaged, with power off and proved dead again before anyone touches it. Both readings are taken on an energized heater, so they belong to whoever is qualified for energized measurement at that voltage.

How to know which voltage you have

Measure, do not assume. A service described as "240" may be 208 V between phases on a three-phase wye, which is common in apartment buildings, offices and light commercial. The difference between 208 and 240 V is visible on any meter set to AC volts across the two legs feeding the heater, read under load if you can. Measuring line voltage at a panel or a disconnect is energized work: it is for a qualified person in the protective equipment the voltage and the panel's arc-flash labeling require. On a ticket, record the voltage you measured, the element's stamped rating, and the resistance you read cold, three lines that let the next tech check your arithmetic without reopening the tank.

References

• NFPA 70E, Article 120, current edition, for establishing an electrically safe work condition
• 29 CFR 1910.333 for electrical safety-related work practices
• Water heater, baseboard and strip heat manufacturer rating plates and replacement charts
• See related: Ohm's Law + Power Formula for Trades Reference; Energy and Power Units: BTU, Kilowatts, Tons and Horsepower