Electrical Thermal Storage (ETS) Calculator: Sizing Formulas & Worked Examples

The direct answer for sizing an Electrical Thermal Storage (ETS) heater is that the required charging power ($P_{charge}$) must exceed the building's daily heat loss divided by your utility's off-peak charging window, adjusted for storage efficiency. For a standard 15m² insulated room in a cold climate, expect a realistic magnitude between 3 kW and 6 kW. If your calculation yields over 15 kW for a single residential zone, stop: the building envelope is too leaky for ETS to be economically viable without a massive service entrance upgrade.

The Core ETS Sizing Formula and Symbol Definitions

To size an ETS unit (often called a storage radiator or thermal battery), you must bridge thermodynamics and electrical power. The master formula calculates the required electrical input power in kilowatts (kW) based on the room's thermal characteristics and the utility's time-of-use tariff window.

Symbol	Definition	Standard Unit
$P_{charge}$	Required electrical charging power (the size of the ETS unit you must buy)	kilowatts (kW)
$U$	Overall heat transfer coefficient of the room envelope (insulation quality)	W / (m²·K)
$A$	Total surface area of the room envelope (walls, ceiling, floor, windows)	square meters (m²)
$\Delta T$	Design temperature difference (Target indoor temp minus Outdoor design temp)	Kelvin (K) or °C
$t_{offpeak}$	Available off-peak charging window provided by the utility	hours (h)
$\eta$	Storage efficiency factor (accounts for standby heat loss from the unit's casing)	dimensionless (0.80 - 0.95)

When This Formula Applies (and When It Breaks)

This formula assumes steady-state heat loss and uniform insulation across the calculated surface area. It is designed for modern, fan-assisted ETS units with high-density magnetite or ceramic cores that charge exclusively during off-peak hours. In 2026, smart ETS units integrate with dynamic time-of-use tariffs (like Octopus Agile), but the baseline thermodynamic sizing remains identical.

Unit Mistakes That Break the Calculation

• Forgetting the 1000 divisor: The numerator calculates total daily Watt-hours (Wh). If you forget to divide by 1000, your $P_{charge}$ will be 1000x too large, leading you to specify a 3,000 kW industrial boiler instead of a 3 kW residential heater.
• Mixing Fahrenheit and Celsius: $\Delta T$ must be in Kelvin or Celsius. A $\Delta T$ of 40°F is roughly 22°C. Plugging '40' directly into the formula will oversize the unit by nearly 80%.
• Using Volume instead of Area: Heat escapes through surfaces ($A$ in m²), not through the air volume. Using cubic meters for $A$ will destroy the math.

Realistic Answer Magnitudes

For a well-insulated modern home (Passivhaus or similar), $U$ is very low (~0.15), yielding $P_{charge}$ values around 0.5 kW to 1.5 kW. For a standard 1990s-built home, expect 3 kW to 8 kW per room. If your result exceeds 15 kW for a single room, the math is telling you that electric thermal storage is the wrong technology for that specific building envelope.

Worked Example 1: Sizing a Residential Living Room ETS Unit

Scenario: A living room in a 1980s insulated house. Dimensions: 4m wide × 5m long × 2.5m high. The local utility offers a 7-hour off-peak window (e.g., 00:30 to 07:30). Target indoor temp is 21°C; outdoor design temp is -5°C.

Step 1: Calculate Surface Area ($A$)
Floor/Ceiling: $2 \times (4 \times 5) = 40 \text{ m}^2$
Long Walls: $2 \times (5 \times 2.5) = 25 \text{ m}^2$
Short Walls: $2 \times (4 \times 2.5) = 20 \text{ m}^2$
Total $A = 40 + 25 + 20 = 85 \text{ m}^2$

Step 2: Identify Known Variables
$U = 1.2 \text{ W/(m}^2\cdot\text{K)}$ (average for older insulated walls/single-glaze mix)
$\Delta T = 21 - (-5) = 26 \text{ K}$
$t_{offpeak} = 7 \text{ hours}$
$\eta = 0.85$ (standard for a modern fan-assisted ETS with good casing insulation)

Step 3: Execute the Formula
$$P_{charge} = \frac{1.2 \cdot 85 \cdot 26 \cdot 24}{1000 \cdot 7 \cdot 0.85}$$
Numerator (Daily Heat Loss in Wh): $1.2 \times 85 \times 26 \times 24 = 63,648 \text{ Wh}$
Denominator (Effective Charge Hours): $1000 \times 7 \times 0.85 = 5,950$
$$P_{charge} = \frac{63,648}{5,950} = 10.697 \text{ kW}$$

Result: You need an ETS unit capable of drawing 10.7 kW during the 7-hour window to maintain 21°C on the coldest day of the year.

Worked Example 2: High-Ceiling Workshop ETS Sizing

Scenario: A drafty metal garage workshop. Dimensions: 6m × 8m × 3m. The utility only offers a 4-hour winter off-peak window. Target temp is 15°C; outdoor design temp is -10°C.

Step 1: Calculate Surface Area ($A$)
$A = 2(6 \times 8) + 2(6 \times 3) + 2(8 \times 3) = 96 + 36 + 48 = 180 \text{ m}^2$

Step 2: Identify Known Variables
$U = 2.5 \text{ W/(m}^2\cdot\text{K)}$ (uninsulated metal building)
$\Delta T = 15 - (-10) = 25 \text{ K}$
$t_{offpeak} = 4 \text{ hours}$
$\eta = 0.75$ (high standby losses expected in a drafty, high-volume space)

Step 3: Execute the Formula
$$P_{charge} = \frac{2.5 \cdot 180 \cdot 25 \cdot 24}{1000 \cdot 4 \cdot 0.75}$$
Numerator: $2.5 \times 180 \times 25 \times 24 = 270,000 \text{ Wh}$
Denominator: $1000 \times 4 \times 0.75 = 3,000$
$$P_{charge} = \frac{270,000}{3,000} = 90 \text{ kW}$$

Result: 90 kW. This is a massive commercial load requiring a 3-phase 400V supply and heavy-gauge feeders. The formula successfully prevents a costly mistake: do not install ETS in this building without first adding spray foam insulation to drop the $U$-value below 0.5.

Rearranged Forms for Field Troubleshooting

When auditing an existing ETS installation that is failing to reach temperature, you rarely need to solve for $P_{charge}$. Instead, use these rearranged forms to diagnose the failure:

• Solving for Storage Efficiency ($\eta$): Use this if the unit is fully charged but the room is cold. It reveals how much heat is escaping the casing rather than the room.
  $$\eta = \frac{U \cdot A \cdot \Delta T \cdot 24}{1000 \cdot t_{offpeak} \cdot P_{charge}}$$
• Solving for Required Off-Peak Time ($t_{offpeak}$): Use this when a utility changes their tariff window and you need to know if the existing heater can still cope.
  $$t_{offpeak} = \frac{U \cdot A \cdot \Delta T \cdot 24}{1000 \cdot \eta \cdot P_{charge}}$$
• Solving for Maximum Allowable U-Value ($U$): Use this during renovation planning to find the target insulation level required to make a specific ETS unit viable.
  $$U = \frac{1000 \cdot P_{charge} \cdot t_{offpeak} \cdot \eta}{A \cdot \Delta T \cdot 24}$$

Decision Path: Picking the Right ETS Unit and Charge Controller

Once you have your $P_{charge}$ value, follow this exact decision tree to select the hardware, wire gauge, and breaker size. Do not guess; let the math dictate the bill of materials.

Calculated $P_{charge}$	Circuit & Wire Specification	Concrete Hardware Pick (2026 Market)
< 3.0 kW	Standard 15A/120V (US) or 13A/230V (UK/EU) plug-in receptacle. No dedicated hardwire needed.	Stiebel Eltron ETS 20 (2.0 kW) or equivalent compact ceramic storage unit.
3.0 kW to 7.0 kW	Dedicated 30A/240V (US) or 32A/230V (EU) circuit. Use 10 AWG THHN copper in conduit, or 10/2 NM-B.	Dimplex Quantum QM100 (or QM150 depending on exact kW). Includes built-in Wi-Fi smart charge controller.
7.0 kW to 15.0 kW	Dedicated 60A/240V breaker. Use 6 AWG THHN copper. Alternatively, split into two 30A circuits to balance the panel.	Two Dimplex Quantum QM070 units linked via the Dimplex app to act as a single distributed thermal battery.
> 15.0 kW	STOP. Do not install ETS. The required 100A+ dedicated subpanel and potential 400A service entrance upgrade destroys the ROI.	Pivot to an Air Source Heat Pump (ASHP) like the Mitsubishi Hyper-Heat series, which delivers 300% COP compared to the 100% efficiency of ETS.

For deeper reading on building envelope heat loss standards that feed the $U$ and $\Delta T$ variables, refer to the ASHRAE Handbook of Fundamentals. For baseline electrical safety and circuit sizing for electric heating equipment, consult the US Department of Energy's guidelines on electric resistance heating.