Heating Time and cost Calculations with Pahlen Electric Heaters

Hot tubs:

• 200 cm round: 1220L
• 225 cm round: 1660L

Electric heaters:

• Pahlen 9 kW
• Pahlen 12 kW

Electricity cost:

• 1 kWh = €0.25

Formulas Used

$$Q = m \cdot c \cdot \Delta T$$ $$Q_{kWh} = \frac{m \cdot 4.186 \cdot \Delta T}{3600}$$ $$t = \frac{Q_{kWh}}{P}$$

Heating cost:

$$Cost = Q_{kWh} \times 0.25$$

Where:

• m = water mass (kg ≈ liters)
• c = 4.186 kJ/kg·°C
• ΔT = temperature difference
• P = heater power (kW)

200 cm Round Hot Tub – 1220L (9 kW)

Scenario 1: 10°C → 37°C

Temperature increase:
27°C

Energy required:

$$Q = 38.29 \text{ kWh}$$

Heating time:

$$t = 38.29 / 9 = 4.25 \text{ h}$$

• Ideal: 4.25 hours
• Real conditions: 5.7 – 6.6 hours

Heating cost:

$$38.29 \times 0.25 = €9.57$$

Scenario 2: 4°C → 37°C

Temperature increase:
33°C

Energy required:

$$Q = 46.82 \text{ kWh}$$

Heating time:

$$t = 46.82 / 9 = 5.20 \text{ h}$$

• Ideal: 5.2 hours
• Real conditions: 7.0 – 8.1 hours

Heating cost:

$$46.82 \times 0.25 = €11.70$$

Scenario 3: 4°C water + (-10°C outside)

Real winter conditions:

• Approximate heating time: 8.5 – 10 hours
• Estimated cost: €13 – €15

225 cm Round Hot Tub – 1660L (12 kW)

Scenario 1: 10°C → 37°C

Energy required:

$$Q = 52.06 \text{ kWh}$$

Heating time:

$$t = 52.06 / 12 = 4.34 \text{ h}$$

• Ideal: 4.3 hours
• Real conditions: 5.9 – 6.7 hours

Heating cost:

$$52.06 \times 0.25 = €13.02$$

Scenario 2: 4°C → 37°C

Energy required:

$$Q = 63.59 \text{ kWh}$$

Heating time:

$$t = 63.59 / 12 = 5.30 \text{ h}$$

• Ideal: 5.3 hours
• Real conditions: 7.2 – 8.2 hours

Heating cost:

$$63.59 \times 0.25 = €15.90$$

Scenario 3: 4°C water + (-10°C outside)

Real winter conditions:

• Approximate heating time: 9 – 11 hours
• Estimated cost: €18 – €21

Summary

1220L + 9 kW

• Normal heating: ~4–6 h
• Winter heating: ~8–10 h
• Typical heating cost: €10–15

1660L + 12 kW

• Normal heating: ~4–7 h
• Winter heating: ~9–11 h
• Typical heating cost: €13–21