Ofuro Hot Tub Heating Calculations – 640L

Hot tub volume:

• 640L

Heating systems:

• 20 kW external wood-burning stove
• 6 kW Pahlen electric heater

Electricity price:

• 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)

Scenario 1: 10°C → 37°C

Temperature increase:
27°C

Energy required:

$$Q = 640 \times 4.186 \times 27$$ $$Q = 20.09 \text{ kWh}$$

20 kW External Wood Stove

Heating time:

$$t = 20.09 / 20$$ $$t = 1.00 \text{ hour}$$

• Ideal: 1.0 hour
• Real conditions: 1.3 – 1.6 hours

Estimated wood consumption:

• ~5–7 kg dry hardwood

6 kW Pahlen Heater

Heating time:

$$t = 20.09 / 6$$ $$t = 3.35 \text{ hours}$$

• Ideal: 3.3 hours
• Real conditions: 4.5 – 5.2 hours

Heating cost:

$$20.09 \times 0.25 = €5.02$$

Scenario 2: 4°C → 37°C

Temperature increase:
33°C

Energy required:

$$Q = 24.55 \text{ kWh}$$

20 kW External Wood Stove

Heating time:

$$t = 24.55 / 20$$ $$t = 1.23 \text{ hours}$$

• Ideal: 1.2 hours
• Real conditions: 1.6 – 2.0 hours

Estimated wood usage:

• ~6–9 kg dry hardwood

6 kW Pahlen Heater

Heating time:

$$t = 24.55 / 6$$ $$t = 4.09 \text{ hours}$$

• Ideal: 4.1 hours
• Real conditions: 5.5 – 6.3 hours

Heating cost:

$$24.55 \times 0.25 = €6.14$$

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

20 kW Wood Stove

• Approximate heating time: 2.0 – 2.5 hours
• Estimated wood usage: 8–12 kg

6 kW Pahlen Heater

• Approximate heating time: 6.5 – 8.0 hours
• Estimated electricity cost: €7 – €9

Summary

640L + 20 kW Wood Stove

• Very fast heating
• Suitable for winter use
• Typical heating time: 1–2.5 hours

640L + 6 kW Electric Heater

• Quiet and convenient
• Slower winter performance
• Typical heating time: 3–8 hours