How to convert between ampere hour and watt hour

The conversion between ampere hour (Ah) and watt hour (Wh) requires consideration of the battery voltage (V), as watt hour is a unit of energy (power x time), while ampere hour is a unit of charge (current x time). The following are detailed conversion methods and examples:

1. Conversion formula

Watt hour (Wh)=voltage (V) x ampere hour (Ah)
or
ampere hour (Ah)=watt hour (Wh) ÷ voltage (V)

2. Conversion steps

1. Determining battery voltage: The nominal voltage of the battery (such as 3.7V, 12V, 24V, etc.) is a key parameter for conversion, usually indicated in the battery casing or specification sheet.

2. Apply formula calculation:

   • If the ampere hour (Ah) and voltage (V) are known, calculate the watt hour (Wh):
     Wh=V × Ah
   • If the watt hour (Wh) and voltage (V) are known, calculate the ampere hour (Ah):
     Ah=VWh

3. Actual examples

Example 1: Mobile phone battery

• Given conditions:
  Battery capacity=4000mAh (i.e. 4Ah), voltage=3.7V
• Calculate watt hour (Wh):
  Wh=3.7V × 4Ah=14.8Wh
• Meaning: This battery can provide 14.8 watt hours of energy. If the device consumes 5W, the theoretical endurance time is; 14.8Wh ÷ 5W=2.96 hours.

Example 2: Electric vehicle battery

• Given conditions:
  Battery energy=60kWh (i.e. 60000Wh), voltage=400V
• Calculate ampere hour (Ah):
  Ah=400V60000Wh=150Ah
• Meaning: The battery capacity is 150 ampere hours. If the motor power is 20 kW, the theoretical endurance time is; 60kWh ÷ 20kW=3 hours.

Example 3: 12V lead-acid battery

• Known conditions:
  Battery capacity=100Ah, voltage=12V
• Calculate watt hour (Wh):
  Wh=12V × 100Ah=1200Wh (i.e. 1.2kWh)
• Meaning: This battery can store 1.2 kWh of energy. If it is used to power a 100W device, the theoretical endurance time is; 1200Wh ÷ 100W=12 hours.

4. Precautions

1. Accuracy of voltage: When converting, the nominal voltage of the battery must be used (such as 3.7V for lithium batteries and 12V for lead-acid batteries). If the voltage fluctuates (such as increasing during charging and decreasing during discharging), the average voltage or rated voltage should be used.

2. Unified Unit:

   • The conversion between ampere hour (Ah) and milliampere hour (mAh) is: 1Ah=1000mAh.
   • The conversion between watt hour (Wh) and kilowatt hour (kWh) is: 1kWh=1000Wh.

3. The difference between reality and theory: The conversion result is the theoretical value, and the actual range or energy output may be reduced due to factors such as battery efficiency, temperature, discharge rate, etc.

5. Quick conversion table

6. Summary

• Ampere hour (Ah) reflects the battery capacity (charge), and watt hour (Wh) reflects the battery energy.
• Conversion key: It is necessary to know the battery voltage, and the formula is; Wh=V × Ah.
• Application Scenario:
  • Computing device battery life: Divide watt hours by device power.
  • Compare the energy of batteries with different voltages: convert to watt hours uniformly.
  • Air transportation restrictions: International regulations require special approval for lithium batteries with energy exceeding 160Wh.

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