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Convert energy in watt-hours (Wh) to battery capacity in amp-hours (Ah). Useful for understanding battery specs and sizing replacements.
Where Ah is capacity in amp-hours, Wh is energy in watt-hours, and V is voltage in volts.
A laptop battery rated 56 Wh at 11.1V:
Ah = 56 ÷ 11.1 = 5.05 Ah (5050 mAh)
| Wh | 3.7V | 5V | 7.4V | 11.1V | 12V |
|---|---|---|---|---|---|
| 10 Wh | 2.70 Ah | 2.00 Ah | 1.35 Ah | 0.90 Ah | 0.83 Ah |
| 20 Wh | 5.40 Ah | 4.00 Ah | 2.70 Ah | 1.80 Ah | 1.67 Ah |
| 37 Wh | 10.00 Ah | 7.40 Ah | 5.00 Ah | 3.33 Ah | 3.08 Ah |
| 50 Wh | 13.50 Ah | 10.00 Ah | 6.76 Ah | 4.50 Ah | 4.17 Ah |
| 74 Wh | 20.00 Ah | 14.80 Ah | 10.00 Ah | 6.67 Ah | 6.17 Ah |
| 100 Wh | 27.00 Ah | 20.00 Ah | 13.50 Ah | 9.00 Ah | 8.33 Ah |
| 200 Wh | 54.00 Ah | 40.00 Ah | 27.00 Ah | 18.00 Ah | 16.67 Ah |
| 500 Wh | 135.00 Ah | 100.00 Ah | 67.60 Ah | 45.00 Ah | 41.67 Ah |
Converting watt-hours (Wh) to amp-hours (Ah) translates a battery's total energy capacity into its charge capacity at a specific voltage. Watt-hours represent total energy – the product of power and time – while amp-hours represent charge flow over time at a given voltage. The formula Ah = Wh ÷ V is derived from the fundamental relationship P = V × I (power equals voltage times current). This conversion is essential for battery sizing, replacement matching, and comparing batteries that operate at different voltages. For example, a 100 Wh battery at 12V has an 8.33 Ah capacity, but at 5V the same energy yields 20 Ah. Wh provides a voltage-independent energy measurement, while Ah is voltage-dependent and only useful for comparing batteries of the same voltage. Understanding both units is critical for solar system design, UPS sizing, electric vehicle range calculations, and complying with airline lithium battery regulations.
Locate the Wh rating on the battery label, datasheet, or device specifications. Laptop batteries typically show this prominently (e.g., 56 Wh, 72 Wh, 99.9 Wh). For power banks, you may need to calculate it from the mAh and voltage.
Find the nominal voltage of the battery. Common values include 3.7V (single lithium cell), 7.4V (2-cell laptop), 11.1V (3-cell laptop), 12V (lead-acid), and 48V (e-bike or solar). Use the nominal voltage, not the fully charged voltage.
Apply the formula: Ah = Wh ÷ V. For example, a 56 Wh laptop battery at 11.1V: 56 ÷ 11.1 = 5.05 Ah. For a 500 Wh e-bike battery at 48V: 500 ÷ 48 = 10.42 Ah.
For smaller batteries (phones, power banks), multiply Ah by 1000 to get milliamp-hours. The 5.05 Ah laptop battery equals 5,050 mAh. This step is common when comparing with phone batteries that are rated in mAh.
When replacing a battery, matching the Ah (or mAh) at the correct voltage ensures your device gets the same runtime. The Wh rating confirms equal total energy even if the Ah differs slightly due to manufacturing tolerances.
Solar battery banks are sized in Ah at a specific voltage (usually 12V, 24V, or 48V). Converting your daily energy needs from Wh to Ah at the system voltage tells you exactly how many battery amp-hours you need.
Airlines limit lithium batteries to 100 Wh for carry-on without approval. If your battery only shows mAh, converting to Wh (mAh × V ÷ 1000) confirms compliance before you travel.
| Device / Battery | Wh Rating | Voltage | Ah Capacity |
|---|---|---|---|
| Smartphone Battery | 18.5 Wh | 3.7V | 5.0 Ah |
| Power Bank (20,000 mAh) | 74 Wh | 3.7V | 20.0 Ah |
| Laptop Battery (3-cell) | 56 Wh | 11.1V | 5.05 Ah |
| Laptop Battery (4-cell) | 99.9 Wh | 14.8V | 6.75 Ah |
| 12V UPS Battery | 108 Wh | 12V | 9.0 Ah |
| E-Bike Battery | 500 Wh | 48V | 10.42 Ah |
| Solar Battery (LiFePO4) | 2,560 Wh | 51.2V | 50.0 Ah |
Watt-hours (Wh) measure total energy stored, while amp-hours (Ah) measure charge capacity at a specific voltage. The relationship is Wh = Ah × V. Two batteries with the same Ah but different voltages store different amounts of energy. Wh is the more universal metric because it accounts for voltage, making it reliable for cross-voltage comparisons.
Only if both batteries have the same voltage. A 10 Ah battery at 12V stores 120 Wh of energy, while a 10 Ah battery at 3.7V stores only 37 Wh – less than a third. Always convert to Wh before comparing batteries of different voltages to get a true energy comparison.
Cold temperatures reduce the available Ah capacity. Lead-acid batteries can lose 20–30% of their rated capacity at 0°C compared to 25°C. Lithium-ion batteries lose 10–20% in cold conditions. When sizing batteries for cold environments, apply a temperature derating factor (typically 1.2–1.5x the calculated Ah) to ensure adequate capacity.
The FAA and IATA allow lithium batteries up to 100 Wh in carry-on baggage without special approval. Batteries between 100–160 Wh require airline approval and are limited to two per passenger. Batteries over 160 Wh are prohibited on passenger aircraft. If your battery label shows mAh, convert to Wh using: Wh = mAh × V ÷ 1000.
Divide the Ah capacity by the current draw in amps: Runtime (hours) = Ah ÷ A. For example, a 100 Ah battery powering a 5A load lasts approximately 20 hours. In practice, actual runtime is lower due to efficiency losses (typically 80–90% for lithium, 50–80% for lead-acid depending on discharge rate). Use the Wh method for more accuracy: Runtime = Wh ÷ Watts.