Battery life depends on the interplay between a battery's capacity and a device's power consumption. While the core formula is simple, real-world factors like temperature, discharge rate, and efficiency losses can impact results. This guide breaks down the process into clear steps and highlights critical considerations.

2. Understanding Battery Specifications

Key Metrics

• Capacity (mAh/Ah): The total charge a battery can deliver (e.g., 3000mAh = 3Ah).

• Voltage (V): Nominal voltage (e.g., 3.7V for Li-ion, 12V for lead-acid).

• Energy (Wh): Capacity × Voltage (e.g., 10Ah × 12V = 120Wh).

Battery Chemistries

• Li-ion: High energy density, minimal self-discharge.

• NiMH: Moderate capacity, better for high-drain devices.

• Lead-Acid: High weight, used in automotive/solar applications.

3. Device Power Consumption

Determining Power Use

• Formula: Power (W) = Voltage (V) × Current (A).

• Example: A device running at 5V and drawing 2A consumes 10W.

Measuring Power

• Use a multimeter to measure current or a USB power meter for USB devices.

• Check manufacturer specs for voltage/current requirements.

4. Basic Battery Life Formula

Core Formula

$$\text{Battery Life (hours)}=\frac{\text{Battery Energy (Wh)}\times \text{Efficiency}}{\text{Device Power (W)}}$$

Step-by-Step Calculation

1. Convert Capacity to Wh:

   $$\text{Energy (Wh)}=\text{Capacity (Ah)}\times \text{Voltage (V)}$$

   Example: A 10Ah, 12V battery stores 120Wh.

2. Account for Efficiency (e.g., 90%):
   Multiply energy by efficiency (0.9 for 90%).

3. Divide by Device Power:
   Example: 120Wh × 0.9 / 10W = 10.8 hours.

5. Advanced Considerations

Discharge Rate (C-Rate)

• C-Rate Formula:

  $$\text{Discharge Time (h)}=\frac{1}{\text{C-Rate}}$$

  A 2Ah battery discharged at 1A has a 0.5C rate (2h runtime).

• Peukert's Law (for lead-acid batteries):

  $$T=\frac{C}{I^n}$$

  Where $n$ = Peukert’s exponent (1.1–1.3).

Temperature Effects

• Cold reduces capacity (e.g., Li-ion loses ~20% at -20°C).

• High temperatures accelerate aging.

Battery Aging

• Capacity degrades over cycles (e.g., 80% after 500 cycles for Li-ion).

Self-Discharge

• NiMH: ~20% monthly; Li-ion: ~2% monthly.

6. Practical Tips for Extending Battery Life

• Optimize Settings: Lower screen brightness, disable unused features.

• Avoid Extremes: Store batteries at 20–25°C.

• Use Efficient Converters: DC-DC converters with >90% efficiency.

7. Example Scenarios

Smartphone Battery

• Battery: 4000mAh, 3.8V → 15.2Wh.

• Usage: Average 1.5W (mixed use).

• Life: 15.2Wh / 1.5W ≈ 10.1 hours.

Solar Power System

• Battery Bank: 24V, 200Ah → 4800Wh.

• Load: 200W (24V inverter, 85% efficient).

• Life: (4800Wh × 0.85) / 200W = 20.4 hours.

Conclusion

While the formula Battery Life = Energy × Efficiency / Power provides a baseline, real-world factors like discharge rate and temperature require adjustments. Always measure actual device consumption and consider battery specifications for accurate estimates.

Appendices

• Peukert’s Calculator: Adjust for high discharge rates.

• Efficiency Chart: Typical converter efficiencies (e.g., buck: 95%, boost: 85%).

• Unit Conversions: mAh to Wh, C-rate to current.

By following this guide, you can confidently estimate battery life and optimize your devices for longevity.