Wh to mAh Calculator

Understanding the conversion between Watt-hours (Wh) and milliampere-hours (mAh) is crucial for battery technology and energy management. This calculation helps determine battery capacity and energy storage efficiency across various devices.

This article explores the technical details of Wh to mAh conversion, including formulas, practical examples, and comprehensive tables. It aims to equip engineers, technicians, and enthusiasts with precise knowledge for accurate battery capacity calculations.

Artificial Intelligence (AI) Calculator for “Wh to mAh Calculator”

• Convert 36 Wh to mAh at 12 V
• Calculate mAh from 50 Wh at 3.7 V
• Find mAh for 100 Wh battery rated at 24 V
• Determine mAh from 10 Wh at 5 V

Comprehensive Tables for Wh to mAh Conversion

Below are detailed tables showing common Wh to mAh conversions at various nominal voltages. These values are practical for typical battery voltages used in consumer electronics, electric vehicles, and industrial applications.

Fundamental Formulas for Wh to mAh Conversion

Converting Watt-hours (Wh) to milliampere-hours (mAh) requires understanding the relationship between energy, voltage, and charge capacity. The core formula is derived from the definition of electrical energy and charge.

• Formula 1: Basic Conversion
  
  mAh = (Wh × 1000) / V
  
  Where:
  • mAh = milliampere-hours (battery capacity)
  • Wh = watt-hours (energy stored)
  • V = nominal voltage of the battery (volts)
• Formula 2: Derivation from Basic Electrical Principles
  
  Wh = V × Ah
  
  Where:
  • Wh = watt-hours
  • V = voltage (volts)
  • Ah = ampere-hours

  Rearranged to find Ah:

  
  Ah = Wh / V
  

  Since 1 Ah = 1000 mAh, multiply by 1000 to convert:

  
  mAh = (Wh / V) × 1000
  

• Formula 3: Considering Battery Efficiency and Discharge Rate
  
  mAh = (Wh × 1000) / (V × η)
  
  Where:
  • η = battery efficiency factor (0 < η ≤ 1)

  This formula accounts for real-world losses during discharge.

Detailed Explanation of Variables

• Watt-hours (Wh): Represents the total energy stored or consumed. It is the product of voltage and ampere-hours.
• Voltage (V): The nominal voltage rating of the battery, which varies by chemistry and design (e.g., 3.7 V for Li-ion cells, 12 V for lead-acid batteries).
• Milliampere-hours (mAh): A measure of electric charge capacity, indicating how much current a battery can supply over time.
• Battery Efficiency (η): Represents the efficiency of energy conversion and discharge, typically between 0.85 and 0.95 for modern batteries.

Real-World Application Examples of Wh to mAh Conversion

Example 1: Calculating mAh for a Li-ion Battery Pack

A Li-ion battery pack is rated at 74 Wh with a nominal voltage of 3.7 V. Calculate the battery capacity in mAh.

• Given: Wh = 74 Wh, V = 3.7 V
• Using Formula 1:

mAh = (74 × 1000) / 3.7

Calculate:

mAh = 74000 / 3.7 ≈ 20000 mAh

This means the battery pack has a capacity of approximately 20,000 mAh, suitable for high-capacity power banks or electric devices.

Example 2: Determining mAh for a Lead-Acid Battery

A sealed lead-acid battery has an energy rating of 120 Wh and a nominal voltage of 12 V. Find the capacity in mAh.

• Given: Wh = 120 Wh, V = 12 V
• Using Formula 1:

mAh = (120 × 1000) / 12

Calculate:

mAh = 120000 / 12 = 10000 mAh

The battery capacity is 10,000 mAh or 10 Ah, which is typical for small lead-acid batteries used in UPS systems or emergency lighting.

Additional Technical Considerations in Wh to mAh Conversion

While the basic formula provides a straightforward conversion, several factors influence the accuracy and practical application of Wh to mAh calculations:

• Nominal Voltage Variability: Battery voltage can fluctuate during charge and discharge cycles. Using nominal voltage is standard, but actual voltage may differ.
• Temperature Effects: Battery capacity and voltage are temperature-dependent. Cold temperatures reduce effective capacity, impacting mAh calculations.
• Battery Aging: Over time, battery capacity degrades, reducing Wh and mAh values. Calculations should consider state-of-health (SOH) for precision.
• Discharge Rate (C-rate): High discharge rates can reduce usable capacity due to internal resistance and heat generation.
• Efficiency Losses: Internal resistance and chemical inefficiencies reduce the effective capacity, which can be accounted for using the efficiency factor η.

Practical Use Cases for Wh to mAh Calculations

Understanding Wh to mAh conversion is essential in various fields, including:

• Consumer Electronics: Designing battery packs for smartphones, tablets, and laptops requires precise capacity calculations.
• Electric Vehicles (EVs): Battery management systems use Wh and mAh to estimate range and energy consumption.
• Renewable Energy Storage: Solar battery banks and off-grid systems rely on accurate capacity conversions for system sizing.
• Uninterruptible Power Supplies (UPS): Ensuring backup power duration depends on correct Wh to mAh conversions.
• Medical Devices: Portable medical equipment requires reliable battery capacity estimations for safety and performance.

Authoritative References and Standards

For further technical details and standards related to battery capacity and energy calculations, consult the following authoritative sources:

• IEEE Standards Association – Standards on battery testing and performance.
• Battery Standards Organization – Guidelines on battery capacity and energy measurement.
• National Renewable Energy Laboratory (NREL) – Research on battery technologies and energy storage.
• U.S. Energy Information Administration (EIA) – Data and analysis on energy storage systems.

Summary of Key Points

• Wh to mAh conversion is essential for understanding battery capacity and energy storage.
• The primary formula is mAh = (Wh × 1000) / V, where V is nominal voltage.
• Battery efficiency, temperature, and aging affect real-world capacity and should be considered.
• Comprehensive tables provide quick reference for common battery voltages and energy ratings.
• Practical examples demonstrate step-by-step calculations for different battery chemistries.

Mastering Wh to mAh calculations enables engineers and technicians to design, evaluate, and optimize battery-powered systems effectively. Accurate conversions ensure reliable performance and energy management across diverse applications.