How is Lithium Battery Runtime Calculated?

 The “run time” of a lithium battery essentially refers to how long it can reliably supply power under specific operating conditions. To accurately calculate it, several key factors must be considered: capacity, voltage, power consumption, efficiency, and safety margin.

Understand what each parameter on the battery specification sheet represents:

  Capacity: Ah / mAh

 Most lithium batteries are labeled with a capacity value, such as 5000 mAh or 10 Ah. The fundamental definition of capacity is:

 This means a battery rated at 10 Ah can discharge at 1 A for 10 hours under ideal conditions, or at 2 A for 5 hours. Redway’s technical article explains battery capacity using this formula and supplements it with relationships converted through energy (Wh) and voltage.

 Many popular science articles also use examples like 1000 mAh = 1 A sustained for 1 hour to help understand capacity. (Zhihu)

 Voltage: V

 The nominal voltage of a single lithium-ion (Li-ion) cell typically ranges around 3.6–3.7 V. Panasonic specifies a nominal cell voltage of 3.6 V in its lithium battery product descriptions, emphasizing that high energy density and high voltage are characteristic features of lithium batteries. When multiple cells are connected in series, their voltages add up. For example:

• 1 cell: 3.7 V
• 10 cells in series: approximately 37 V
• Connecting 96 3.7 V cells in series yields a battery pack nominal voltage of approximately 355 V, comparable to the high-voltage battery packs used in electric vehicles like the BMW i3.

 Energy: Wh = Ah × V

 Capacity only indicates “electric charge,” but energy varies significantly at different voltages. Therefore, manufacturers also specify energy (Wh).
  For example, the Samsung SDI 94 Ah prismatic cell listed by EVLithium has a nominal voltage of 3.7 V and a capacity of 94 Ah, yielding a total energy of approximately 3.7 × 94 ≈ 348 Wh. This cell is used in electric vehicles and energy storage systems.

 With Wh, you can directly calculate runtime by multiplying it with the device’s power (W).

 C-rate

 C-rate indicates the discharge/charge current relative to capacity:

• 1C: Discharging at a current equal to the capacity (Ah)
• 5C: Discharges at half the capacity current
• 2C: Discharging at twice the capacity current

 Some engineering blogs correlate C-rate with cycle life, e.g., typical cycles of 500–1000 at 0.5C, 300–500 at 1C, and 200–300 at 2C. They note that higher C-rates not only shorten lifespan but also reduce usable capacity. (CSDN Blog)

 This is crucial when calculating “how long continuous full-power operation lasts”—some rates are inherently not recommended for sustained use.

 Formula for Estimating Runtime Under Ideal Conditions

 Let’s start with the most ideal and simplified model: moderate temperature, brand-new battery, constant load, discharged to safe cut-off voltage, and no conversion losses considered.

 Constant Current Load: Direct Calculation Using Ah and A

 If the device operates under a constant current load (e.g., simple LED lighting or constant-current circuits), use:

 For example, a CSDN article provides a similar formula: Operating time (hours) = Battery capacity (mAh) / Discharge current (mA). (CSDN Blog)

 Example:

• Battery: 5000 mAh
• Device operating current: 500 mA

 Theoretical runtime = 5000 ÷ 500 = 10 hours

 This formula is also directly used in many online “battery life calculators,” such as the expression Battery Life = Battery Capacity / Average Current Consumption provided by the battery-calculator website.

 Constant-power loads: Calculate using Wh and W

 For most devices (phones, laptops, inverters, electric vehicles), the “constant power” perspective is more intuitive—you care more about “how long a 15 W device will run” or “how long a 300 W inverter will last.”

 The commonly used formula here is:

 Multiple battery manufacturers and technical blogs provide similar expressions. For example, Large Battery’s technical article explicitly states:

  Battery Run Time (hours) = Battery Capacity (Wh) ÷ Device Power Consumption (W).

 EVLithium itself employs the same approach in its tutorials, converting Ah × V to Wh before dividing by power. (Evlithium)

 Example:

• Battery pack: 3.7 V, 10 Ah
• Battery Energy: 3.7 × 10 = 37 Wh
• Device Power Consumption: 15 W

 Theoretical runtime:
  t = 37 ÷ 15 ≈ 2.47 hours

 Handling Series-Parallel Battery Packs

 For battery packs composed of multiple cells:

• Series connection: Voltage is the sum of individual voltages; capacity remains unchanged
• n cells in series:
• Nominal voltage: n × V_cell
• Capacity: Remains Ah_cell
• Energy: n × V_cell × Ah_cell
• Parallel connection: Voltage remains unchanged, capacity is added
• m Series-parallel: Total capacity = m × Ah_cell

 Most electric vehicles and energy storage systems provide specifications this way. For example, the BMW i3 battery: N cells of 3.7 V NCM cells connected in series and parallel to form a battery pack in the tens of kWh range. (PushEVs)

 When calculating range, use the “total Wh” directly, regardless of internal series/parallel combinations.

 From “Paper Formulas” to “Real-World Range”: A Three-Step Method

 Formulas alone aren’t enough—we need to translate them into practical calculation steps. The general process can be summarized as:

 Step 1: Read capacity and voltage from nameplate or datasheet

• Single cells: Consult the datasheet (e.g., Panasonic or Samsung SDI) for nominal voltage (e.g., 3.6/3.7 V) and rated capacity (e.g., 3 Ah, 94 Ah).
• Battery Packs: Many directly state total energy (e.g., 36 V 10 Ah → 360 Wh, or simply labeled as 0.36 kWh).

If only Ah and V are available, first calculate Wh = Ah × V.

 Step 2: Estimate the device’s average power consumption

 This is where the largest error occurs.

• For devices like smartphones, tablets, and laptops, power adapters may be labeled as 65 W or 90 W, but this represents the maximum power rating. Actual average power consumption is often significantly lower.
• For IoT devices and small appliances, measure the current under typical operating conditions using an ammeter, then multiply by the operating voltage to obtain the average power.

 TI’s application notes for low-power chips like CC26xx and CC13xx emphasize using “average current” to evaluate battery life: measure current waveforms across various active/sleep modes, then calculate an average to estimate runtime.

 First calculate power, then revert to the Wh ÷ W formula above.

 Step 3: Consider Depth of Discharge (DoD) and System Efficiency (η)

 In engineering practice, lithium batteries are rarely discharged from 100% to 0%, as this significantly shortens lifespan. Many professional calculators incorporate a “Discharge Safety Percentage” (DSP). For example, battery-calculator explicitly includes DSP in its formula, indicating a general recommendation to reserve 20% of capacity unused.

 Tutorials like EVLithium and Ufine Battery also recommend multiplying ideal calculations by the depth of discharge (DoD) and conversion efficiency (η): (Ufine Battery [Official])

 Typical values include:

• DoD: 0.8–0.9 (reserving 10–20% capacity)
• η: 0.85–0.95 (accounting for losses including DC-DC conversion, line losses, BMS, self-discharge, etc.)

 Continuing the previous example:

• Theoretical range: 2.47 h
• Assuming DoD = 0.9 (discharging down to 10% capacity)
• Conversion efficiency η = 0.9

 Then:
  t_actual ≈ 2.47 × 0.9 × 0.9 ≈ 2.0 hours

 This is about 20% less than the “paper figure,” which aligns well with real-world experience.

Why does real-world battery life always fall short of calculations? — Key correction factors

 Even with the three-step method above providing clear calculations, real-world usage reveals: significantly shorter battery life in winter, rapid power drain during high-power usage, and battery life halving after two to three years… These are all real-world factors beyond the formula.

Temperature’s Impact on Capacity

 Lithium battery capacity is highly temperature-sensitive. Capacity retention rates at 0°C, 25°C, 40°C, and 60°C are approximately 98%, 96%, 85%, and 75%, respectively. Both extreme heat and cold reduce usable capacity and accelerate aging.

 This means:

• Winter outdoor use of e-bikes or power tools suffers significant range reduction
• Poor battery pack cooling and prolonged exposure to high temperatures also reduce usable capacity

Discharge Rate (C-rate) and Capacity/Lifespan

 As mentioned earlier, higher C-rates place greater stress on batteries. Under high-rate discharge:

• Instantaneous usable capacity falls below the rated value
• Cycling life also decreases significantly

 Some engineering articles provide typical cycle life ranges for 0.5C, 1C, and 2C rates, noting that sustained operation above the design rate rapidly degrades capacity.

 Therefore, for high-rate applications like drones and power tools, even batteries with large nominal capacities may not deliver full-power output for durations simply proportional to “Ah/A.”

Aging and Cycling: A new battery is not the same as one used for two years

 After multiple cycles, lithium-ion battery capacity gradually declines. Taking Samsung SDI cells as an example, official data indicates a cycle life exceeding 3000 cycles. However, this represents data measured under specific conditions—a fixed rate and temperature. In real-world use, mixed temperatures, varying rates, and deep discharges accelerate actual capacity degradation.

 Therefore:

• A new device’s “battery life test” is merely a starting point.
• Calculating range based on the nominal capacity of a two-year-old battery typically yields an “optimistic” estimate.

 BMS, Self-Discharge, and System-Level Losses

 In complex applications like electric vehicles and energy storage systems, batteries aren’t operating in isolation. They also include:

• BMS (Battery Management System)
• High-voltage relays and monitoring circuits
• DC-DC converters, inverters

 The power consumption of circuits like the BMS can account for 3–5% of total energy, rising to as much as 8% under conditions like low temperatures. These losses must be factored into η.

How to determine average current when load is non-constant?

 Real-world device loads are almost always dynamic:

• Mobile phones: Standby at tens of mA, video streaming increases to hundreds of mA, gaming even higher
• Wireless sensors: Sleep most of the time, occasionally wake up to transmit data

 TI application notes and numerous engineering discussions emphasize: For pulsed loads, calculate an “equivalent average current” based on duty cycles across different operational phases before applying it to capacity/current formulas—rather than using peak or RMS current values alone.

 This is why professional devices employ “fuel gauge + algorithm” to track SOC (State of Charge) in real-time, rather than relying solely on voltage estimation.

Smart Fuel Gauges and the “Extra 30% Range”

 A note on “algorithms”:
  Texas Instruments’ 2025 Dynamic Z-Track predictive battery management technology claims that by more accurately tracking battery state, it can achieve up to 30% longer range on the same battery hardware, primarily by reducing overly conservative safety margins.

 This demonstrates: For the same battery, algorithm quality directly impacts real-world endurance.

A Complete Example: Selecting a Lithium Battery for a 15W Device

 Suppose you have a 15W portable device powered by a single 3.7V lithium battery, with a boost circuit outputting higher voltage. You select a 3.7V 10Ah battery (37Wh) under these conditions:

• Battery: 3.7 V, 10 Ah → 37 Wh
• Device average power: 15 W
• Depth of Discharge (DoD): 0.85 (15% reserve capacity)
• System efficiency (DC-DC + line loss + BMS): η = 0.9

 Steps:

1. Theoretical range (unadjusted):
     t_theoretical = 37 ÷ 15 ≈ 2.47 h
2. Considering DoD and η:
   t_actual ≈ 2.47 × 0.85 × 0.9 ≈ 1.89 h

 That is, approximately 1.9 hours.

 If you find the actual measurement is only around 1.5 hours, it’s highly likely that:

• Actual average power > 15 W (e.g., higher load)
• Temperature is too low or too high
• The battery has aged to some extent
• Lower conversion efficiency

Differences in Calculation Approaches Across Scenarios

 Consumer electronics like smartphones and laptops

• Focus more on average power consumption in “typical usage scenarios” rather than instantaneous full-load conditions
• Manufacturers typically use complex power consumption models + battery calculation methods to provide official ratings like “X hours of video playback, Y hours of web browsing”

Electric Vehicles and Two-Wheeled Vehicles

• These prioritize metrics like Wh/km or kWh/100km.
• Range calculations incorporate additional factors like vehicle weight, aerodynamic drag, road conditions, and temperature. Platforms like Zhihu host numerous discussions deriving theoretical range using the formula: “Battery voltage × Capacity × Efficiency ÷ Motor power × Speed.”

Energy Storage & Power Systems

• Common design metrics focus on “discharge duration (e.g., 2 hours, 4 hours)”
• System-level efficiency (inverter + BMS + line losses) has a greater impact and requires correction using actual measured efficiency curves.

Summary: Practical Formulas and Conventions for Calculating Lithium Battery Range

1. Basic Formula

• Constant Current: t(h) ≈ C(mAh) ÷ I(mA)
• Constant power: t(h) ≈ C(Wh) ÷ P(W)

2. Battery Pack Energy

• Wh = Ah × V. Total Wh depends solely on total voltage and total capacity, regardless of series/parallel configuration

3. Engineering Correction

• t_(actual) ≈ t_(theoretical) × DoD × η
• DoD typically 0.8–0.9, η 0.85–0.95; adjust based on application scenario

4. Key Factors Affecting Real-World Range

• Temperature (extreme cold/heat)
• Discharge rate (high current/high load)
• Battery aging (cycle count, calendar life)
• BMS and system self-consumption
• Whether load is constant, how average current is calculated, and whether algorithms are conservative

 By mastering this approach, you can:

• Quickly estimate theoretical range based on battery specifications and device power consumption
• Then apply experience-based adjustments for temperature, aging, efficiency, etc., to arrive at a more realistic figure
• Make informed decisions when selecting battery capacity and designing product-rated range, rather than relying on guesswork

 If convenient, send me your specific battery specs (voltage, Ah/Wh) and device power consumption. I can calculate “how long this setup will actually last” using the steps above and identify potential optimization opportunities.