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Battery Runtime Estimator

Estimate runtime based on load type, internal resistance, temperature, and capacity adjustments.

Tool Purpose & README

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Inputs

Choose a chemistry preset, then set pack or cell specs. Use the load tab to define current, power, or resistance, and refine runtime with environment and degradation factors.

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When cell specs are enabled, pack-level values update automatically.

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Enter parameters and click Calculate to estimate runtime.

Discharge Curve (Placeholder)

Provide a reference discharge profile to visualize voltage vs capacity.

Battery Runtime Estimation

This tool estimates the runtime of a battery pack under specified load conditions, accounting for internal resistance losses, temperature effects, capacity degradation, and the nonlinear behavior captured by Peukert's law.

The model uses a constant nominal open-circuit voltage with a lumped internal resistance to approximate the loaded terminal voltage. While real battery discharge curves are nonlinear, this simplified approach provides practical estimates for initial design and feasibility studies.

Key Capabilities

  • Multiple load types: Constant current, constant power, and constant resistance loads
  • Cell-to-pack aggregation: Derive pack parameters from individual cell specs
  • Temperature correction: Adjust capacity based on ambient temperature deviation
  • Peukert effect: Model capacity reduction at high discharge rates
  • Degradation modeling: Account for state-of-health and depth-of-discharge limits
  • Efficiency losses: Include converter/regulator efficiency in power calculations

Model Assumptions

  • The open-circuit voltage remains constant throughout discharge (nominal voltage approximation)
  • Internal resistance is constant and does not vary with state-of-charge or temperature
  • Temperature effects are linear around the reference temperature
  • Duty cycle averaging accurately represents intermittent loads
  • All cells in the pack are identical and balanced

When to Use This Tool

This estimator is ideal for preliminary sizing, feasibility studies, and comparative analysis between battery chemistries or configurations. For detailed design validation, always verify results against manufacturer discharge curves and, where possible, empirical testing.

Parameter Glossary

Complete reference for all input parameters and output values used in the estimator.

Pack Configuration

Chemistry Preset chemistry
Selects default values for cell voltage, capacity, internal resistance, cutoff voltage, Peukert exponent, and temperature coefficient based on common battery chemistries. The calculation itself uses numeric parameters; the chemistry label provides sensible starting points.
Options: Li-ion (NMC/NCA), LiPo, LiFePO4, NiMH, Lead-acid
Use Cell Specs use_cell_specs
When enabled, pack-level parameters (voltage, capacity, resistance, cutoff) are computed from cell-level values and series/parallel counts. When disabled, pack values are used directly.
Pack Nominal Voltage pack_nominal_voltage_v
The average voltage of the battery pack during normal discharge. This is used as the open-circuit voltage (OCV) in calculations. For lithium cells, nominal voltage is typically the midpoint of the discharge curve.
Unit: Volts (V)
Typical: 3.2-3.7V per Li-ion cell, 2.0V per lead-acid cell
Pack Capacity pack_capacity_ah
The rated capacity of the pack in amp-hours, typically specified at a standard discharge rate (C/20 for lead-acid, C/5 or 1C for lithium). This is the total charge the battery can deliver from full to empty.
Unit: Amp-hours (Ah)
Pack Internal Resistance pack_internal_resistance_ohm
The lumped DC internal resistance of the pack. This causes voltage sag under load and power loss as heat. For a pack with cells in series and parallel: R_pack = (N_s / N_p) * R_cell.
Unit: Ohms
Typical: 20-100 mOhm for small Li-ion packs, lower for high-power cells
Pack Cutoff Voltage pack_cutoff_voltage_v
The minimum safe discharge voltage for the pack. Discharging below this voltage can damage cells and reduce cycle life. The estimator checks that loaded voltage stays above this threshold.
Unit: Volts (V)
Typical: 2.5-3.0V per Li-ion cell, 1.75V per lead-acid cell

Cell Configuration

Series Cells series_cells
Number of cells connected in series (Ns). Series cells increase voltage: V_pack = Ns * V_cell. Common configurations: 3S (11.1V nominal Li-ion), 4S (14.8V), 6S (22.2V).
Unit: Count (dimensionless)
Parallel Cells parallel_cells
Number of cells connected in parallel (Np). Parallel cells increase capacity and reduce pack resistance: C_pack = Np * C_cell, R_pack = R_cell / Np (before series scaling).
Unit: Count (dimensionless)
Cell Nominal Voltage cell_nominal_voltage_v
The nominal (average) voltage of a single cell. This is chemistry-dependent: 3.6-3.7V for NMC/NCA, 3.2V for LiFePO4, 1.2V for NiMH, 2.0V for lead-acid.
Unit: Volts (V)
Cell Capacity cell_capacity_ah
The rated capacity of a single cell. Common 18650 cells range from 2.0-3.5 Ah; 21700 cells from 4.0-5.0 Ah. Larger format cells (pouch, prismatic) can be 10-100+ Ah.
Unit: Amp-hours (Ah)
Cell Internal Resistance cell_internal_resistance_ohm
The DC internal resistance of a single cell. Lower resistance means higher power capability and less voltage sag. High-power cells may have 10-20 mOhm; high-energy cells 30-60 mOhm.
Unit: Ohms
Cell Cutoff Voltage cell_cutoff_voltage_v
The minimum safe voltage per cell. Typically 2.5-3.0V for Li-ion, 2.5V for LiFePO4, 1.0V for NiMH, 1.75V for lead-acid.
Unit: Volts (V)

Load Parameters

Load Type load_type
Defines how the load draws power. Constant current: motors, LED drivers (I = fixed). Constant power: DC-DC converters, regulated loads (P = fixed, I varies with V). Constant resistance: resistive heaters, simple loads (R = fixed, I = V/R).
Load Current load_current_a
For constant current mode: the current drawn by the load (after any conversion). The battery current is scaled by converter efficiency: I_battery = I_load / efficiency.
Unit: Amperes (A)
Load Power load_power_w
For constant power mode: the power consumed by the load. The tool solves for battery current considering internal resistance losses and converter efficiency.
Unit: Watts (W)
Load Resistance load_resistance_ohm
For constant resistance mode: the equivalent resistance of the load at the battery terminals. Current is determined by V_pack / (R_load + R_internal).
Unit: Ohms
Converter Efficiency converter_efficiency
The efficiency of any power conversion between battery and load (DC-DC converter, motor controller, etc.). A value of 0.90 means 10% of battery power is lost in conversion.
Unit: Fraction (0-1)
Typical: 0.85-0.95 for switching regulators, 0.70-0.85 for linear regulators
Duty Cycle duty_cycle
The fraction of time the load is active. For continuous loads, use 1.0. For intermittent loads (e.g., a motor running 30% of the time), use 0.30. The average current becomes I_avg = I_load * duty_cycle.
Unit: Fraction (0-1)

Environment & Degradation

Ambient Temperature ambient_temperature_c
The operating temperature of the battery. Capacity decreases at low temperatures and may increase slightly at moderate high temperatures (though cycle life suffers). Extreme temperatures should be avoided.
Unit: Degrees Celsius
Optimal: 20-25 C for most chemistries
Reference Temperature reference_temperature_c
The temperature at which rated capacity was measured (typically 25 C or 20 C per manufacturer specs). The temperature coefficient adjusts capacity relative to this baseline.
Unit: Degrees Celsius
Capacity Temp Coefficient capacity_temp_coeff_per_c
The fractional change in capacity per degree Celsius deviation from reference. A value of 0.004 means capacity drops by 0.4% for each degree below reference (and increases for temperatures above).
Unit: 1/C
Typical: 0.003-0.006 for lithium, 0.005-0.01 for lead-acid
Peukert Exponent peukert_exponent
Captures the reduction in effective capacity at high discharge rates. Named after Wilhelm Peukert (1897). A value of 1.0 means no rate dependence; lead-acid batteries have k = 1.1-1.4. Lithium cells are typically 1.02-1.10.
Unit: Dimensionless (k >= 1)
Typical: 1.02-1.05 (Li-ion), 1.1-1.3 (lead-acid)
Reference Current reference_current_a
The discharge current at which rated capacity was measured. Peukert's correction compares actual current to this reference. Often specified as C/20 or C/5 rate.
Unit: Amperes (A)
Depth of Discharge depth_of_discharge
The fraction of capacity you intend to use. Using only 80% (DoD = 0.80) extends cycle life significantly. For critical applications, 50% DoD may be appropriate.
Unit: Fraction (0-1)
Typical: 0.80-1.00 for Li-ion, 0.50-0.80 for lead-acid
State of Health state_of_health
The remaining capacity as a fraction of original rated capacity. A new battery has SOH = 1.0; an aged battery with 80% of original capacity has SOH = 0.80. End-of-life is often defined as SOH = 0.70-0.80.
Unit: Fraction (0-1)

Output Values

Runtime runtime_hours, runtime_minutes
The estimated operating time until the battery reaches cutoff voltage or depletes usable capacity. Calculated as effective capacity divided by average current.
Units: Hours (h) or Minutes (min)
Effective Capacity effective_capacity_ah
The usable capacity after all adjustments: temperature correction, SOH, DoD limits, and Peukert derating. This is the capacity available for the specified operating conditions.
Unit: Amp-hours (Ah)
Average Current average_current_a
The time-averaged current drawn from the battery, including duty cycle effects. For continuous operation at fixed current, this equals the instantaneous current.
Unit: Amperes (A)
Average Power average_power_w
The power delivered by the battery at the loaded terminal voltage: P = V_load * I_avg. This is less than V_nominal * I_avg due to internal resistance losses.
Unit: Watts (W)
Energy Delivered energy_delivered_wh
The total energy the battery can deliver: E = V_load * C_effective. This accounts for voltage sag and capacity derating.
Unit: Watt-hours (Wh)
Loaded Voltage loaded_voltage_v
The terminal voltage under load: V_load = V_nominal - I_load * R_internal. This is the voltage available to the load and is lower than open-circuit voltage.
Unit: Volts (V)
Voltage Sag voltage_sag_v
The voltage drop across internal resistance: V_sag = I_load * R_internal. Large sag indicates high power loss and potential thermal issues.
Unit: Volts (V)
C-rate c_rate
The discharge rate relative to capacity: C-rate = I_avg / C_rated. A 1C rate fully discharges the battery in 1 hour; 2C in 30 minutes; 0.5C in 2 hours.
Unit: 1/hour
Heat Dissipation power_loss_w
Power lost as heat in the internal resistance: P_loss = I_load^2 * R_internal. This energy heats the battery and is not delivered to the load. High values indicate thermal management may be required.
Unit: Watts (W)
Concern threshold: varies, but >5-10% of output power warrants attention

Battery Fundamentals

The Basic Runtime Equation

At its simplest, battery runtime is capacity divided by current: t = C / I. A 10 Ah battery discharged at 2 A runs for 5 hours. However, real batteries are more complex due to voltage variations, efficiency losses, temperature effects, and rate-dependent capacity.

Open-Circuit Voltage vs. Loaded Voltage

A battery's open-circuit voltage (OCV) is measured with no current flowing. Under load, the terminal voltage drops due to internal resistance:

V_terminal = V_OCV - I * R_internal

This voltage sag reduces available power and causes energy to be dissipated as heat inside the battery. High-power applications require low internal resistance cells.

Internal Resistance

Internal resistance has multiple components: ionic resistance in the electrolyte, charge-transfer resistance at electrode surfaces, and ohmic resistance in current collectors. For simplified modeling, these are lumped into a single DC resistance value.

Internal resistance increases with age and decreases with temperature (within safe operating limits). Cold batteries have higher resistance and more voltage sag.

Series and Parallel Cell Combinations

Battery packs combine cells in series (S) and parallel (P) to achieve desired voltage and capacity:

  • Series (S): Increases voltage. V_pack = N_s * V_cell. Resistance adds: R_series = N_s * R_cell.
  • Parallel (P): Increases capacity. C_pack = N_p * C_cell. Resistance divides: R_parallel = R_cell / N_p.
  • Combined: For a pack with S cells in series and P cells in parallel: R_pack = (N_s / N_p) * R_cell.

Pack notation like "4S2P" means 4 cells in series (voltage x4) with 2 parallel groups (capacity x2).

Peukert's Law

Wilhelm Peukert observed in 1897 that lead-acid batteries deliver less total charge when discharged rapidly. This is expressed as:

C_effective = C_rated * (I_ref / I_actual)^(k-1)

where k is the Peukert exponent (k >= 1). Lead-acid batteries have k = 1.1-1.4; lithium batteries are closer to ideal with k = 1.02-1.10. At 2x the reference current, a battery with k = 1.2 delivers only (0.5)^0.2 = 87% of rated capacity.

Temperature Effects

Battery capacity is temperature-dependent. The electrochemical reactions slow at low temperatures, reducing available capacity. A typical Li-ion cell may lose 10-20% capacity at 0 C compared to 25 C.

The linear approximation used here is:

C_temp = C_rated * [1 + alpha * (T - T_ref)]

This is accurate for moderate deviations (e.g., 0-40 C) but breaks down at extreme temperatures.

State of Health and Cycle Life

Batteries degrade over time and with use. State of Health (SOH) represents the current capacity as a fraction of original capacity. A battery with SOH = 0.80 has lost 20% of its original capacity.

Degradation accelerates with:

  • High temperatures (especially when fully charged)
  • Deep discharge cycles
  • High charge/discharge rates
  • Storage at high or very low state-of-charge

Depth of Discharge

Depth of Discharge (DoD) is the fraction of capacity used per cycle. Using 80% of capacity (DoD = 0.80) leaves a 20% buffer. Limiting DoD significantly extends cycle life - a Li-ion cell cycled to 80% DoD may last 2-3x longer than one cycled to 100% DoD.

C-Rate

The C-rate normalizes discharge current to capacity. A 10 Ah battery:

  • At 1C (10 A): depletes in 1 hour
  • At 2C (20 A): depletes in 30 minutes
  • At 0.5C (5 A): depletes in 2 hours
  • At C/10 (1 A): depletes in 10 hours

Maximum continuous C-rate is a key cell specification. High-power cells may support 3-5C continuous; high-energy cells may be limited to 1C.

Constant Power Loads

Many modern devices use DC-DC converters that draw constant power regardless of input voltage. As the battery voltage drops, current must increase to maintain power output:

I = P / V

This creates a feedback loop: lower voltage -> higher current -> more voltage sag -> even lower voltage. If internal resistance is too high, the battery cannot deliver the requested power.

Mathematical Model

The following equations define the battery runtime estimation model.

Battery Chemistry Comparison

Different battery chemistries have distinct characteristics that affect runtime, power capability, cycle life, and safety. This comparison helps select the appropriate chemistry for your application.

Property Li-ion NMC/NCA LiPo LiFePO4 NiMH Lead-Acid
Nominal Voltage 3.6-3.7 V 3.7 V 3.2 V 1.2 V 2.0 V
Cutoff Voltage 2.5-3.0 V 3.0-3.2 V 2.5 V 1.0 V 1.75 V
Energy Density 150-250 Wh/kg 150-200 Wh/kg 90-120 Wh/kg 60-120 Wh/kg 30-50 Wh/kg
Cycle Life 500-1000 300-500 2000-5000 500-1000 200-500
Peukert Exponent 1.02-1.05 1.02-1.04 1.03-1.06 1.05-1.15 1.10-1.30
Temp Coefficient 0.3-0.5%/C 0.3-0.4%/C 0.2-0.4%/C 0.4-0.6%/C 0.5-1.0%/C
Self-Discharge 2-3%/month 3-5%/month 1-3%/month 15-30%/month 3-20%/month
Max C-Rate 1-3C 3-10C 1-3C 1-2C 0.2-1C
Best For EVs, laptops, power tools Drones, RC, high-power Solar storage, EVs, safety-critical Hybrid vehicles, consumer devices UPS, SLI, low-cost storage

Representative Discharge Curves

The shape of the discharge curve varies significantly by chemistry. Flat curves provide stable voltage; sloped curves give better state-of-charge indication.

Li-ion NMC/NCA
4.2V 2.5V 100%
Gradual slope from 4.2V to ~3.5V, then steeper drop to cutoff at 2.5-3.0V. Most capacity delivered between 3.4-3.9V. Good voltage indication of SOC.
LiFePO4
3.6V 2.5V 100%
Very flat plateau at ~3.2-3.3V for 80%+ of capacity. Excellent for applications needing stable voltage. Poor SOC indication from voltage.
Lead-Acid
2.15V 1.75V 100%
Steady linear decline. Strong Peukert effect - capacity drops significantly at high discharge rates. Must limit DoD for cycle life.
NiMH
1.4V 1.0V 100%
Relatively flat at ~1.2V for most of discharge. Sharp drop at end. High self-discharge rate. Memory effect largely eliminated in modern cells.

Chemistry Selection Guidelines

  • Maximum energy density: Li-ion NMC/NCA - best for weight/volume constrained applications
  • High power bursts: LiPo - drones, RC vehicles, peak power applications
  • Long cycle life: LiFePO4 - stationary storage, commercial EVs, where longevity matters
  • Safety-critical: LiFePO4 - thermal stability, no thermal runaway risk
  • Low cost: Lead-acid - UPS, backup power, automotive starting
  • Extreme cold: Lithium with heating or lead-acid (tolerates cold better when charged)

References & Further Reading

Authoritative sources for battery modeling, characterization, and application design.

Textbooks & Handbooks

Handbook of Batteries (4th Edition)
D. Linden, T. B. Reddy (eds.)
McGraw-Hill, 2011. ISBN: 978-0071624213
Access Engineering Library
Battery Technology Handbook (2nd Edition)
H. A. Kiehne (ed.)
CRC Press, 2003. ISBN: 978-0824742492
Electrochemical Power Sources: Batteries, Fuel Cells, and Supercapacitors
V. S. Bagotsky, A. M. Skundin, Y. M. Volfkovich
Wiley, 2015. ISBN: 978-1118460238
Lithium-Ion Batteries: Science and Technologies
M. Yoshio, R. J. Brodd, A. Kozawa (eds.)
Springer, 2009. ISBN: 978-0387344447

Technical Papers

Peukert's Law and the Prediction of Battery Life
W. Peukert (original 1897); modern analysis in various sources
Describes rate-dependent capacity in lead-acid batteries
Wikipedia Overview
A Review of Lithium-Ion Battery State of Health Estimation
M. Berecibar et al.
Renewable and Sustainable Energy Reviews, 2016
DOI: 10.1016/j.rser.2015.11.042
Modeling of Lithium-Ion Battery Thermal Behavior
Various authors - extensive literature
Journal of Power Sources, Electrochimica Acta, etc.

Online Resources

Battery University
Cadex Electronics
Comprehensive educational resource on battery technology
batteryuniversity.com
Battery Design and Safety
MIT OpenCourseWare
Lecture notes and materials on battery fundamentals
MIT OCW 10.426
Cell Database - Battery Archive
Various Contributors
Real-world test data for many commercial cells
batteryarchive.org
NREL Battery Thermal Testing
National Renewable Energy Laboratory
Research on thermal management and safety
NREL Battery Thermal Testing

Manufacturer Datasheets

Cell Manufacturer Technical Resources
For accurate parameters, always consult manufacturer datasheets:
Panasonic | LG Chem | Samsung SDI | CATL

Standards & Safety

UN 38.3 - Transport Testing
UN Manual of Tests and Criteria for lithium battery transport
UN Manual of Tests
IEC 62133 - Safety Requirements
International standard for portable sealed secondary cells
UL 2054 / UL 2271 / UL 1973
UL standards for household batteries, light EV batteries, and stationary storage