Skip to content
RFrftools.io
Motor

Battery Runtime (Motor Load)

Calculate battery runtime for motor-driven systems accounting for motor current draw, efficiency, and depth of discharge.

Loading calculator...

Formula

t=Cusable/Idraw,Cusable=C×DoDt = C_usable / I_draw, C_usable = C × DoD
C— Battery capacity (mAh)
DoD— Depth of discharge (%)

How It Works

This calculator determines battery runtime for motor-driven systems from battery capacity, motor power consumption, and system efficiency. Electric vehicle designers, robotics engineers, and portable equipment developers use it to size batteries for required operating duration. Accurate runtime prediction prevents undersized batteries that strand vehicles or oversized packs that waste weight and cost.

Per battery engineering fundamentals (Linden's 'Handbook of Batteries', 4th ed., McGraw-Hill) and IEC 61960 (Secondary lithium cells and batteries for portable applications), runtime = (Battery_Wh × DoD) / P_average, where DoD is depth of discharge (typically 80% for lead-acid, 90% for Li-ion, 95% for LiFePO4 per manufacturer guidelines). Motor efficiency ratings that determine P_average follow IEC 60034-30-1 (Rotating electrical machines — Efficiency classes) and NEMA MG-1-2021 (NEMA Premium efficiency standards for electric motors). For motor systems, P_average must include all losses: P_total = P_motor / (η_motor × η_controller × η_wiring), typically 75-85% total system efficiency.

The Peukert effect significantly impacts lead-acid batteries: capacity decreases at higher discharge rates following C_effective = C_rated × (I_rated/I_actual)^(k-1), where k = 1.1-1.3 for lead-acid and 1.02-1.08 for lithium chemistries. A 100 Ah lead-acid battery at 2C discharge (200A) delivers only 70-80 Ah usable capacity—30% less than the 1C rating. Temperature also affects capacity: Li-ion delivers ~80% capacity at 0°C and ~60% at -20°C per manufacturer specifications.

Worked Example

Calculate runtime for an electric golf cart. Battery: 48V, 150 Ah LiFePO4 pack. Motors: two 1.5 kW hub motors. Typical usage: 70% duty cycle at 50% throttle, hilly terrain.

Step 1 — Calculate battery usable energy: E_total = V × Ah = 48 × 150 = 7200 Wh DoD for LiFePO4: 95% E_usable = 7200 × 0.95 = 6840 Wh

Step 2 — Estimate average motor power consumption: At 50% throttle: P_motors = 0.50 × (2 × 1500W) = 1500W mechanical output Motor efficiency (85%): P_motor_elec = 1500 / 0.85 = 1765W Controller efficiency (95%): P_system = 1765 / 0.95 = 1858W

Step 3 — Account for duty cycle: Average power: P_avg = 1858W × 0.70 = 1301W Average current: I_avg = 1301 / 48 = 27.1A

Step 4 — Verify C-rate and Peukert effect: C-rate = 27.1 / 150 = 0.18C LiFePO4 Peukert exponent ≈ 1.05 Capacity derating: (1/0.18)^0.05 = 1.09 (9% bonus vs. 1C rating) Effective capacity: 150 × 1.09 = 163 Ah equivalent

Step 5 — Calculate runtime: Runtime = (48 × 163 × 0.95) / 1301 = 7430 / 1301 = 5.71 hours

Result: The golf cart operates approximately 5.7 hours (34 km at 6 km/h average) under typical 70% duty cycle conditions. Add 20% safety margin: plan for 4.6 hours between charges to account for aging and temperature variation.

Practical Tips

  • ✓Per battery longevity guidelines, limit DoD to 80% for NMC lithium (1000+ cycles) and 50% for lead-acid (500+ cycles); deeper discharge accelerates capacity fade—a 100% DoD NMC cell lasts only 300-500 cycles
  • ✓Log actual current with a coulomb counter during representative operation cycles—real-world average is typically 40-60% of worst-case estimates due to coasting, regeneration, and variable loads
  • ✓Per cold-weather guidelines, derate Li-ion capacity by 20% at 0°C and 40% at -20°C; lead-acid loses 50% capacity at 0°C—critical for outdoor winter applications

Common Mistakes

  • ✗Using peak motor current instead of average: Per battery sizing practice, a robot at 60% duty cycle draws average current of 0.6× peak; using peak overestimates consumption by 67%, causing unnecessary battery oversizing
  • ✗Ignoring Peukert effect on lead-acid batteries: At 2C discharge, lead-acid delivers only 70-80% of rated Ah per Peukert equation; lithium batteries (k≈1.05) are nearly immune to this effect
  • ✗Forgetting controller and wiring losses: Per system analysis, motor controller efficiency is 90-97% and cable losses add 1-5%; total system efficiency of 80-90% reduces runtime 10-20% versus motor-only calculations

Frequently Asked Questions

Per Linden's 'Handbook of Batteries': Peukert effect describes capacity reduction at high discharge rates. The empirical formula C_eff = C_rated × (I_rated/I)^(k-1) uses Peukert exponent k: 1.1-1.3 for lead-acid, 1.02-1.08 for lithium. Example: 100 Ah lead-acid (k=1.2) at 100A (1C) delivers 100 Ah, but at 200A (2C) delivers only 100×(100/200)^0.2 = 87 Ah. Always check manufacturer discharge curves at actual operating C-rate for accurate runtime.
Per battery sizing methodology: Size energy (Wh) for average power to meet runtime requirement. Size continuous current rating (C-rate) for peak current to avoid excessive voltage sag (>10% causes controller brownout). For pulsed loads, add bulk capacitance (1-10 mF per amp of pulse current) to smooth current demand—the battery then sees only average current while capacitors supply peaks.
Per manufacturer data across chemistries: Li-ion capacity drops to 80% at 0°C and 60% at -20°C due to increased internal resistance. Lead-acid drops to 50% at 0°C. High temperatures (>45°C) accelerate permanent capacity degradation at 2-3% per year above baseline. For reliable outdoor operation, insulate batteries and use thermal management to maintain 15-35°C operating range. Derate capacity 20% minimum for uncontrolled outdoor applications.

Shop Components

As an Amazon Associate we earn from qualifying purchases.

NEMA 17 Stepper Motor

NEMA 17 bipolar stepper motors for precision motion control

Amazon →

Stepper Motor Driver (A4988)

A4988 stepper driver modules for microstepping control

Amazon →

DC Motor with Encoder

12 V DC motors with encoders for closed-loop drive applications

Amazon →

Related Calculators

Power

Battery Life

Estimate battery runtime for IoT and portable devices given average current draw, duty cycle, self-discharge rate, and depth-of-discharge cutoff. Suitable for LiPo, alkaline, NiMH, and coin-cell batteries.

Motor

Motor Efficiency

Calculate motor efficiency, power losses, and heat dissipation from electrical input and mechanical output measurements.

Motor

DC Motor

Calculate DC motor speed, torque, power, and efficiency from electrical parameters

Motor

Stepper Motor

Calculate stepper motor speed, step frequency, and travel per revolution