Battery Calculator

Battery capacity is measured in Amp-hours (Ah) or Watt-hours (Wh). Ah indicates how much current a battery can provide for one hour.

Wh = Ah × Voltage gives total energy storage.

For off-grid solar, size batteries for 2-3 days autonomy. Consider depth of discharge (DoD) to protect battery lifespan.

Lithium batteries offer higher DoD than lead-acid.

Battery runtime in hours equals the usable energy in watt-hours divided by the load power in watts: Runtime = (Ah x V x DoD) / Load Power (W). First convert capacity to energy with Wh = Ah x V, then multiply by the depth of discharge fraction to get usable energy.

For example, a 100 Ah 12 V lithium battery stores 100 x 12 = 1200 Wh; at 80% DoD, 960 Wh is usable, so a 200 W load runs for 960 / 200 = 4.8 hours.

The watt-hour is a unit of energy equal to 3600 joules, as defined by the SI framework maintained by NIST and BIPM. Real runtime is shorter once inverter and conversion losses are included.

Amp-hours (Ah) and milliamp-hours (mAh) measure electric charge capacity, while watt-hours (Wh) measure energy. One Ah equals 1000 mAh and represents a current of one ampere sustained for one hour, equal to 3600 coulombs of charge.

Because charge alone ignores voltage, Wh is the more meaningful energy unit: Wh = Ah x V. The ampere is one of the seven SI base units defined by BIPM, and the joule (1 Wh = 3600 J) is the coherent SI unit of energy per NIST.

This is why a 10,000 mAh power bank at 3.7 V holds only 37 Wh, and comparing two batteries fairly requires converting both to watt-hours rather than trusting mAh alone.

To convert amp-hours to watt-hours, multiply the capacity in Ah by the nominal battery voltage: Wh = Ah x V. A 50 Ah battery at 24 V stores 50 x 24 = 1200 Wh.

To reverse the conversion, divide energy by voltage: Ah = Wh / V. For mAh, first divide by 1000 to get Ah, so a 5000 mAh cell at 3.7 V holds (5000 / 1000) x 3.7 = 18.5 Wh.

Khan Academy and HyperPhysics (Georgia State University) both frame this as the electrical-power relationship P = VI integrated over time, giving energy = voltage x charge. Always use nominal voltage, not fully-charged voltage, for realistic comparisons across chemistries.

To size a battery bank, divide daily energy demand by the usable fraction and system voltage, then scale for days of autonomy: Required Ah = (Daily Wh x Days) / (DoD x V x Efficiency).

Suppose you need 2000 Wh per day, want 2 days of backup, use a 12 V lead-acid bank at 50% DoD with 90% system efficiency: (2000 x 2) / (0.5 x 12 x 0.9) = 4000 / 5.4 = about 741 Ah. Lithium banks at 80% DoD need far less capacity for the same load.

The U.S. Department of Energy recommends sizing for local sun-hours and worst-case cloudy periods, and rounding up to standard battery increments.

Charging time in hours is approximately the battery capacity in amp-hours divided by the charger current in amps, adjusted for efficiency: Charge Time = Ah / (Charger A x Efficiency). A depleted 100 Ah battery with a 10 A charger and 85% charging efficiency takes about 100 / (10 x 0.85) = 11.8 hours.

Lithium chemistries commonly use constant-current then constant-voltage (CC-CV) charging, so the final 10-20% tapers and takes longer than the linear estimate suggests.

IEC and IEEE battery standards specify safe charge rates as a C-rate; charging at 0.5C (half capacity in amps) is gentler and extends cycle life compared with aggressive 1C fast charging.

C-rate expresses charge or discharge current relative to capacity:

• a rate of 1C fully charges or discharges the battery in one hour
• 0.5C takes two hours
• 2C takes 30 minutes

The current equals C-rate x capacity, so 2C on a 50 Ah cell is 100 A. Higher C-rates generate more internal heat and voltage sag, reducing effective capacity and accelerating degradation, a behavior described by the Peukert effect for lead-acid batteries.

HyperPhysics and Battery University note that manufacturers rate capacity at a specified discharge rate (often 0.05C or the 20-hour rate), so drawing current faster than that rating delivers less usable energy than the label implies.

Wiring batteries in series adds their voltages while capacity in Ah stays the same; wiring in parallel adds capacity while voltage stays the same.

Four 12 V 100 Ah batteries in series give 48 V 100 Ah (4800 Wh), whereas the same four in parallel give 12 V 400 Ah (also 4800 Wh) - total energy is identical either way. Series-parallel combinations set both target voltage and capacity.

This follows the same rules as resistors and cells in circuits described by Khan Academy and HyperPhysics. Always match battery type, age, and state of charge within a bank, because mismatched cells cause uneven current sharing, overcharging, and premature failure.

Battery calculations underpin many systems:

• sizing UPS units for server backup
• designing off-grid and RV solar banks
• estimating electric-vehicle range from pack energy
• choosing power banks for travel
• specifying medical or marine backup power

For a UPS, runtime = (pack Wh x DoD x inverter efficiency) / load W tells you how long equipment survives an outage. EV range roughly equals pack energy in kWh divided by consumption in kWh per mile, so a 60 kWh pack at 0.3 kWh/mi covers about 200 miles.

Encyclopaedia Britannica notes that lithium-ion's high energy density (per unit mass and volume) is why it dominates portable and automotive applications where weight and space matter.

The most common mistake is comparing batteries by mAh alone while ignoring voltage - always convert to watt-hours (Wh = Ah x V) for a fair comparison.

Others include:

• forgetting depth of discharge (using full capacity instead of usable capacity)
• ignoring inverter and conversion losses of 10-30%
• assuming rated capacity holds at high discharge rates when the Peukert effect reduces it

People also overlook temperature: cold weather can cut usable capacity noticeably, and heat shortens lifespan. Finally, do not confuse charge (Ah, coulombs) with energy (Wh, joules) - they are different SI quantities per NIST.

Building a safety margin of 20-30% into any real design absorbs these combined real-world losses.