BAAD

Engineering

Battery Autonomy and Discharge Calculator

Convert battery voltage and amp-hours to watt-hours, apply a usable-capacity limit, add standby load, adjust for conversion efficiency, and calculate runtime with an hourly remaining-energy schedule.

Nominal battery voltage (V)Rated battery capacity (Ah)Selected usable capacity (%)Connected load power (W)Conversion efficiency (%)Standby and auxiliary power (W)Maximum schedule hours

Nominal stored energy (Wh)-

Selected usable energy (Wh)-

Load plus standby demand (W)-

Battery-side power draw (W)-

Estimated runtime (hours)-

Modeled conversion loss (W)-

Energy delivered through estimated runtime (Wh)-

Schedule horizon minus estimated runtime (hours)-

Decision view

Usable-energy discharge area and runtime threshold

Usable-energy discharge area and runtime thresholdBattery-side demand depletes the selected usable energy until the exact runtime crossing, with the planning horizon shown separately.

Exact scenario comparisonConnected load power (W) changes while all other entered assumptions remain constant.

Connected load power (W)	Nominal stored energy (Wh)	Selected usable energy (Wh)	Load plus standby demand (W)	Battery-side power draw (W)	Estimated runtime (hours)	Modeled conversion loss (W)	Energy delivered through estimated runtime (Wh)	Schedule horizon minus estimated runtime (hours)

Period-by-period detail

Hourly battery discharge schedule

Remaining usable energy and delivered demand update for every modeled elapsed hour.

How to use Battery Autonomy and Discharge Calculator

Enter nominal voltage and amp-hour capacity.
Choose a usable-capacity percentage appropriate to the battery policy.
Enter connected load, standby load, and conversion efficiency.
Compare the discharge curve with the planning horizon.

Calculator guide

Understanding Battery Autonomy and Discharge Calculator

Battery runtime depends on usable stored energy and battery-side demand, not rated amp-hours alone. This calculator exposes nominal energy, selected usable energy, inverter or conversion loss, discharge time, and the gap to a planning horizon.

Wh, not Ah alone Voltage is required to obtain energy.

Reserve matters Only the selected usable fraction is discharged.

Loss adds draw Battery-side watts exceed delivered watts.

Timeline reveals gap Runtime is compared with the planning horizon.

Calculation method

How the calculation works

Convert rated voltage and amp-hours to nominal energy, apply an explicit usable fraction, and divide by efficiency-adjusted battery-side demand. Multiply volts by amp-hours for nominal Wh, apply the usable percentage, divide delivered load plus standby by efficiency for battery-side watts, then divide usable Wh by battery-side watts.

Detailed calculation process

Translate battery nameplate capacity into a discharge timeline

The defaults use a 48 V, 200 Ah battery, 80% usable capacity, a 1,200 W load, 35 W standby, and 90% conversion efficiency.

General formula: E_nom = V Ah; E_use = E_nom u; P_load = P_connected + P_standby; P_bat = P_load/eta; t = E_use/P_bat Voltage times amp-hours produces nominal watt-hours. The usable fraction limits depth of discharge, while efficiency increases the watts that must leave the battery for a given delivered load.

What each symbol means

V Nominal battery voltage, measured in volts (V).

Ah Rated battery capacity, measured in ampere-hours (Ah).

u Selected usable fraction, unitless.

P_load Connected plus standby demand, measured in watts (W).

eta Conversion efficiency, unitless.

t Idealized autonomy, measured in hours.

Worked substitution with the default inputs

1. Calculate nominal energy: E_nom = 48 V x 200 Ah = 9,600 Wh The voltage and amp-hour ratings combine into an energy nameplate.

2. Apply usable capacity: E_use = 9,600 x 0.80 = 7,680 Wh The remaining 20% is held outside the selected discharge window.

3. Combine delivered loads: P_load = 1,200 + 35 = 1,235 W Standby and auxiliary demand reduce autonomy too.

4. Convert to battery-side draw: P_bat = 1,235/0.90 = 1,372.222 W; loss = 137.222 W Efficiency loss must be supplied by the battery.

5. Calculate runtime and reconcile delivered energy: t = 7,680/1,372.222 = 5.5968 h; delivered = 1,235 x 5.5968 = 6,912 Wh Delivered energy also equals usable battery energy multiplied by 90% efficiency.

The default battery has 7.680 kWh usable energy and supports the modeled 1.235 kW delivered load for about 5.597 hours, 4.403 hours short of the 10-hour schedule.

Discharge path

Watch usable energy cross the zero threshold

The area curve makes the runtime and schedule gap visible.

Starting energy Selected usable Wh at hour zero.

Slope Battery-side watts determine depletion rate.

Runtime marker Exact zero-energy crossing.

Planning horizon Entered maximum schedule duration.

Worked situations

Practical examples

The 48 V by 200 Ah nameplate equals 9.6 kWh.
An 80% window leaves 7.68 kWh usable.
At 1.372 kW battery draw, runtime is about 5.60 hours.

Better inputs

Useful tips

Use measured load rather than nameplate maximum when possible.
Include inverter idle and auxiliary loads.
Keep a reserve beyond the selected usable fraction where operations require it.

Before relying on the result

Limitations and common mistakes

Actual capacity varies with chemistry, discharge rate, age, temperature, and cutoff voltage.
Surge power and BMS or inverter limits are not modeled.
The linear discharge curve is an energy-accounting view, not a cell-voltage prediction.

Reference

Key terms

Usable capacity: Energy allowed within the selected discharge window.
Battery-side draw: Power removed before conversion losses.
Autonomy: Modeled time until usable energy reaches zero.

Important note

Calculated from the entered values using the displayed engineering relationship. Confirm design values, load cases, safety factors, standards, and field conditions with a qualified professional.

Frequently asked questions

Why divide the load by efficiency?

The battery must supply both the delivered load and conversion losses.

Why is delivered energy below usable battery energy?

The difference is conversion loss over the runtime.

Does this model battery voltage sag?

No. It uses idealized energy accounting.

Can the schedule extend beyond runtime?

Yes; the curve remains at zero after usable energy is exhausted.