TAHA Engineering Toolsby TAHA Knowledge Lab

Electrical Engineering

Battery Runtime Calculator

Estimated running time of a battery from its capacity and the load power or current.

Inputs

Calculate from
A battery connected through an optional inverter to a load drawing power P.BatteryC, V or EInverterηLoadP or It = E × u × η ÷ P
The battery stores energy E (= C × V). Only the usable share u is taken out, and an inverter or converter wastes some (efficiency η). Runtime t = E × u × η ÷ P. Diagram not to scale.

Rated (nameplate) energy. For several batteries, enter the total.

Average power drawn by everything connected. For an inverter, this is the AC power of the appliances.

How much of the rated capacity you allow to be used before recharging. Check your battery’s data: lead-acid batteries are often limited to about 50%; many lithium batteries allow 80–100%. 100% means the full rated capacity.

100% if the load runs directly from the battery. If an inverter or DC-DC converter is used, enter its efficiency from its data sheet.

Result

Estimated runtime
6
Runtime (hours and minutes)
6 h 0 min
Usable energy
1,200
Power drawn from the battery
200

With 1,200 Wh usable and 200 W drawn from the battery, it should last about 6 h (6 h 0 min).

Educational estimate — check the assumptions below.

About this calculator

How long will a battery keep something running? Divide the energy you can actually take out of the battery by the power the load draws. This calculator works from a battery’s energy rating in watt-hours (Wh), or from its ampere-hour (Ah) rating and voltage, or — for a load drawing a known current straight from the battery — from Ah and amps alone.

Nothing is assumed silently: you enter how much of the rated capacity is usable and, if an inverter or converter is used, its efficiency. The result is an estimate for planning, such as UPS backup time, a solar battery bank, a camping power station or a battery-powered device.

Formula

Energy (Wh) and load power

t (h) = E (Wh) × u × η ÷ P (W)

E = rated energy, u = usable share of capacity (fraction), η = inverter or converter efficiency (fraction), P = load power.

Ah, voltage and load power

E (Wh) = C (Ah) × V (V)    t (h) = E × u × η ÷ P

C = rated capacity, V = nominal battery voltage, u = usable share, η = conversion efficiency, P = load power.

Ah and load current

t (h) = C (Ah) × u ÷ I (A)

C = rated capacity, u = usable share (fraction), I = average current drawn from the battery.

Worked example

  • Energy: a 1200 Wh power station running a 100 W load, 100% usable, no inverter loss: 1200 ÷ 100 = 12 h.
  • Ah and voltage: a 12 V, 100 Ah battery = 1200 Wh. Allow 80% usable and an inverter of 90% efficiency, with a 200 W load: 1200 × 0.8 × 0.9 ÷ 200 = 4.32 h (4 h 19 min).
  • Ah and current: a 2000 mAh cell feeding a device drawing 250 mA: 2 Ah ÷ 0.25 A = 8 h.

Assumptions and limitations

  • The load is steady. Loads that cycle on and off (fridges, pumps) should be entered as their average power or current.
  • Rated capacity is measured under specific test conditions. At high discharge currents (especially lead-acid batteries), in cold weather, or with an ageing battery, the real capacity can be much lower.
  • Only the losses you enter are included. Battery management systems, cables and standby consumption of an inverter also use energy.
  • Ah and current mode is for loads drawing current directly from the battery at the battery voltage.

References

  • Energy = capacity × voltage (1 Ah at 1 V = 1 Wh); runtime = usable energy ÷ power drawn.