Battery runtime
E (Wh) = capacity (Ah) × voltage (V)
The energy of a battery (Ah × V, in watt-hours), its runtime under a given load, or the capacity to plan to hold a target: three directions of the same calculation, with the two discounts naive calculations forget, the actually usable share of the capacity (50% for lead-acid, 80-90% for LiFePO₄) and the inverter efficiency. The note dismantles the power-bank trap: 20,000 mAh counted at 3.7 V make 74 Wh, and the watt-hour is what compares batteries, never the mAh alone.
8 h 30 min
- Calculation
- t = available E / P = 510 Wh / 60 W = 8.5 h
- Available energy
- 510 Wh
The battery lasts 8 h 30 min under this load.
The mAh of a power bank are counted at the cell voltage, 3.7 V, not at the 5 V of the USB plug: 20,000 mAh make 74 Wh, the value printed next to it for airlines (usual cabin limit: 100 Wh). The Wh is what compares two batteries, never the mAh alone.
The usable share is not a defect, it is a lifespan choice: a lead-acid battery discharged flat survives a few dozen cycles, half-discharged several hundred. Lithium chemistries tolerate deeper discharges; the proposed values are common practice, your datasheet prevails.
Nameplate capacity is measured at low current (C/20 for lead-acid): drawing hard shrinks the Ah actually served (Peukert effect), and cold shrinks them further. For serious sizing, keep a margin beyond this calculation.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasE (Wh) = capacity (Ah) × voltage (V)
E (Wh) = capacity (Ah) × voltage (V)
runtime (h) = E × usable × efficiency / P
capacity (Ah) = P × t / (V × usable × efficiency)
The watt-hour is the unit that crosses voltages: a 74 Wh power bank, an 840 Wh car battery and a 500 Wh bike battery compare directly, their mAh do not. The two discount factors multiply: the share of capacity you allow yourself to draw, then what the conversion lets through.
- Ampere-hour (Ah)
- · the charge: one ampere for one hour. Only compares two batteries at equal voltage; 1000 mAh = 1 Ah.
- Watt-hour (Wh)
- · the energy: Ah × V. The unit of airline labels and the only one that compares batteries of different voltages.
- Depth of discharge
- · the share of capacity drawn before recharging. Limiting it extends the life: a usage setting, not a loss.
- Nominal voltage
- · the average voltage of the chemistry: 3.7 V per li-ion cell, 12 V for six lead cells, 12.8 V for four LiFePO₄. The real voltage drifts along the discharge.
Validity domainThe model is linear: constant nameplate capacity, constant nominal voltage.
The model is linear: constant nameplate capacity, constant nominal voltage. Two real effects degrade it, stated rather than modelled: the Peukert effect (a lead-acid battery drawn hard serves fewer ampere-hours than its nameplate, measured at C/20) and temperature (cold reduces the served capacity, noticeably below 0 °C). The proposed usable shares are common practice; your battery’s datasheet prevails.
The power-bank trap"20,000 mAh" says nothing without the voltage.
"20,000 mAh" says nothing without the voltage. Those milliampere-hours are counted at 3.7 V, the voltage of the internal cells: 74 Wh. Recounted at the 5 V of USB, only a theoretical 14,800 mAh remain, minus conversion losses, and that is why the "20,000" power bank only recharges a 4500 mAh phone three times. The manufacturer did not lie, it counted in the unit that suits it. The Wh does not cheat: it is also the value airlines check, 100 Wh in cabin without approval.
Reading the resultThe nameplate energy is the label’s; the available energy is what actually feeds the load, after the usable share and the efficiency.
The nameplate energy is the label’s; the available energy is what actually feeds the load, after the usable share and the efficiency. To size a battery, start from the need (power × duration), walk back up the chain of losses, and round up to the next commercial model: the calculation returns the exact lower bound, not the safety margin.