Calculate This № 11 · Power
Instrument № 11 - Power

Amp-Hour
Conversions

Three related calculations in one place: watts to amp-hours, amps to amp-hours, and runtime from a battery you already own.

See the math behind this calculator
Energy
Wh = V × Ah

Current
I = P ÷ V

Runtime
t = capacity ÷ load
What are you calculating?
Load & duration
System
Recommended capacity -
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The relationships

Amp-hours, watts, voltage, and runtime are all the same physics expressed four different ways. Each calculation is just an algebraic rearrangement of the same equation.

energy_Wh = capacity_Ah × voltage
current_A = power_W ÷ voltage
runtime_h = capacity_Ah ÷ current_A

Every real-world correction (efficiency, usable depth-of-discharge, Peukert effects) shows up as a multiplier on one of those three numbers.

Frequently asked

Do I need to apply efficiency twice?

Once is usually right. If your load is a DC device on the battery directly (no inverter), set efficiency to 100%, because there’s no AC conversion happening. If it’s an AC appliance through an inverter, 85–92% is realistic.

Why does the Watts → Ah tab give a different number than Amps → Ah?

Because Watts → Ah assumes AC loads through an inverter (with inverter losses), and Amps → Ah assumes a DC load drawing current directly. For the same energy, the AC path needs a bigger battery to cover the inverter overhead.

What’s a sensible usable DoD?

LiFePO₄: 80–95% (most BMS protect at 10%). AGM: 60% comfortable. Flooded lead-acid: 50% for daily cycling; 80% for occasional deep discharge if you accept shorter life.

Show the working

Everything here routes through watt-hours, because that’s the only unit that stays honest across different battery voltages. If any of it looks wrong, it might be. Tell us what we got wrong.

Starting from watts watt-hours = watts × hours amp-hours drawn = (watts ÷ (volts × efficiency)) × hours
Starting from amps amp-hours drawn = (amps ÷ efficiency) × hours watt-hours = amp-hours × volts
Battery capacity required capacity Ah = amp-hours drawn ÷ depth of discharge

Constants used

  • Efficiency: inverter and wiring losses. 90% is a reasonable default for an inverter, 100% for a direct DC load
  • Depth of discharge: how much of the battery you’re willing to use. 80% for lead-acid, higher for lithium

Amp-hours only mean something alongside a voltage. 100 Ah at 12 V and 100 Ah at 24 V are different amounts of energy, which is why the watt-hour figure is the one to compare with.