"I have a 200 Ah battery and a 2,000W inverter — how long will it run my fridge and lights?" is the off-grid question with the most wrong answers, and the wrong answers come from one place: people divide amp-hours by watts, a unit mismatch that produces numbers 12× too optimistic.

The correct calculation has three ingredients most attempts skip — the Ah→Wh conversion, the depth of discharge you're allowed to use, and the inverter efficiency you lose on the way out. This article gives the formula, walks through real examples at 12/24/48V, and hands you a free calculator that does it in seconds.

TL;DR — the formula: Run time (h) = Ah × V × DoD × efficiency ÷ load (W)

● Ah × V = Wh — the unit fix (200 Ah at 12V = 2,400 Wh).

● DoD — how much you may use: LiFePO4 ~80–100%, AGM/lead-acid ~50% 

● Efficiency — the inverter's loss, ~0.85 median (our [efficiency guide] has the full curve)

● Example: 200 Ah · 12V · 0.80 · 0.85 ÷ 100W =~16 h— not the 24 h a raw Ah÷W math suggests, and not the 200 h a unit-mismatch suggests

Ingredient 1: Ah → Wh (The Unit Fix)

Battery capacity comes in two shapes, and they're not interchangeable:

●Amp-hours (Ah) — the DIY/off-grid unit. It's current × time at the battery's voltage— a measure of charge, not energy. A "200 Ah" battery is 200 Ah at 12V, 24V, or 48V— those are three different amounts of stored energy.

●Watt-hours (Wh) — the energy unit, the one your load actually consumes.

The conversion is one multiplication:

Wh = Ah × V

This single table is why "my 200 Ah battery" is a meaningless question until the voltage is attached — 200 Ah at 48V is four times the energy of 200 Ah at 12V (the full system-level case is in our [12/24/48V guide]). Once you're in Wh, you're speaking the same language as the load, and the division finally makes sense.

Ingredient 2: Depth of Discharge (How Much You May Actually Use)

Rated Wh isn't usable Wh. The depth of discharge (DoD) is the fraction of the bank you can draw without aging the chemistry:

Two notes. First, 0.80 is the honest planning number for LFP even though the chemistry tolerates 100% — the BMS cut-off sits around 80–90% anyway, and planning to the floor of the usable band keeps the pack young (our [battery life guide] covers why). Second, the lead-acid 50% is the silent capacity halver: a 200 Ah AGM bank is a 100 Ah bank in real terms, which is why so many "my inverter dies at half the rated time" stories trace back to chemistry, not math.

Ingredient 3: Inverter Efficiency (The Loss on the Way Out)

The inverter doesn't pass 100% of the DC to the AC side. Our [efficiency guide] breaks down the curve; for planning, 0.85 is the median honest number — you'll land closer to 0.90–0.93 at a well-matched mid load, and closer to 0.75–0.80 at very light or near-full loads. Use 0.85 and you're in the right neighborhood; use 1.00 and your runtime is fantasy.

(And the no-load standby draw — 5–15W on a mid-size inverter — is a real line item for long light-load runs, not a rounding error.)

The Formula, Assembled

Run time (h) = (Ah × V × DoD × efficiency) ÷ load (W)

or, if you already know the Wh:

Run time (h) = (Wh × DoD × efficiency) ÷ load (W)

This is the same family as the station formula from the [Wh calculator] — where a station's "rated Wh" already folds in the usable fraction, so you just apply the ~0.85 end-to-end. A DIY bank keeps the three ingredients separate because you chose the chemistry, the voltage, and the inverter.

Worked Examples (12 / 24 / 48V)

Example A — 200 Ah · 12V · LFP, running 100W (lights + router + fan). 200 × 12 × 0.80 × 0.85 ÷ 100 = 16.3 h. A full night plus margin.

Example B — same bank, running 500W (add a hot plate / small kitchen). 200 × 12 × 0.80 × 0.85 ÷ 500 = 3.3 h. The bank is the same; the load is 5×; the time is ~5× less. Linearity is the whole point.

Example C — 200 Ah · 24V · LFP, running 500W. 200 × 24 × 0.80 × 0.85 ÷ 500 = 6.5 h. Same Ah count as A and B, but double the voltage — double the Wh, double the runtime. This is the [voltage decision] made visible in one number.

Example D — 200 Ah · 48V · LFP, running 1,000W. 200 × 48 × 0.80 × 0.85 ÷ 1,000 = 6.5 h. The solar-first class, doing a kilowatt for half a day.

The AGM shock (Example E) — 200 Ah · 12V AGM, running 100W. 200 × 12 × 0.50 × 0.85 ÷ 100 = 10.2 h. Against the 16.3 h of the LFP bank above, that's 37% less time for the identical "200 Ah" label — and it's the DoD, not the math, that did it: the AGM bank's usable energy (1,020 Wh) is half of LFP's (2,040 Wh).

Quick-Reference: 200 Ah · 12V · LFP (1,920 Wh usable, at 0.85 efficiency)

(At 1,000W the inverter is also near full load, so real efficiency dips a bit — treat the right column as "a little under.")

Free Run-Time Calculator (Embeddable)

Drop this self-contained calculator into a page — it takes Ah, voltage, chemistry (DoD), load, and efficiency, and returns Wh, usable Wh, and hours:

<div id="rt-calc" style="max-width:520px;margin:0 auto;font-family:inherit">
  <style>#rt-calc{border:1px solid #ddd;border-radius:12px;padding:20px}
  #rt-calc input,#rt-calc select{width:100%;padding:8px;margin:4px 0 12px;box-sizing:border-box}
  #rt-calc .row{display:flex;gap:8px}#rt-calc .row>div{flex:1}
  #rt-calc .out{font-size:15px;line-height:1.6}
  #rt-calc button{width:100%;padding:10px;border:0;border-radius:8px;background:#1a7f37;color:#fff;font-size:15px;cursor:pointer}
  #rt-calc .big{font-size:20px;font-weight:700}</style>
  <h3 style="margin-top:0">Inverter Run-Time Calculator</h3>
  <div class="row"><div><label>Battery Ah</label><input id="ah" type="number" value="200"></div>
  <div><label>Voltage</label><select id="v"><option>12</option><option>24</option><option>48</option></select></div></div>
  <label>Chemistry / usable (DoD)</label>
  <select id="dod"><option value="0.8">LiFePO4 (80%)</option><option value="1">LiFePO4 (100%)</option>
  <option value="0.5">AGM / lead-acid (50%)</option></select>
  <div class="row"><div><label>Load watts</label><input id="lw" type="number" value="100"></div>
  <div><label>Inverter eff.</label><select id="eff"><option value="0.75">0.75 (light/heavy)</option>
  <option value="0.85" selected>0.85 (median)</option><option value="0.93">0.93 (well-matched)</option></select></div></div>
  <button onclick="rt.run()">Calculate run time</button>
  <div id="rres" class="out" style="margin-top:12px"></div>
</div>
<script>
const rt={run(){const ah=+document.getElementById('ah').value||0,
  v=+document.getElementById('v').value,d=+document.getElementById('dod').value,
  w=+document.getElementById('lw').value||0,e=+document.getElementById('eff').value;
  if(ah<=0||w<=0){document.getElementById('rres').innerHTML='<em>Enter battery Ah and load watts.</em>';return;}
  const wh=ah*v,usable=wh*d*e;
  const h=usable/w;
  document.getElementById('rres').innerHTML=
   `<div><b>Bank energy:</b> ${wh.toLocaleString()} Wh</div>
    <div><b>Usable (DoD × efficiency):</b> ${Math.round(usable).toLocaleString()} Wh</div>
    <div class="big">→ Run time at ${w} W: ${h>=10?h.toFixed(1):h.toFixed(2)} h</div>
    <div>${h>=48?'≈ '+(h/24).toFixed(1)+' days — plenty of margin.':(h<4?'Under 4 h — consider a bigger bank or a smaller load.':'A few hours of coverage.')}
    ${e<0.85?' (light/heavy-load efficiency applied — a well-matched mid load runs longer.)':''}</div>`;}};
</script>

The Four Things That Shrink Real Runtime (vs the Formula)

The formula gives the number; these decide how far below it you actually land:

1. Efficiency at your actual load — the U-curve from the [efficiency guide]. A 2,000W inverter at 50W is far from its 0.85 assumption; at 1,000–1,500W it's right on it.

2. Cold — a bank at 0°C delivers 10–20% less; the inverter may also refuse to charge it. Winter math uses a colder 0.85.

3. Age — a 4-year-old LFP bank at 85% health is a 170 Ah bank. Re-measure against what it holds now, not what the label said.

4. Cables and joints — the I²R loss from the [12/24/48V guide] is real energy, mostly in the wires at 12V. Thick, short, clean runs protect the number you just calculated.

Frequently Asked Questions

How long will a 200 Ah battery run an inverter? It depends on voltage and load: 200 Ah at 12V is 2,400 Wh (~1,920 Wh usable for LFP), so ~16 h at 100W, ~3.3 h at 500W, ~1.6 h at 1,000W. At 24V it's double; at 48V, four times. The Ah alone doesn't answer it — voltage and load do.

What's the difference between Ah and Wh for run time? Ah is charge at a fixed voltage; Wh is energy. Multiply Ah by volts to get Wh, and then divide by the load's watts. Dividing Ah by watts directly (the common mistake) mixes units and inflates the answer by roughly the system voltage.

Should I use 50% or 100% depth of discharge? LFP: plan on 80% (the BMS cut-off and longevity both live there). AGM/lead-acid: 50%, full stop — that's the chemistry's safe floor. Using the wrong DoD is the #1 reason real runtimes come in at "half what I calculated."

Does a bigger inverter drain the battery faster? At the same load, a well-matched larger inverter is often more efficient (it sits mid-curve), not less. The inverter's own no-load draw (5–15W) is the real penalty of an oversized unit left running at light loads.

Why is my real run time shorter than the formula? Efficiency at your actual load, cold, age, and cable loss — the four shruners above. If it's far shorter (half), check the chemistry's DoD first; that's where the silent capacity halves live.

Final Thoughts

Inverter run time is one formula with three honest ingredients: Ah × V to get real energy, DoD to get the fraction you may use, and efficiency to get what survives the conversion. Do the unit fix first (the Ah÷W mistake is where 12× fantasies are born), plan LFP at 80% and lead-acid at 50%, use 0.85 as the median efficiency, and then let the four shruners — load-position, cold, age, and cable loss — tell you how much margin to keep. Run the numbers through the calculator, trust the conservative end, and the "how long will it last?" question stops being a guess at the inverter and becomes a schedule you can plan a day around.

[Optional CTA: The no-cables version of this math — NEJoye stations publish rated Wh, DoD, and measured efficiency in the spec sheet, so the run-time formula runs itself → NEJoye Power Inverters]