03 // Bidirectional STEM Calculators // EVERYDAYT (hr) = (C_Ah × V × (η / 100)) / P_load

Battery Runtime, Amp-Hour Capacity & Inverter Load Calculator

Battery bank backup runtime T (in hours) equals total nominal Watt-hour energy (C_Ah × V) scaled by usable depth-of-discharge & inverter efficiency η, divided by continuous load power P_load.

T (hr) = (C_Ah × V × (η / 100)) / P_load

Pick which value you want to calculate (or type into any field):Solving for: T (hr) — Battery Backup Runtime (Hours)

Battery Backup Runtime (Hours)Calculated

Continuous operating duration in hours

0.11,000.00

unit

Battery Capacity (Amp-Hours)

Rated charge capacity in Amp-hours

110,000.00

unit

Nominal Battery Bank Voltage

DC bus voltage (12V, 24V, or 48V)

3.2800

Usable DoD × Inverter Efficiency

Combined usable fraction in percent (LiFePO4 ≈ 85%, AGM ≈ 45%)

20100

Continuous Load Power

Connected device power draw in Watts (switch unit to kW)

150,000.00

Calculated Result · Battery Backup Runtime (Hours) (T (hr))

8.5

Step-by-Step Calculation

01Canonical Law: T (hr) = (C_Ah × V × (η / 100)) / P_load

02Given Inputs (Base Units): C (Ah) = 200, V = 12.8 V, η (%) = 85, P_load = 256 W

03Solve for T (hr) (Battery Backup Runtime (Hours)): T (hr) = 8.5

Battery bank backup runtime T (in hours) equals total nominal Watt-hour energy (C_Ah × V) scaled by usable depth-of-discharge & inverter efficiency η, divided by continuous load power P_load.

Real-World Reference Values

LiFePO4 4S Nominal Voltage12.8 V (80%–90% Usable DoD)

200 Ah × 12.8 V = 2,560 Wh nominal energy

Lead-Acid AGM Deep Cycle12.0 V (50% Max Recommended DoD)

Discharging below 50% sulfates plates rapidly

48V Server Rack Battery (100 Ah)51.2 V × 100 Ah = 5.12 kWh

Standard solar / UPS modular storage brick

20-Row Comparison Table

Battery Backup Runtime (Hours) (T (hr)) · Battery Capacity (Amp-Hours) (C (Ah))

Compare across:

Battery Runtime, Amp-Hour Capacity & Inverter Load Calculator — Battery Capacity (Amp-Hours) → Battery Backup Runtime (Hours)
#	Battery Capacity (Amp-Hours) (C (Ah))	Battery Backup Runtime (Hours) (T (hr))	Δ %
01	1	0.0425	-99.50%
02	83.8349	3.563	-58.08%
03	200 Current	8.5	0.00%
04	249.5046	10.6039	+24.75%
05	332.3395	14.1244	+66.17%
06	415.1743	17.6449	+107.59%
07	498.0092	21.1654	+149.00%
08	580.8441	24.6859	+190.42%
09	663.6789	28.2064	+231.84%
10	746.5138	31.7268	+273.26%
11	829.3487	35.2473	+314.67%
12	912.1836	38.7678	+356.09%
13	995.0184	42.2883	+397.51%
14	1,077.85	45.8088	+438.93%
15	1,160.69	49.3292	+480.34%
16	1,243.52	52.8497	+521.76%
17	1,326.36	56.3702	+563.18%
18	1,409.19	59.8907	+604.60%
19	1,492.03	63.4112	+646.01%
20	1,574.86	66.9317	+687.43%

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Frequently Asked Questions

How do I size the Amp-hour (Ah) battery bank needed for 24 hours of backup?+

Click SOLVE FOR on C (Ah), set T = 24 hours, and enter your load wattage P_load, bank voltage V, and usable efficiency η.

Why is nominal LiFePO4 voltage 12.8V instead of 12.0V?+

A 12V LiFePO4 battery consists of 4 cells in series (4S) each with a 3.20V flat discharge plateau (4 × 3.2V = 12.8V).

What is Peukert's Law for high discharge currents?+

At high C-rates (>0.5C), internal resistance reduces effective lead-acid capacity; LiFePO4 has a Peukert exponent near 1.02 with minimal capacity loss.