How it is calculated

The formulas each tool uses, so you can check them.

Consumption of one appliance

E = P \times h \times n

E is the energy in Wh, P the power in W, h the hours of use per day and n the number of units.

Daily consumption

E_{day} = (E_{direct} + \frac{E_{converter}}{0,90} + \frac{E_{inverter}}{0,88}) \times (1 + m)

Appliances that run through a converter (USB or another voltage) or through the inverter (230 V or 120 V) use more because of the losses. m is the safety margin.

Battery

C = \frac{E_{day} \times d}{V \times D}

C is the capacity in Ah, d the days without charging, V the battery voltage and D the usable depth of discharge of the battery type, between 0.5 for lead and 0.8 for lithium.

Solar panels

P_{panels} = \frac{E_{day}}{HSP \times 0,7}

HSP are the peak sun hours. The 0.7 covers losses from temperature, dirt, tilt and wiring.

MPPT charge controller

I_{controller} = \frac{P_{panels}}{V} \times 1,25

Current in A that the controller must handle, with a 25 % margin.

Inverter

P_{inverter} = P_{max} \times 1,25

P max is the most powerful AC appliance. It is sized for using them one at a time.

Cable cross-section

S = \frac{2 \times L \times I}{56 \times 0,03 \times V}

S is the cross-section in mm², L the one-way length in m and I the current in A. The 56 is the conductivity of copper and the 0.03 the maximum voltage drop (3 %). The cross-section is then increased if needed so that the cable can carry more current than its fuse.

Fuse

I_{fuse} \geq I \times 1,25

The first standard rating above that result is chosen.

Power station capacity

C_{station} = \frac{E_{appliances} \times (1 + m) \times d}{0,85}

Capacity in Wh. E is the daily consumption of the appliances, m the margin and d the days without charging. The 0.85 reflects that not all the advertised capacity is usable.

Output power

P_{output} = P_{max} \times 1,25

P max is the most powerful mains appliance.

Runtime of a power station

t = \frac{C_{station} \times 0,85}{E_{day}}

t is the number of days a station of that capacity lasts with your daily consumption.

Usable energy

E_{usable} = C \times V \times (s - (1 - D))

C is the capacity in Ah, V the voltage, s the current charge (1 if full) and D the usable depth of discharge of the battery type, between 0.5 for lead and 0.8 for lithium.

Days of runtime

t = \frac{E_{usable}}{E_{day}}

E day is the daily consumption of your appliances, including the losses of the inverter (0.88) and the converter (0.90).

Hours with everything on

t_{hours} = \frac{E_{usable}}{P_{total}}

P total is the sum of the watts of all the appliances running at once.

Charge to put back

C_{refill} = \frac{C \times (s_{final} - s_{initial})}{η}

C is the capacity in Ah and s the charge as a fraction of one. η is the charging efficiency of the battery type, between 0.80 for flooded lead-acid and 0.97 for LiFePO4 lithium.

With solar panels

t_{days} = \frac{C_{refill} \times V}{P_{panels} \times HSP \times 0,7}

Days of sun needed. HSP are the peak sun hours.

With a charger

t_{hours} = \frac{C_{refill}}{I_{charger}}

Applies to both the alternator charger and the mains charger. I is its current in A.

Values for each battery type

Type	Usable discharge	Charging efficiency	Weight per 100 Ah at 12 V	Cycles	Max. years
LiFePO4 lithium	80 %	97 %	11 kg	3,000	10
AGM	50 %	85 %	30 kg	500	5
Gel	55 %	85 %	30 kg	700	6
Lead-carbon	65 %	88 %	30 kg	1,500	8
Flooded lead-acid	50 %	80 %	27 kg	300	4
NMC lithium	80 %	95 %	7 kg	800	8
Sodium-ion	80 %	92 %	14 kg	3,000	10

Typical, indicative values. Each manufacturer gives its own on the data sheet, and those are the ones that count.

Capacity to buy

C_{buy} = \frac{C_{usable}}{D}

C usable is the Ah you use between charges and D the usable depth of discharge of the battery type, between 0.5 for lead and 0.8 for lithium. It is rounded up to the next commercial size.

Years of life

a = \min (a_{max}, \frac{N}{u})

N is the number of cycles the battery withstands and u the days of use per year. a max is the limit set by ageing.

Cost per year

c_{year} = \frac{price}{a}

The price of the battery spread over the years it lasts.