Series and parallel
In series the voltages add up: U = S x U1. In parallel the capacities add up: C = P x C1. A 2s2p bank of 12 V 200 Ah batteries: U = 2 x 12 = 24 V, C = 2 x 200 = 400 Ah, and 2 x 2 = 4 batteries in all.
Reference tool — arithmetic, not a battery design
Work out a battery bank from batteries in series and parallel.
Series · parallel · energy · running time · counts
Volts, amp hours, hours.
Type a line (4 x 12 V 200 Ah 2s2p, 24 V bank 8 x 6 V 225 Ah, need 24 V 400 Ah from 12 V 100 Ah; add load 300 W for the running time) or fill in the fields: the line and the fields stay in step.
Examples:
All 130 engineering tools
Enter the voltage and capacity of one battery (or cell) and how the batteries are connected — 2s2p, in series or in parallel — and the calculator gives the bank voltage, the capacity in Ah and the stored energy in Wh and kWh. Add a load in A or W and a depth of discharge in per cent, and it gives the load current and the ideal running time from full to that depth. In reverse, enter the voltage and capacity you need and it counts the batteries in series and the strings in parallel. The working is shown with your numbers, and the result is a line you can copy.
Arithmetic only: no Peukert correction, no temperature derating, no charge rates and no recommended depth of discharge. At high discharge rates and at low temperature the real running time is shorter than worked out; the data of the battery maker and, for an emergency supply, the rules of the class society govern. Connect in parallel only batteries of the same type, capacity and age, each charged to the same state.
How it is worked out
Layout, energy, time.
Energy and current
The stored energy is E = U x C: 24 V x 400 Ah = 9600 Wh = 9.6 kWh, at the nominal voltage and capacity. A load given in watts draws I = power / U: 300 W at 24 V is 12.5 A.
Running time and counts
The ideal running time is t = C x depth of discharge / I: 400 Ah x 50 % / 12.5 A = 16 h, with 50 % as an example. For a target bank, S = target voltage / battery voltage must be a whole number; P = target capacity / battery capacity, rounded up.
| Layout | Batteries | Voltage, V | Capacity, Ah | Energy, kWh |
|---|---|---|---|---|
| 1s1p | 1 | 12 | 100 | 1.20 |
| 1s2p | 2 | 12 | 200 | 2.40 |
| 2s1p | 2 | 24 | 100 | 2.40 |
| 2s2p | 4 | 24 | 200 | 4.80 |
| 4s1p | 4 | 48 | 100 | 4.80 |
| 2s4p | 8 | 24 | 400 | 9.60 |
| 4s2p | 8 | 48 | 200 | 9.60 |
| 4s4p | 16 | 48 | 400 | 19.20 |
The figures are arithmetic for 12 V 100 Ah batteries; for another battery multiply its voltage by the number in series and its capacity by the number of strings. The energy is at the nominal voltage and capacity.
Sources
The working is the arithmetic of cells and batteries in series and parallel. The nominal cell voltages offered as picks — lead-acid 2.0 V, NiCd 1.2 V and LiFePO4 3.2 V per cell — are each checked against two independent references; the voltage on the label or in the data of the maker always comes first. The note on connecting in parallel only batteries of the same type, capacity and age, charged to the same state, is checked against two independent references as well.
Before you work it out
Questions about battery banks
What does 2s2p mean?
Two batteries in series make one string, and two such strings are connected in parallel: four batteries in all. With 12 V 200 Ah batteries the bank is 2 x 12 = 24 V and 2 x 200 = 400 Ah, and it stores 24 x 400 = 9600 Wh, or 9.6 kWh.
How do series and parallel change the voltage and the capacity?
In series the voltages add up and the capacity stays that of one battery; in parallel the capacities add up and the voltage stays that of one string. Twelve 2 V 600 Ah cells in series give 24 V and 600 Ah; four 12 V 100 Ah batteries in parallel give 12 V and 400 Ah.
How long will a battery bank run a load?
Ideally, t = usable capacity / current. A load given in watts draws I = P / U: 300 W at 24 V is 12.5 A. With 400 Ah and a depth of discharge of 50 % entered as an example, the usable capacity is 200 Ah and t = 200 / 12.5 = 16 h. The 50 % is an example, not a recommendation.
How many 12 V 100 Ah batteries make a 24 V 400 Ah bank?
In series 24 / 12 = 2, in parallel 400 / 100 = 4: eight batteries as 2s4p. When the voltage asked for is not a whole multiple of the battery voltage, as 24 V from 9 V batteries (24 / 9 = 2.67), the bank cannot be built from them in series, and the page says so; when the capacity asked for is not a whole multiple of the battery capacity, the number of strings is rounded up to the next whole number.
Why is the real running time shorter than the result?
The calculation takes the rated capacity as fixed. At high discharge rates and at low temperature a battery gives less than its rated capacity, so the real running time is shorter. The page gives no correction figures: the data of the battery maker and, for an emergency supply, the rules of the class society govern.
Which depth of discharge should be used?
This page does not give one. The usable depth of discharge depends on the battery and the way it is used, and is set by the data of the battery maker and, for an emergency supply, by the class rules. The examples use 50 % as a round example only.
Batteries or a part for the bank?
Send the line with a photograph of the battery label.
The calculator works out the bank from the figures you enter. When batteries, cables, lugs or a battery switch are needed, attach a photograph of the label or the diagram, and Vessel Core checks the details before an offer goes back.
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