Battery Series-Parallel Bank Calculator
Bank voltage, capacity and energy from the number of series and parallel batteries. With the formula, a worked example and typical values.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates bank voltage, bank capacity and bank energy from battery or cell voltage, battery capacity, batteries in series per string and parallel strings. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Keep parallel strings to four or fewer in lead-acid banks to limit current imbalance.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Series voltage and parallel capacity are basic circuit relationships. Battery chemistry, cell arrangement and safety standards may apply to a project, but no single standard governs this generic relationship calculator. |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Battery or cell voltage | 12 V |
| Battery capacity | 100 Ah |
| Batteries in series per string | 4 |
| Parallel strings | 2 |
- V = 4 × 12 = 48 V
- Ah = 2 × 100 = 200 Ah
- E = 48 × 200 = 9.6 kWh
Assumptions
- Identical batteries at the same state of charge
Keep parallel strings to four or fewer in lead-acid banks to limit current imbalance.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Battery or cell voltage | V | greater than 0 V | |
| Battery capacity | Ah | greater than 0 Ah | |
| Batteries in series per string | (number) | 1 or more, up to 500 | |
| Parallel strings | (number) | 1 or more, up to 100 |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Bank voltage | V | Shown to 1 decimal place | |
| Bank capacity | Ah | Shown to 1 decimal place | |
| Bank energy | kWh | Shown to 2 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with battery or cell voltage
| Battery or cell voltage (V) | Bank voltage (V) | Bank capacity (Ah) | Bank energy (kWh) |
|---|---|---|---|
| 1.2 | 4.8 | 200 | 0.96 |
| 3 | 12 | 200 | 2.4 |
| 6 | 24 | 200 | 4.8 |
| 12 | 48 | 200 | 9.6 |
| 24 | 96 | 200 | 19.2 |
| 48 | 192 | 200 | 38.4 |
| 120 | 480 | 200 | 96 |
Other inputs are the same as in the worked example above.
Standards and further reading
- IEC 60909-0 (short-circuit currents)
- IEEE Std 519 (harmonic limits)
Check results against your utility's connection requirements and the equipment data sheets. These are named as background reading. Elecmetric does not embed clause text or rating tables, and the reviewer record for this calculator is separate from this list.
Frequently asked questions
What do I need to enter?
Enter battery or cell voltage, battery capacity, batteries in series per string and parallel strings. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Identical batteries at the same state of charge.
Which calculators should I use next?
Common next steps are Battery Bank Sizing and UPS Battery Runtime. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Battery Pack Formulas: Series and Parallel: Battery pack formulas: cells in series for voltage, strings in parallel for capacity
- Battery Formulas: Capacity and Runtime: Battery formulas for energy in Wh, bank capacity from load and depth of discharge, runtime
- Battery Internal Resistance Formulas: Battery internal resistance formulas: the terminal voltage under load, the resistance from two readings
More Power Systems calculatorsAll engineering calculatorsBattery Series-Parallel Bank in Elecmetric