UPS Battery Runtime Calculator
Backup time and usable energy from battery bank size, depth of discharge, ageing and UPS efficiency. 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 usable battery energy and runtime from load, UPS efficiency, battery bank voltage, battery capacity and 2 more inputs. 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
High discharge rates deliver less than rated Ah (Peukert effect), so confirm against the battery discharge table for short runtimes.
Cross-check: 8 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: Indicative
Indicative. Estimation only; further engineering checks are required. Basis: Runtime estimate; discharge-rate effects are simplified.
What this calculator checks
- The arithmetic of the simplified model for the values you entered.
What remains unverified
- Whether the simplifying assumptions listed on this page hold for your case.
- Any standard, manufacturer or site data. Treat the result as an estimate and confirm it by a further engineering check.
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 | IEC 62040-3; IEEE 485, IEC 62040-3:2021 Ed 3.0; IEEE 485-2020 (active) |
| Standard review state | Public-scope screened; licensed clause review still pending |
| Scope-screening note | UPS performance and stationary lead-acid battery sizing are relevant. The runtime equation is an energy-balance estimate, not a guaranteed discharge curve; IEEE 485 applies only to lead-acid stationary batteries in float service. |
| Cross-check test cases | 8 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Indicative |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; licensed clause-by-clause standard review; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Load | 10 kW |
| UPS efficiency | 0.95 |
| Battery bank voltage | 240 V |
| Battery capacity | 100 Ah |
| Usable depth of discharge | 0.8 |
| Ageing and temperature factor | 0.8 |
- E = 240 V × 100 Ah × 0.8 × 0.8 = 15.36 kWh
- Input power = Load / η = 10.526 kW
- t = 15.36 / 10.526 = 1.459 h
Assumptions
- Constant power load
- Capacity is the rated value at the stated discharge rate
High discharge rates deliver less than rated Ah (Peukert effect), so confirm against the battery discharge table for short runtimes.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Load | kW | greater than 0 kW | |
| UPS efficiency | (number) | greater than 0, up to 1 | |
| Battery bank voltage | V | greater than 0 V | |
| Battery capacity | Ah | greater than 0 Ah | |
| Usable depth of discharge | (number) | greater than 0, up to 1 | |
| Ageing and temperature factor | (number) | greater than 0, up to 1 | 0.8 allows for end-of-life capacity |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Usable battery energy | kWh | Shown to 2 decimal places | |
| Runtime | min | Shown to 1 decimal place |
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 load
| Load (kW) | Usable battery energy (kWh) | Runtime (min) |
|---|---|---|
| 1 | 15.36 | 875.5 |
| 2.5 | 15.36 | 350.2 |
| 5 | 15.36 | 175.1 |
| 10 | 15.36 | 87.6 |
| 20 | 15.36 | 43.8 |
| 40 | 15.36 | 21.9 |
| 100 | 15.36 | 8.8 |
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 load, uPS efficiency, battery bank voltage, battery capacity, usable depth of discharge and ageing and temperature factor. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Constant power load. Capacity is the rated value at the stated discharge rate.
Which calculators should I use next?
Common next steps are Generator kVA Selection and Appliance Running Cost (Energy and Cost). 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. 8 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.
- UPS Formulas: kVA, DC Current and Battery: UPS formulas for kVA from load kW and power factor, growth margin
- Power Supply Hold-Up Time Formulas: Hold-up time formulas: the energy a bulk capacitor gives between two voltages
- Peukert Law and Battery Runtime Formulas: Peukert law formulas: the runtime of a battery at a given current
- Supercapacitor Energy Formulas: Supercapacitor formulas: the usable energy between two voltages
More Power Systems calculatorsAll engineering calculatorsUPS Battery Runtime in Elecmetric