How to use this calculator
- Enter the load in W or in VA and the load power factor, then the design margin (25 % is a common practice, not a standard).
- Describe the battery bank: the voltage and Ah of one battery, how many are in series per string and how many strings are in parallel. To type a bank directly, enter its voltage and Ah with 1 and 1.
- Enter the usable depth of discharge and the inverter efficiency from the UPS datasheet.
- Enter the backup time you need. The result shows whether the bank covers it and how many Ah would.
- For lead-acid batteries, turn on the Peukert correction and enter the exponent and the hour rate from the battery datasheet.
How it works: the formula
A UPS has a VA rating and a W rating, and the load has to fit within both, so the load is converted to both forms and increased by the margin. The runtime is an energy balance: the usable battery energy (Ah × V × DoD) passes through the inverter with efficiency η and is used by the load at P watts. The battery current at the DC bus is the load power divided by the bank voltage and the inverter efficiency. Solving the same relation for C gives the capacity needed for a target time.
Variables and units
| Symbol | Meaning | Unit |
|---|---|---|
| P | Load real power | W |
| S | Load apparent power | VA |
| PF | Load power factor | — |
| m | Design margin | % |
| V, C | Bank voltage and capacity | V, Ah |
| DoD | Usable depth of discharge | — |
| η | Inverter efficiency | — |
| t | Backup runtime | h |
Worked example
A 1200 W load with PF 0.8, a 25 % margin, four 12 V 100 Ah batteries in series, DoD 0.8 and inverter efficiency 0.9:
For a four-hour target the bank would need 1200 × 4 / 34.56 = 138.9 Ah, that is two parallel strings of 100 Ah batteries.
Assumptions
- Constant power load for the whole discharge.
- The battery voltage is taken as the nominal bank voltage.
- The inverter efficiency is constant over the load range.
- All batteries are identical, healthy and fully charged at the start of the outage.
- The design margin is a common practice for growth and ageing, not a requirement of a standard.
Limitations
- The UPS maker's runtime chart for the actual battery model overrides this estimate; it already includes the battery's behaviour at high discharge rates and the UPS's cut-off voltage.
- Lead-acid capacity falls at high discharge rates, which is normal in UPS service; the simple formula overestimates short runtimes unless the Peukert option or the battery maker's constant-power table is used.
- Battery capacity falls with age and at low temperature. Many designers add an ageing factor (for example 1.25 in IEEE 485 for lead-acid).
- Loads with high inrush or surge current (laser printers, heaters, motors, compressors) need a check of the UPS overload capability, and many UPS makers advise against connecting them.
- The listed catalogue sizes are only a hint; makers offer different steps.
References
Standards and texts that cover this topic. Use the edition adopted in your jurisdiction.
- IEC 62040-3, Uninterruptible power systems (UPS) — Method of specifying the performance and test requirements (rated output in VA and W, stored energy time).
- IEC 62040-1, Uninterruptible power systems (UPS) — Safety requirements.
- IEEE 485, Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications (ageing and temperature factors).
- W. Peukert (1897) and D. Linden, T. B. Reddy, Linden's Handbook of Batteries, for the Peukert relation between discharge current and capacity.
Frequently asked questions
What is the difference between the VA and W ratings of a UPS?
VA is the apparent power the UPS can deliver and W the real power. The ratio between them is the UPS's output power factor, which differs from model to model. A load must stay within both: a 2000 VA unit with a lower W rating cannot carry 2000 W even if the load power factor is 1.
Why add a design margin?
Loads tend to grow, batteries lose capacity with age, and a UPS running close to its rating has little headroom for switching surges. A margin of about 25 % is a common practice; it is not set by a standard, so use your own policy if you have one.
Why is the maker's runtime chart different from the result?
UPS runtimes are short, so the batteries discharge at a high rate, where lead-acid batteries deliver less than their rated Ah. The UPS also cuts off at a set end voltage and its efficiency changes with load. The maker's chart is measured with the real batteries and UPS, so it takes precedence.
Can I use this for a home inverter with batteries?
Yes. The relation is the same for a standalone inverter: enter the load, the inverter efficiency and the battery bank. For lead-acid batteries used every day, a lower depth of discharge, such as 0.5, extends battery life.
How do I get the current that the battery cables must carry?
The result shows the battery current at the DC bus, I = P / (V × η). Cable and fuse sizing should use the current at the maximum load and at the lowest battery voltage before cut-off, which is higher than this nominal figure.