Battery runtime and UPS sizing
A battery rated at 100 Ah does not deliver 100 Ah to a heavy load. The rated figure is measured over twenty hours, and the capacity you actually get falls as the current rises — which is why a runtime estimate that ignores Peukert can be out by a factor of two.
| Quantity | Value | Note |
|---|---|---|
| Battery | 100 Ah at 12 V | 1200 Wh nominal |
| Load | 500 W | at the inverter output |
| Inverter efficiency | 90.0% | 556 W drawn from the battery |
| DC current | 46.3 A | 0.46C |
| Twenty-hour current | 5.00 A | the rate the capacity is rated at |
| Peukert exponent | 1.20 | 1.0 ideal, 1.15–1.3 lead-acid |
| Capacity at this rate | 64.1 Ah | 36% below rated |
| Depth of discharge | 80% | how far you are willing to run it down |
| Temperature derating | 100% | capacity falls in the cold |
| Age derating | 100% | end-of-life capacity as a fraction of new |
| Usable capacity | 51.3 Ah | after every derating |
| Runtime | 1.11 h | usable capacity divided by current |
| Usable energy | 615 Wh | at the nominal voltage |
| Inverter loss over the run | 62 Wh | heat in the inverter |
| Recharge time | 5.0 h | at 20.0 A |
The nominal runtime ignores Peukert entirely, which is why the two columns differ. On a heavy load the real figure can be half the nominal one — the single largest source of error in small UPS sizing.
t = C_usable / I · Current is the DC load divided by the inverter efficiency.
C = C₂₀ (C₂₀ / (I·20))^(k−1) · Referred to the twenty-hour rate.
C·DoD·f_temp·f_age · Every derating multiplies.
t = C·DoD·1.25 / I_charger · The 1.25 covers charging losses and the taper.
A clear path from inputs to results.
A battery rated at 100 Ah does not deliver 100 Ah to a heavy load. The rated figure is measured over twenty hours, and the capacity you actually get falls as the current rises — which is why a runtime estimate that ignores Peukert can be out by a factor of two.
How to use
- Enter the rated capacity and the nominal voltage.
- Set the load at the inverter output and the inverter efficiency.
- Choose the depth of discharge you are willing to run to.
- Apply the temperature and age derating, and set the Peukert exponent.
- Read the runtime, the usable energy and the recharge time.
The formula
Reference: Peukert's equation (1897); depth, temperature and age derating follow IEEE 485 battery-sizing practice.
Worked example
100 Ah at 12 V running a 500 W load
- 100 Ah battery at 12 V, 500 W load.
- 90% inverter efficiency, 80% depth of discharge.
- Peukert exponent 1.2, new battery at room temperature.
- 1
The inverter draws 500 / 0.9 = 556 W from the battery, which at 12 V is 46.3 A.
- 2
The twenty-hour current is 5 A, so the discharge is 9.3 times the rated rate.
- 3
Peukert gives 100 × (5 / 46.3)^0.2 = 64.1 Ah of usable capacity at that rate — 36% below the nameplate.
- 4
At 80% depth of discharge that is 51.3 Ah, or 615 Wh.
- 5
Runtime is 51.3 / 46.3 = 1.11 hours, about 67 minutes.
- 6
Recharging at 20 A takes 5 hours, including the absorption taper.
1.11 h · 64.1 Ah effective · 615 Wh usable · 5 h to recharge.
Interpreting the result
The gap between 100 Ah and 64.1 Ah is the whole point. A runtime estimate that divides nameplate capacity by current gives 1.73 hours here — 56% longer than the battery will actually deliver. Lead-acid is worse than lithium because its Peukert exponent is higher, which is why a lithium pack's runtime tracks the simple arithmetic so much more closely.
Assumptions & limitations
- Capacity is rated at the twenty-hour rate, which is the standard for lead-acid.
- The Peukert exponent is constant over the discharge range; 1.15–1.3 for flooded lead-acid, about 1.1 for AGM, 1.02–1.05 for lithium.
- The load is constant and the inverter efficiency is constant; both vary in practice.
- Depth of discharge, temperature and age derating multiply.
- Recharge assumes 1.25 times the removed charge at a constant current.
- Self-discharge and the battery's internal resistance rise at end of life are not modelled separately.
Frequently asked questions
What is the Peukert exponent?
A number that describes how much capacity falls as the discharge current rises. A value of 1.0 means no effect; 1.2 means a heavy load gets about 60% of the rated capacity. Lead-acid is 1.15–1.3, AGM about 1.1, lithium close to 1.0.
How much does cold weather cost me?
About 1% of capacity per degree below 25 °C for lead-acid, so a battery at 0 °C delivers roughly 75–80% of its rating. Lithium is far less sensitive but cannot be charged below freezing without damage.
How long should a UPS last?
Long enough to ride through the outage or to shut down cleanly — usually 5–15 minutes. Sizing for hours is a generator's job, not a battery's, and a battery sized for hours is expensive to replace every few years.
Why does depth of discharge matter?
Because the runtime is linear in it, but the cycle life is not. A lead-acid battery cycled to 50% lasts several times longer than one cycled to 80%. The usual compromise is 50% for daily cycling and 80% for standby use.
Is the inverter efficiency constant?
No. It peaks at perhaps 30–60% of rated load and falls away at very light loads, where standby consumption dominates. Using the nameplate efficiency is optimistic for a small load and pessimistic for a large one.
Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.