Battery Life Calculator
Battery Life Calculator
How long a battery will run a load: from its capacity in mAh, Ah or Wh, the load current or power, how deeply you will discharge it and Peukert’s exponent — with a duty-cycle option for devices that sleep most of the time.
Battery runtime
100 Ah (C20) 12 V lead-acid battery, 10 A load, 50% usable, Peukert 1.25
Runtime with Peukert’s law
- C
- rated capacity in Ah (Wh ÷ nominal voltage)
- H
- the hour-rate at which C is rated (C20: H = 20)
- I
- load current in A (W ÷ voltage), or its average for a duty-cycled load
- k
- Peukert exponent; 1 = ideal. From two ratings: k = ln(t2 ÷ t1) ÷ ln(I1 ÷ I2)
- DoD
- usable share of the capacity (depth of discharge)
Worked example
100 Ah (C20) 12 V lead-acid battery, 10 A load, 50% usable, Peukert 1.25
Rated current = 100 ÷ 20 = 5 A; the load is twice that, so Peukert applies
t = 0.5 × 20 × (100 ÷ (10 × 20))1.25 = 10 × 0.51.25 = 4.20 h
Capacity ÷ current alone would say 50 ÷ 10 = 5.0 h
Effective capacity at 10 A = 84.1 Ah, 15.9% below the rating
Peukert’s effect on a 100 Ah (C20) battery, k = 1.25
| Load | Runtime to empty | Effective capacity | Capacity ÷ current |
|---|---|---|---|
| 2 A | 50.00 h | 100.0 Ah | 50.00 h |
| 5 A | 20.00 h | 100.0 Ah | 20.00 h |
| 10 A | 8.41 h | 84.1 Ah | 10.00 h |
| 20 A | 3.54 h | 70.7 Ah | 5.00 h |
| 50 A | 1.12 h | 56.2 Ah | 2.00 h |
Estimating battery runtime
The simplest estimate is capacity divided by current: a 100 Ah battery supplies 10 A for 10 hours. Two corrections make it realistic. First, you rarely use the whole rating: lead-acid batteries last far longer if they are discharged to about half, and many devices shut down before a lithium cell is completely flat. The usable-capacity percentage handles that. Second, batteries deliver less charge when discharged faster than their rating. That is Peukert’s law, published in 1897 for lead-acid cells.
Peukert’s exponent. Capacity is quoted at a stated discharge time — 20 hours (C20) for most lead-acid batteries, often 5 hours (0.2C) for lithium-ion. Draw more current than capacity ÷ hours and the runtime shrinks faster than the current rises, by the power k. An ideal battery has k = 1. Victron Energy’s battery monitors default to 1.25 for lead-acid and recommend 1.05 for lithium when the datasheet gives nothing better. If the datasheet lists capacity at two discharge times, compute your own: k = ln(t2 ÷ t1) ÷ ln(I1 ÷ I2). A battery giving 85 Ah over 5 hours (17 A) and 100 Ah over 20 hours (5 A) has k = ln 4 ÷ ln 3.4 = 1.13. In the example, 10 A from a 100 Ah C20 battery at k = 1.25 yields only 84.1 Ah, so half of it lasts 4.20 hours, not 5.
Below the rated current Peukert’s formula predicts more than the rated capacity, and real batteries do give a little more at very low rates, but the formula overstates it. This page takes the cautious view and credits no more than the rated capacity there.
Sleeping devices. A sensor node that wakes for a moment and sleeps the rest of the time drains its battery at the average current. A 225 mAh coin cell running a device at 10 mA for 1% of the time and 2 µA asleep averages 102 µA and lasts about 2,206 hours, 91.9 days. Coin cells have high internal resistance, so short pulses of several milliamps can trigger a brown-out long before the rated capacity is used; a reservoir capacitor helps. Self-discharge, which can matter over years, is not included.
What is left out. The model assumes a steady load and about 25 °C. Cold weather cuts available capacity sharply, especially for lead-acid; capacity also fades with age and cycling; and a load behind a DC-DC converter or inverter draws more from the battery than it uses, so enter the battery-side power. For the energy stored, capacity in Ah × nominal voltage gives Wh. The Ohm’s law calculator converts between watts, volts and amps.
Frequently asked questions
How do I calculate battery life?
Divide the usable capacity by the load current: hours = Ah × usable fraction ÷ A. For fast discharges apply Peukert’s law. A 100 Ah battery at 10 A, 50% usable, k = 1.25 runs 4.2 hours.
How long will a 100Ah battery last?
At the 5 A it is rated at (C20), 20 hours to empty, or 10 hours to 50%. At 10 A, Peukert’s law cuts full-discharge runtime to 8.4 hours for a typical lead-acid battery (k = 1.25), not 10.
What is Peukert’s exponent?
A number that describes how much capacity a battery loses at high discharge rates. 1.0 is ideal. Victron uses 1.25 as an average for lead-acid and 1.05 for lithium. You can compute it from two datasheet capacities at different rates: k = ln(t2 ÷ t1) ÷ ln(I1 ÷ I2).
How do I convert Wh to mAh?
Divide by the nominal voltage and multiply by 1,000. 50 Wh at 3.7 V is 13,514 mAh. The page does this when you choose Wh.
How long will a coin cell last in a sensor?
Work out the average current: active current × active share + sleep current × the rest. 10 mA for 1% of the time plus 2 µA asleep averages 102 µA; a 225 mAh cell lasts about 92 days.
Related calculators
References
- Peukert W. Über die Abhängigkeit der Kapazität von der Entladestromstärke bei Bleiakkumulatoren. Elektrotechnische Zeitschrift 1897;18:287–288.
- Victron Energy. SmartShunt / BMV battery monitor manual, battery settings: Peukert exponent (“set it at 1.25 for lead-acid batteries and set it at 1.05 for lithium batteries” if unknown; 1.00 is ideal).
- Reddy TB (ed.). Linden’s Handbook of Batteries, 4th ed. McGraw-Hill, 2011. Discharge rate, temperature and capacity; battery rating conventions.