Hong Life CalculatorsUnderstanding the battery energy and C-rate calculator — concept and principle
Battery capacity in amp-hours (Ah) tells you how much charge a battery holds, but not how much work it can do. Multiplying by voltage gives energy in watt-hours (Wh), the number you need to compare batteries of different voltages, size a solar or camping system, or check airline limits. The C-rate expresses a charge or discharge current relative to the battery's capacity, which is how manufacturers specify safe and rated currents.
How it is calculated
- Energy: E (Wh) = capacity (Ah) × nominal voltage (V).
- C-rate: C = I (A) ÷ capacity (Ah).
- Time at this current: t (h) = capacity (Ah) ÷ I (A) = 1 ÷ C-rate.
The principle
Ah is charge (current × time) and volts are energy per unit charge, so Ah × V = (A × V) × h = W × h. The nominal voltage is a representative mid-discharge value: the real voltage starts higher on a full battery and falls as it empties, so Wh = Ah × V_nominal is a good average rather than an exact integral. The C-rate normalises current to capacity: 1C is the current that would, in theory, empty the battery in one hour, 0.5C in two hours and 2C in half an hour. That makes the same number meaningful for a 2 Ah phone cell and a 100 Ah house battery.
Worked example
- Inputs: capacity 100 Ah, nominal voltage 12.8 V, current 50 A.
- Energy = 100 × 12.8 = 1,280 Wh (1.28 kWh).
- C-rate = 50 ÷ 100 = 0.5C.
- Time = 100 ÷ 50 = 2 h.
A nominal 12.8 V corresponds to four lithium iron phosphate (LiFePO4) cells in series at 3.2 V each.
| Capacity (Ah) | Energy (Wh) |
|---|---|
| 25 | 320 |
| 50 | 640 |
| 75 | 960 |
| 100 | 1,280 |
| 125 | 1,600 |
| 150 | 1,920 |
| 200 | 2,560 |
How to read the result
Compare the C-rate with the datasheet's continuous and peak ratings for both charge and discharge; charge limits are often lower. Higher C-rates generally deliver somewhat less usable capacity, produce more heat and shorten cycle life, and the effect is much stronger for lead-acid than for lithium-ion. The time result is an ideal upper limit; real run time is shorter once the depth-of-discharge limit, temperature and inverter losses are counted. For air travel, carriers commonly use 100 Wh and 160 Wh per battery as thresholds, so check the airline's current rules.
Common mistakes
- Comparing batteries by Ah when their voltages differ; compare Wh instead.
- Adding Ah for cells in series (only voltage adds) or adding volts for cells in parallel (only Ah adds).
- Assuming the full rated energy is usable; lead-acid batteries are often limited to about half for long life.
Frequently asked questions
How do I convert mAh to Wh?
Divide mAh by 1000 to get Ah, then multiply by voltage. A 5000 mAh cell at 3.7 V holds 5 × 3.7 = 18.5 Wh.
What does 0.2C mean on a datasheet?
A current equal to one-fifth of the capacity, so about 5 hours to discharge. Many rated capacities are measured at this gentle rate.
How long will a 1,280 Wh battery run a 200 W load?
Ideally 1280 ÷ 200 = 6.4 hours, less after inverter losses and any depth-of-discharge limit.
Sources: K. W. Beard (ed.), Linden's Handbook of Batteries, 5th ed., McGraw-Hill · IATA, Lithium Battery Guidance Document (passenger and cargo limits by watt-hour rating)