Battery sizing helps engineers choose a battery that can safely power a load for the required amount of time. This cheat sheet covers amp-hour capacity, watt-hour energy, runtime estimates, C-rate, depth of discharge, and design margin. Students need these ideas when designing robots, solar systems, backup power, portable devices, and electric vehicles.
A clear reference helps prevent undersized batteries, unsafe current draw, and unrealistic runtime claims.
The most important relationship is that energy equals voltage times capacity, so Wh = V x Ah. Runtime can be estimated from available capacity divided by load current, or from available energy divided by load power. Real designs must account for depth of discharge, battery efficiency, temperature, aging, and safety margin.
Engineers also check that the battery can provide the required current without exceeding its C-rate or discharge limit.
Key Facts
- Amp-hour capacity is calculated as Ah = current in amperes x time in hours.
- Watt-hour energy is calculated as Wh = voltage x amp-hours, or Wh = V x Ah.
- Estimated runtime is t = usable Ah / load current when the load current is approximately constant.
- Estimated runtime is t = usable Wh / load power when the load power is approximately constant.
- Usable capacity is usable Ah = rated Ah x depth of discharge x efficiency.
- A battery's discharge current limit can be estimated from maximum current = C-rate x Ah rating.
- Required battery capacity can be estimated as required Ah = load current x runtime / (depth of discharge x efficiency).
- A safety margin of 20% to 50% is often added because real batteries lose capacity with age, cold temperature, and high discharge current.
Vocabulary
- Amp-hour
- An amp-hour is a unit of electric charge equal to one ampere of current delivered for one hour.
- Watt-hour
- A watt-hour is a unit of energy equal to one watt of power used for one hour.
- Depth of discharge
- Depth of discharge is the fraction or percentage of a battery's rated capacity that is used before recharging.
- C-rate
- C-rate describes how fast a battery is charged or discharged compared with its rated amp-hour capacity.
- Load current
- Load current is the current drawn by the device, circuit, or system powered by the battery.
- Efficiency
- Efficiency is the fraction of stored battery energy that is actually delivered to the load after losses.
Common Mistakes to Avoid
- Confusing amp-hours with amps is wrong because amp-hours measure capacity over time, while amps measure current at an instant.
- Ignoring voltage when comparing batteries is wrong because a 10 Ah battery at 12 V stores twice the energy of a 10 Ah battery at 6 V.
- Using the full rated capacity without depth of discharge is wrong because many batteries should not be fully drained and may have reduced life or damage.
- Forgetting efficiency and safety margin is wrong because wiring losses, converters, aging, and temperature reduce the usable runtime.
- Assuming runtime is exact is wrong because battery voltage, capacity, and current draw can change during discharge, especially under heavy loads.
Practice Questions
- 1 A 12 V battery is rated at 20 Ah. What is its energy capacity in watt-hours?
- 2 A device draws 2.5 A from a usable battery capacity of 15 Ah. Estimate the runtime in hours.
- 3 A robot needs 4 A for 3 hours. If depth of discharge is 80% and efficiency is 90%, what rated amp-hour capacity is required?
- 4 Two batteries both have a 10 Ah rating, but one is 6 V and the other is 12 V. Explain which stores more energy and why.