Formula & Calculator
Battery Capacity (Amp-Hours)
Defines a battery's charge capacity as the current it can supply over a given time.
Interpretation
Battery capacity in amp‑hours: Ah = I × t, where I is the discharge current and t is the time (hours).
It indicates the total charge a battery can deliver.
Example: A battery discharging at 5A for 20 hours has capacity 5 × 20 = 100Ah.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Ah | Battery capacity (ampere-hours) | Ah |
| I | Discharge current (constant) | A |
| t | Discharge duration | h |
What it means
Battery capacity in ampere‑hours (Ah) is the product of the discharge current I and the time t (hours) for which it can supply that current: Ah = I × t. It indicates the total charge a battery can deliver. For example, a battery rated at 100Ah can supply 5A for 20 hours (5×20=100). However, the actual capacity depends on the discharge rate; higher currents reduce the effective capacity (Peukert effect). This rating is used for sizing batteries for backup power, electric vehicles, and renewable energy systems. Example: A 12V, 100Ah battery stores 1200Wh of energy (12×100), but the usable amount depends on the depth of discharge.
Worked example
Battery Capacity (Ah) – Practical Example
Real‑World| Parameter | Value |
|---|---|
| I | 5 A |
| t | 20 h |
| Formula | Ah = I × t |
Common mistakes
Watch for unit mismatches (W vs kW, single- vs three-phase) and remember to include power factor or efficiency where the formula requires it.Applications
Battery capacity in amp‑hours Ah = I × t indicates the total charge a battery can deliver. This is used to size batteries for various applications, from consumer electronics to backup power. Engineers use it to select batteries, to calculate runtime, and to design energy storage systems.
- Battery selection for portable and stationary applications
- Backup power and UPS sizing
- EV and hybrid vehicle battery sizing
- Energy storage for solar and wind systems
- Educational understanding of battery capacity
Frequently Asked Questions
Capacity is Ah = I × t, where I is the current in amperes and t is the time in hours. It represents the total charge a battery can deliver.
Ah is the charge capacity; Wh is the energy capacity. Wh = Ah × V (voltage).
Determine the daily energy requirement (Wh), divide by the battery voltage to get Ah, and add a safety margin (e.g., 20% for depth of discharge).
Common errors: 1) not considering the depth of discharge, 2) using the wrong voltage, 3) ignoring the effect of discharge rate on capacity, 4) using the battery's nominal capacity without derating.
High discharge rates reduce the effective Ah capacity (Peukert effect). The capacity is usually specified at a 20‑hour rate.
Battery sizing for solar systems, electric vehicles, and UPS.
DoD is the fraction of the battery capacity that has been used. It affects battery life; deeper discharges reduce cycle life.
t = Ah / I_load (hours), but consider the DoD limit.