State of Charge (Coulomb Counting)
SoC = SoC_init + (I × t / Q) × 100
Quick answer
This calculator solves SoC = SoC_init + (I × t / Q_nom) × 100% for SoC. With Initial SoC 20 %, Charge Current 2 A, Charge Time 5 h, Nominal Capacity 20 Ah, the result is 70.
Calculator
Formula
Description
Coulomb counting estimates the state of charge by integrating current over time and comparing it to the battery nominal capacity. Charging current is positive (increases SoC) and discharging current should be entered as negative (decreases SoC). This is the simplest SoC estimation method, used in battery management systems (BMS) for electric vehicles, power tools, and energy storage systems. The main limitation is accumulated error from current measurement inaccuracy and capacity variation with temperature and aging.
Variables
- SoC_init — Initial state of charge (ratio, e.g., 0.5 for 50%)
- I — Current (A, positive for charging, negative for discharging)
- t — Time period (s)
- Q — Nominal battery capacity (Ah, enter in base unit mAh or Ah)
Practical Notes
Coulomb counting drifts over time due to measurement errors and must be periodically recalibrated against voltage-based SoC or other reference points (e.g., fully charged at 4.2 V for Li-ion). The Coulombic efficiency (charge out vs. charge in) is typically 99.5% for Li-ion but only 80-85% for lead-acid, introducing additional error if not compensated.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| SoC_init | Initial SoC | % | —, % |
| I | Charge Current | A | pA, nA, µA, mA, A, kA |
| t | Charge Time | h | ps, ns, µs, ms, s, min, h |
| Q | Nominal Capacity | Ah | mAh, Ah |
Step by step
- 1. What you know: Initial SoC 20 %, Charge Current 2 A, Charge Time 5 h, Nominal Capacity 20 Ah
- 2. The relation: SoC = SoC_init + (I × t / Q_nom) × 100%
- 3. Substitute: SoC_init = 20 %, I = 2 A, t = 5 h, Q = 20 Ah
- 4. Result: SoC = 70
Worked examples
Minimum range
Given: Initial SoC 0.5 %, Charge Current 2 mA, Charge Time 6 min, Nominal Capacity 0.2 Ah
Result: SoC = 0.6
Low range
Given: Initial SoC 5 %, Charge Current 20 mA, Charge Time 1 h, Nominal Capacity 2 Ah
Result: SoC = 6
Typical
Given: Initial SoC 20 %, Charge Current 2 A, Charge Time 5 h, Nominal Capacity 20 Ah
Result: SoC = 70
High range
Given: Initial SoC 80 %, Charge Current 100 A, Charge Time 24 h, Nominal Capacity 200 Ah
Result: SoC = 1280
Maximum range
Given: Initial SoC 800 %, Charge Current 1 kA, Charge Time 240 h, Nominal Capacity 2000 Ah
Result: SoC = 12800
How SoC changes with Initial SoC
| Initial SoC (input) | SoC (result) |
|---|---|
| 2 % | 52 |
| 5 % | 55 |
| 10 % | 60 |
| 15 % | 65 |
| 20 % | 70 |
| 30 % | 80 |
| 40 % | 90 |
| 80 % | 130 |
| 140 % | 190 |
| 200 % | 250 |
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<p><a href="https://vbatpower.com/formulas/state-of-charge/">State of Charge (Coulomb Counting)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate State of Charge (Coulomb Counting)?
Use SoC = SoC_init + (I × t / Q_nom) × 100%. With Initial SoC 20 %, Charge Current 2 A, Charge Time 5 h, Nominal Capacity 20 Ah, SoC works out to 70.
How do you calculate soc calculation formula using coulomb counting?
Rearrange for SoC: with Initial SoC 5 %, Charge Current 20 mA, Charge Time 1 h, Nominal Capacity 2 Ah, SoC is 6.
What is the formula for State of Charge (Coulomb Counting)?
The formula is SoC = SoC_init + (I × t / Q_nom) × 100%. Coulomb counting estimates the state of charge by integrating current over time and comparing it to the battery nominal capacity.
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