Battery Self-Discharge
Crem = C0 × (1 − rate)^days
Quick answer
This calculator solves Crem = C0 × (1 − rate)^days for Days. With Remaining Capacity 2.5 Ah, Initial Capacity 5.5 Ah, Daily Self-Discharge Rate 50 %, the result is 1.138.
Calculator
Formula
Description
Batteries lose charge over time even when disconnected, due to internal chemical reactions. The self-discharge rate varies dramatically by chemistry: lithium-ion cells lose 1-5% per month, NiMH batteries 15-30% per month (low-self-discharge NiMH like Eneloop only 1-3%), and lead-acid batteries 3-20% per month. This exponential decay model helps predict shelf life and plan maintenance charging schedules. Temperature significantly affects self-discharge, roughly doubling for every 10°C increase.
Variables
- Crem — Remaining capacity after storage (mAh)
- C0 — Initial capacity (mAh)
- rate — Daily self-discharge rate (decimal)
- days — Number of days in storage
Practical Notes
For monthly rate conversion to daily: daily_rate = 1 - (1 - monthly_rate)^(1/30). Primary (non-rechargeable) lithium batteries have extremely low self-discharge (less than 1% per year), making them ideal for emergency equipment and long-term deployments. Store batteries at 40-60% SOC and cool temperatures for minimum degradation.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Crem | Remaining Capacity | mAh | mAh, Ah |
| C0 | Initial Capacity | mAh | mAh, Ah |
| rate | Daily Self-Discharge Rate | — | —, % |
| days | Days | — | — |
Step by step
- 1. What you know: Remaining Capacity 2.5 Ah, Initial Capacity 5.5 Ah, Daily Self-Discharge Rate 50 %
- 2. The relation: Crem = C0 × (1 − rate)^days
- 3. Substitute: Crem = 2.5 Ah, C0 = 5.5 Ah, rate = 50 %
- 4. Result: Days = 1.138
Worked examples
Minimum range
Given: Remaining Capacity 50 mAh, Initial Capacity 110 mAh, Daily Self-Discharge Rate 2.5 %
Result: Days = 31.14
Low range
Given: Remaining Capacity 0.5 Ah, Initial Capacity 1.1 Ah, Daily Self-Discharge Rate 25 %
Result: Days = 2.741
Typical
Given: Remaining Capacity 2.5 Ah, Initial Capacity 5.5 Ah, Daily Self-Discharge Rate 50 %
Result: Days = 1.138
High range
Given: Remaining Capacity 10 Ah, Initial Capacity 22 Ah, Daily Self-Discharge Rate 0.8
Result: Days = 0.4899
Maximum range
Given: Remaining Capacity 100 mAh, Initial Capacity 0.22 Ah, Daily Self-Discharge Rate 0.8 %
Result: Days = 98.16
How Days changes with Remaining Capacity
| Remaining Capacity (input) | Days (result) |
|---|---|
| 0.25 Ah | 4.459 |
| 0.625 Ah | 3.138 |
| 1.25 Ah | 2.138 |
| 1.875 Ah | 1.553 |
| 2.5 Ah | 1.138 |
| 3.75 Ah | 0.5525 |
| 5 Ah | 0.1375 |
| 10 Ah | -0.8625 |
| 17.5 Ah | -1.67 |
| 25 Ah | -2.184 |
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<p><a href="https://vbatpower.com/formulas/battery-self-discharge/">Battery Self-Discharge</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Battery Self-Discharge?
Use Crem = C0 × (1 − rate)^days. With Remaining Capacity 2.5 Ah, Initial Capacity 5.5 Ah, Daily Self-Discharge Rate 50 %, Days works out to 1.138.
What is the formula for Battery Self-Discharge?
The formula is Crem = C0 × (1 − rate)^days. Batteries lose charge over time even when disconnected, due to internal chemical reactions.
Related Concepts
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