Battery Cycle Life Capacity Fade
Qn = Q0 × (1 − fade)^n
Quick answer
This calculator solves Qₙ = Q₀ × (1 − fade)ⁿ for Number of Cycles. With Capacity After n Cycles 2.5 Ah, Initial Capacity 5.5 Ah, Fade Rate per Cycle 50 %, the result is 1.138.
Calculator
Formula
Description
Battery capacity degrades with each charge-discharge cycle due to irreversible chemical and mechanical changes in the electrode materials. The exponential fade model assumes a constant percentage loss per cycle. While simplified (real fade is not perfectly constant), it provides useful estimates for battery lifetime planning. Li-ion cells are typically considered end-of-life at 80% of initial capacity. The fade rate depends on chemistry, depth of discharge, charge rate, temperature, and voltage limits. LFP chemistry typically has lower fade rates than NMC or NCA.
Variables
- Qₙ — Remaining capacity after n cycles (Ah)
- Q₀ — Initial capacity (Ah)
- fade — Fractional capacity loss per cycle (e.g., 0.0002 for 0.02%/cycle)
- n — Number of charge-discharge cycles
Practical Notes
Example: Q₀ = 3000 mAh, fade = 0.0002/cycle, after 1000 cycles: Q = 3000 × (1 − 0.0002)^1000 ≈ 2456 mAh (81.9%). Solving for n at 80% capacity: n = ln(0.8)/ln(0.9998) ≈ 1116 cycles. Higher temperatures, deeper discharge, and faster charging all increase the fade rate. Calendar aging also contributes to capacity loss independent of cycling.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Qn | Capacity After n Cycles | mAh | mAh, Ah |
| Q0 | Initial Capacity | mAh | mAh, Ah |
| fade | Fade Rate per Cycle | — | —, % |
| n | Number of Cycles | — | — |
Step by step
- 1. What you know: Capacity After n Cycles 2.5 Ah, Initial Capacity 5.5 Ah, Fade Rate per Cycle 50 %
- 2. The relation: Qₙ = Q₀ × (1 − fade)ⁿ
- 3. Substitute: Qn = 2.5 Ah, Q0 = 5.5 Ah, fade = 50 %
- 4. Result: Number of Cycles = 1.138
Worked examples
Minimum range
Given: Capacity After n Cycles 50 mAh, Initial Capacity 110 mAh, Fade Rate per Cycle 2.5 %
Result: Number of Cycles = 31.14
Low range
Given: Capacity After n Cycles 0.5 Ah, Initial Capacity 1.1 Ah, Fade Rate per Cycle 25 %
Result: Number of Cycles = 2.741
Typical
Given: Capacity After n Cycles 2.5 Ah, Initial Capacity 5.5 Ah, Fade Rate per Cycle 50 %
Result: Number of Cycles = 1.138
High range
Given: Capacity After n Cycles 10 Ah, Initial Capacity 22 Ah, Fade Rate per Cycle 0.8
Result: Number of Cycles = 0.4899
Maximum range
Given: Capacity After n Cycles 100 mAh, Initial Capacity 0.22 Ah, Fade Rate per Cycle 0.8 %
Result: Number of Cycles = 98.16
How Number of Cycles changes with Capacity After n Cycles
| Capacity After n Cycles (input) | Number of Cycles (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/cycle-life-fade/">Battery Cycle Life Capacity Fade</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Battery Cycle Life Capacity Fade?
Use Qₙ = Q₀ × (1 − fade)ⁿ. With Capacity After n Cycles 2.5 Ah, Initial Capacity 5.5 Ah, Fade Rate per Cycle 50 %, Number of Cycles works out to 1.138.
How do you calculate battery capacity fade value?
Rearrange for Number of Cycles: with Capacity After n Cycles 0.5 Ah, Initial Capacity 1.1 Ah, Fade Rate per Cycle 25 %, Number of Cycles is 2.741.
What is the formula for Battery Cycle Life Capacity Fade?
The formula is Qₙ = Q₀ × (1 − fade)ⁿ. Battery capacity degrades with each charge-discharge cycle due to irreversible chemical and mechanical changes in the electrode materials.
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