| Model | Inputs | Time (h) | Time (min) |
|---|---|---|---|
| Battery capacity | 2.5 Ah, 0.5 A, 95% efficiency, 80% DoD | 3.8 | 228 |
| Faraday charge | 0.020 mol, n=2, 1.0 A, 90% efficiency | 0.964853 | 57.8912 |
| RC threshold | R=1000 Ω, C=0.001 F, V0=5 V, Vt=1 V | 0.00044707 | 0.026824 |
- Select a model that matches your chemistry or device setup.
- Enter required inputs with consistent units, then set efficiency.
- Press Submit to display time results above the form.
- Review the plot to understand discharge behavior over time.
- Download CSV or PDF to archive your calculation history.
- Use the example table to sanity-check your outputs.
Model coverage and typical use cases
This calculator supports three discharge models used in chemistry and electrochemical systems. Use the battery-capacity model for practical cells and packs, the Faraday model for reaction-limited charge transfer, and the RC threshold model for capacitor networks and sensor hold-up circuits. Choosing the right model keeps assumptions explicit when switching between molar quantities and electrical ratings.
Battery-capacity discharge with efficiency and DoD
For cells rated in ampere-hours, time is computed from usable capacity divided by discharge current. Usable capacity is adjusted by efficiency and depth of discharge. In field data, η often ranges from 85–99%, while DoD is commonly limited to 70–90% for longevity. Example: 2.50 Ah, 0.50 A, 95% efficiency, 80% DoD gives 3.80 h, or 228.0 min.
Faraday charge for reaction-controlled systems
Faraday’s law converts moles to charge using Q = n·F·moles·η, with F = 96485.33212 C·mol⁻¹. This fits electrolysis, plating, and coulomb counting. With 0.020 mol, n = 2, η = 90%, Q ≈ 3473.5 C. At 1.00 A, time is 3473.5 s, or 57.89 min. At 0.25 A, the same charge needs about 3.86 h.
RC threshold discharge for voltage decay
When voltage falls exponentially, the time to reach a threshold is t = −RC·ln(Vt/V0). With R = 1000 Ω and C = 0.001 F, the time constant is 1.0 s. From 5 V to 1 V, t ≈ 1.609 s. Increasing C to 0.010 F scales time tenfold, while raising Vt closer to V0 shortens time sharply.
Unit conversions and interpretation
Results are presented in seconds, minutes, hours, and days to match lab notebooks and process logs. For comparisons, keep one variable fixed, such as current, and vary efficiency, DoD, or threshold. Small changes in η or DoD can shift runtime noticeably in low-current applications. The included plot visualizes depletion or decay over time, helping identify knee points, threshold margins, and practical sampling intervals during experiments quickly for teams.
Exportable history for reporting
Each submitted run is saved in a session table (up to 30 rows) and can be exported as CSV for spreadsheets or as a compact PDF for sharing. Use exports to document assumptions, compare model outputs, and preserve calculation inputs alongside computed time values for traceable reporting.
FAQs
Which model should I use for a rechargeable cell?
Use the battery-capacity model when you know capacity in ampere-hours and a discharge current. It is best for practical runtime estimates with efficiency and depth of discharge limits.
How does efficiency affect discharge time?
Efficiency scales usable charge. A drop from 95% to 85% reduces time by about 10.5% at the same current, so losses matter most in long-duration, low-current runs.
What does n mean in the Faraday model?
n is electrons transferred per mole of species in the reaction stoichiometry. For example, Zn → Zn²⁺ has n = 2, while Al → Al³⁺ has n = 3.
Why must threshold voltage be lower than initial voltage?
The RC model calculates the time for voltage to decay from V0 to Vt. If Vt is not lower than V0, the logarithm term is invalid and no discharge time exists.
Can I compare results across models directly?
Yes, but only when the underlying assumptions match. Battery and Faraday models estimate charge availability, while RC estimates voltage decay to a threshold, which may end sooner than full charge depletion.
What is saved in the exported files?
Exports include timestamps, the chosen model, input summaries, and time in seconds, minutes, hours, and days. Data is stored in the current session and limited to the most recent 30 calculations.