Battery Formulas
Battery formulas let you predict runtime, estimate usable capacity, and translate between C-rate and current draw. These calculators help you size packs for a target endurance and understand discharge behaviour. They are vital for portable, off-grid, and IoT power budgeting.
Battery Formula Calculators
- Battery Runtime t = Capacity / Current Battery Capacity 50 mAh, Load Current (mA) 0.1 mA → Runtime = 500 h
- Battery Energy E = V × Capacity Voltage 0.33 V, Capacity 0.2 Ah → Energy = 0.2376 kJ
- Battery Loaded Voltage Vload = Voc − I × Rint Open-Circuit Voltage 0.726 V, Load Current 2 mA, Internal Resistance 0.1 mΩ → Loaded Voltage = 0.726 V
- Battery Charge Time t = Capacity / Icharge Battery Capacity 50 mAh, Charge Current 0.1 mA → Charge Time = 500 h
- Battery Self-Discharge Crem = C0 × (1 − rate)^days Remaining Capacity 50 mAh, Initial Capacity 110 mAh, Daily Self-Discharge Rate 2.5 % → Days = 31.14
- Battery Temperature Derating Ceff = Cnom × factor Nominal Capacity 110 mAh, Derating Factor 2.5 % → Effective Capacity = 2.75 mAh
- Cell Balancing Current Ibal = ΔV / Rbal Voltage Difference 10 mV, Balance Resistor 1 Ω → Balancing Current = 10 mA
- State of Charge (Coulomb Counting) SoC = SoC_init + (I × t / Q) × 100 Initial SoC 0.5 %, Charge Current 2 mA, Charge Time 6 min, Nominal Capacity 0.2 Ah → SoC = 0.6
- Battery Internal Resistance Rint = (Voc − Vload) / I Open-Circuit Voltage 3.3 V, Loaded Voltage 1.55 V, Load Current 20 mA → Internal Resistance = 87.5 Ω
- Battery Pack Series-Parallel Vpack = Ns × Vcell, Qpack = Np × Qcell Series Cells 0.025, Cell Voltage 0.33 V, Cell Capacity 50 mAh → Parallel Cells = 0.00825
- Battery Cycle Life Capacity Fade Qn = Q0 × (1 − fade)^n Capacity After n Cycles 50 mAh, Initial Capacity 110 mAh, Fade Rate per Cycle 2.5 % → Number of Cycles = 31.14
- C-Rate to Current I = C_rate × Q C-Rate 0.025, Battery Capacity 50 mAh → Current = 1.25 mA
- Battery Voltage Sag Vsag = Voc − Crate × Q × Rint Open-Circuit Voltage 0.33 V, C-Rate 0.025, Battery Capacity 50 mAh, Internal Resistance 0.1 mΩ → Vsag = 0.33
Worked result for every Battery formula
| Formula | Expression | Worked result |
|---|---|---|
| Battery Runtime | t = Capacity / Current | Battery Capacity 50 mAh, Load Current (mA) 0.1 mA → Runtime = 500 h |
| Battery Energy | E = V × Capacity | Voltage 0.33 V, Capacity 0.2 Ah → Energy = 0.2376 kJ |
| Battery Loaded Voltage | Vload = Voc − I × Rint | Open-Circuit Voltage 0.726 V, Load Current 2 mA, Internal Resistance 0.1 mΩ → Loaded Voltage = 0.726 V |
| Battery Charge Time | t = Capacity / Icharge | Battery Capacity 50 mAh, Charge Current 0.1 mA → Charge Time = 500 h |
| Battery Self-Discharge | Crem = C0 × (1 − rate)^days | Remaining Capacity 50 mAh, Initial Capacity 110 mAh, Daily Self-Discharge Rate 2.5 % → Days = 31.14 |
| Battery Temperature Derating | Ceff = Cnom × factor | Nominal Capacity 110 mAh, Derating Factor 2.5 % → Effective Capacity = 2.75 mAh |
| Cell Balancing Current | Ibal = ΔV / Rbal | Voltage Difference 10 mV, Balance Resistor 1 Ω → Balancing Current = 10 mA |
| State of Charge (Coulomb Counting) | SoC = SoC_init + (I × t / Q) × 100 | Initial SoC 0.5 %, Charge Current 2 mA, Charge Time 6 min, Nominal Capacity 0.2 Ah → SoC = 0.6 |
| Battery Internal Resistance | Rint = (Voc − Vload) / I | Open-Circuit Voltage 3.3 V, Loaded Voltage 1.55 V, Load Current 20 mA → Internal Resistance = 87.5 Ω |
| Battery Pack Series-Parallel | Vpack = Ns × Vcell, Qpack = Np × Qcell | Series Cells 0.025, Cell Voltage 0.33 V, Cell Capacity 50 mAh → Parallel Cells = 0.00825 |
| Battery Cycle Life Capacity Fade | Qn = Q0 × (1 − fade)^n | Capacity After n Cycles 50 mAh, Initial Capacity 110 mAh, Fade Rate per Cycle 2.5 % → Number of Cycles = 31.14 |
| C-Rate to Current | I = C_rate × Q | C-Rate 0.025, Battery Capacity 50 mAh → Current = 1.25 mA |
| Battery Voltage Sag | Vsag = Voc − Crate × Q × Rint | Open-Circuit Voltage 0.33 V, C-Rate 0.025, Battery Capacity 50 mAh, Internal Resistance 0.1 mΩ → Vsag = 0.33 |
Variables used across Battery formulas
- t — Runtime in hours (h)
- Capacity — Battery capacity in milliamp-hours (mAh)
- Current — Average load current in milliamps (mA)
- E — Energy in watt-hours (Wh)
- V — Nominal battery voltage (V)
- Vload — Terminal voltage under load (V)
- Voc — Open-circuit voltage (V)
- I — Load current (A)
- Rint — Battery internal resistance (Ω)
- Icharge — Charging current (mA)
- Crem — Remaining capacity after storage (mAh)
- C0 — Initial capacity (mAh)
- rate — Daily self-discharge rate (decimal)
- days — Number of days in storage
- Ceff — Effective usable capacity at operating temperature (mAh)
- Cnom — Nominal capacity at 25°C (mAh)
- factor — Temperature derating factor (0 to 1)
- Ibal — Balancing current through the bleed resistor (A)
- ΔV — Voltage difference between highest and target cell (V)
- Rbal — Balance resistor value (Ω)
- SoC_init — Initial state of charge (ratio, e.g., 0.5 for 50%)
- Q — Nominal battery capacity (Ah, enter in base unit mAh or Ah)
- R_int — Internal resistance (Ω)
- V_oc — Open-circuit voltage, no load (V)
- V_load — Terminal voltage under load (V)
- Ns — Number of cells in series (dimensionless)
- Np — Number of parallel strings (dimensionless)
- V_cell — Single cell nominal voltage (V)
- Q_cell — Single cell capacity (Ah or mAh)
- 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
- C_rate — C-rate multiplier (dimensionless, e.g., 0.5, 1, 2)
Questions people ask about Battery
- Battery derating factor — Battery Temperature Derating
- Soc calculation formula using coulomb counting — State of Charge (Coulomb Counting)
- Battery capacity fade value — Battery Cycle Life Capacity Fade
Related Formula Categories
Browse the full formulas index for all 32 categories.