Calculator · Electrical · Lead / AGM / Gel / LFP / Li-ion / NiMH

Battery calculator

The power of a battery — how long it lasts, how much energy it stores, and what size you need — comes down to three values: capacity in amp-hours (Ah), nominal voltage, and depth-of-discharge limit. Three modes in one tool: runtime ("how long"), sizing ("what capacity"), and energy (Wh / kWh). Six chemistries with Peukert correction and cycle-life estimation. Reviewed by a licensed PE.

Use the battery calculator

Pick the mode at the top — Runtime ("how long"), Sizing ("what capacity do I need"), or Energy ("how many kWh") — then choose chemistry and enter your values. The calculator applies Peukert correction and chemistry-specific DoD limits automatically.

CALC.008 Battery · Runtime + Sizing + Energy · 6 chemistries · Peukert

Chemistry[Chem]

Battery voltage[V]

Depth of discharge[DoD]

Runtime

— h

—

Linear runtime (no Peukert): —
Peukert-corrected runtime: —
Usable energy at DoD: — Wh
Total stored energy: — Wh
C-rate (load / capacity): —
Estimated cycles to 80%: —
Estimated weight: — kg
Standard 100 Ah modules: —

FORMULA · t = (C × DoD) / I × Peukert SOURCE · IEEE 485 · IEC 60896 · PEUKERT 1897

Figure 1 — Battery runtime: capacity (Ah) divided by load current (A) yields hours of useful operation

Battery power — at a glance

Runtime formula: runtime (h) = (Ah × DoD) / I_load. Multiply by Peukert factor for lead-acid at high discharge rates.
Wh from Ah: Wh = Ah × V. A 100 Ah / 12 V battery stores 1 200 Wh = 1.2 kWh; usable Wh = total × DoD.
How long does a 100 Ah battery last?: At 12 V powering a 100 W load (≈ 8.3 A): ~10 hr at 100% DoD or ~8 hr at 80% DoD on LFP. Lead-acid loses 20–30% more to Peukert.
Common AA / AAA capacity: Alkaline AA: ~2 500 mAh at 1.5 V; AAA: ~1 000 mAh; 9 V: ~550 mAh; D-cell: ~12 000 mAh. NiMH AA: 1 900–2 700 mAh at 1.2 V.
BCI car battery group sizes: Most US passenger cars use BCI Group 24, 35, 65, 75, 78 at 12 V, 50–100 Ah. Trucks: Group 31 (~100 Ah). The owner manual lists the exact group.
Lead-acid vs LFP cycle life: Lead-flooded at 50% DoD: ~500 cycles (~3 yr daily). LFP at 80% DoD: ~3 000 cycles (~8 yr daily). LFP costs more upfront but 5–10× longer life.
Depth of discharge limits: Lead-flooded: 50% DoD max; AGM / Gel: 80%; LFP: 80–100%. Cycling deeper than the chemistry allows cuts cycle life sharply.
Battery weight by chemistry: Energy density: lead-acid ~35 Wh/kg, AGM ~40, LFP ~110, Li-ion NMC ~200. A 1.2 kWh (100 Ah / 12 V) lead-acid weighs ~30 kg; LFP ~12 kg.

The battery formulas

Eq. 01 — Runtime with Peukert correction SI · Peukert 1897

t = \frac{C \cdot \mathrm{DoD}}{I} \cdot \left(\frac{I_{ref}}{I}\right)^{k-1}

t: runtime, h
C: rated capacity, Ah
DoD: depth-of-discharge fraction (0–1), —
I: load current, A
I_ref: rated reference current (typically C/20), A
k: Peukert exponent (1.05 LFP, 1.15–1.30 lead), —

Eq. 02 — Energy stored SI · Definition of energy

E_{Wh} = C \cdot V \qquad E_{usable} = C \cdot V \cdot \mathrm{DoD}

E_Wh: total stored energy, Wh
E_usable: usable after DoD, Wh
V: nominal voltage, V

Eq. 03 — Required capacity for a given runtime SI · Inverse of Eq. 01

C = \frac{I \cdot t}{\mathrm{DoD}} \cdot (1 + \mathrm{margin})

C: required capacity (rated), Ah
margin: safety margin (e.g. 0.20), —

Worked example: solar off-grid 5 kWh / day

Cabin off-grid system: average daily energy use 5 kWh, 48 V LFP bank, 2 days autonomy without sun, 80% DoD, inverter efficiency 95%.

Step	Calculation	Result
Daily load	given	5 kWh
Total energy needed (2 days)	5 × 2	10 kWh
Account for inverter loss	10 / 0.95	10.5 kWh
Account for DoD limit	10.5 / 0.80	13.2 kWh
Add 20% safety margin	13.2 × 1.20	15.8 kWh
Convert to Ah at 48 V	15 800 / 48	329 Ah
Standard sizing	round up to 4 × 100 Ah modules	400 Ah / 19.2 kWh
Cost at typical $400/kWh LFP	19.2 × 400	~$7700
Cycle life at 80% DoD (LFP)	~3000 cycles	~8 years daily cycling

How to size a battery, step by step

Pick the chemistry. Lead-acid is cheapest but has shorter cycle life and stricter DoD limit (50%). LFP costs more upfront but lasts 5–10× longer at 80–100% DoD. Match chemistry to application: emergency backup vs daily cycling vs weight-sensitive use.
Decide DoD limit. Lead-flooded: max 50% DoD for cycle life. AGM/gel: 80%. LFP: 80–100%. Higher DoD = more usable energy per cycle but fewer cycles. The cycle-life-vs-DoD curve is steep — going from 80% to 50% DoD often triples cycle count.
Compute load current. For DC load: I = P / V. For AC load through inverter: I = P / (V × η), where η is inverter efficiency (typically 92–96%). Note: small loads pull more current per watt because of fixed inverter overhead.
Apply Peukert correction. High discharge rate (large I relative to capacity C) reduces effective capacity. The Peukert exponent k captures this: t = (C × DoD) × (I_ref/I)^(k−1). Lithium k ≈ 1.05 (linear); lead-acid k ≈ 1.15–1.30 (significant correction at high rates).
For sizing, work backwards. Given runtime t and load I: required Ah = (I × t) / DoD, then divide by Peukert factor. Add 20–25% safety margin for ageing and temperature variation.
Verify with cycle life. Pick chemistry and DoD that give enough cycles for your replacement budget. 365 cycles/year × 10 year life = 3650 cycles needed — only LFP at modest DoD reaches that without replacement.

Reference table — common battery chemistries

Chemistry comparison — V, DoD, cycles, energy density

SOURCE · Manufacturer spec sheets + IEEE 485 + IEC 60896

Chemistry	V/cell	Peukert k	Max DoD	Cycles @ rated DoD	Wh/kg
Lead-acid (flooded)	2.0	1.30	50%	500	35
AGM (sealed lead)	2.0	1.10	80%	600	40
Gel cell	2.0	1.10	80%	700	38
LFP (LiFePO4)	3.2	1.05	90%	3000	110
Li-ion NMC	3.7	1.05	80%	1500	200
NiMH	1.2	1.10	80%	800	75

Variants and special cases

Lead-acid (flooded)

The cheapest chemistry per kWh. Vents hydrogen (needs ventilated room), heavy, high Peukert losses. Maximum 50% DoD for full cycle life. Standard car-starter batteries (CCA-rated) are NOT deep-cycle — only true deep-cycle marine/RV batteries should be cycled regularly.

AGM (Absorbed Glass Mat)

Sealed lead-acid with electrolyte absorbed in glass mat separator. No venting, can be installed in any orientation, tolerates 80% DoD. More expensive than flooded but lower maintenance. Standard for UPS, solar, RV/marine.

Gel cell

Sealed lead-acid with thixotropic gel electrolyte. Even better discharge tolerance than AGM, slower charging (sensitive to overvoltage). Common in mobility scooters, telecom backup.

Lithium iron phosphate (LFP / LiFePO4)

The dominant chemistry for solar, marine, RV, and EV deep-cycle applications. 3000+ cycles at 80–90% DoD, half the weight of lead-acid for the same energy, no thermal runaway risk. Higher upfront cost ($300–500/kWh) offset by 5–10× longer life.

Li-ion NMC (Nickel Manganese Cobalt)

Highest energy density (~200 Wh/kg) used in laptops, phones, EVs (Tesla, etc). Tighter thermal management required; thermal runaway risk if abused. Better for weight-sensitive applications, worse for cycle life and cost than LFP.

NiMH (Nickel-Metal Hydride)

Older rechargeable chemistry, common in hybrid cars (Toyota Prius), tools, AA-format consumer cells. Higher self-discharge than lithium (~2% per day for old chemistries, <1% per month for "low self-discharge" modern variants).

C-rate and discharge rate

C-rate is current as a multiple of capacity. 1C means a current equal to capacity (full discharge in 1 hr). 0.05C is the standard 20-hour rated discharge for lead-acid. Lead-acid loses dramatic capacity at >0.2C; lithium handles 1C continuous well.

Peukert\'s law

Empirical observation that lead-acid effective capacity decreases at higher discharge rates: t = C / I^k, where k is the Peukert exponent (1.0 = perfectly linear, 1.30 = strong loss). At 1C discharge, a lead-acid battery delivers only ~70% of its rated 20-hour capacity. Lithium chemistries have k ≈ 1.05 — almost linear.

Depth of discharge vs cycle life

Discharging to 100% (full DoD) every cycle drastically reduces battery life. Lead-acid at 100% DoD: ~200 cycles; at 50% DoD: ~1500 cycles; at 25%: ~5000 cycles. LFP scales similarly but with a much higher absolute count: 100% DoD ~1000 cycles, 50% DoD ~5000+. The "deeper less often" trade-off is the central design knob in battery sizing.

State of charge (SoC) measurement

Voltage-only SoC is unreliable under load. Coulomb-counting battery monitors (Victron BMV, Renogy BT) integrate current in and out and report SoC accurately. For lithium with a BMS, the BMS tracks SoC internally. Open-circuit-voltage method works only after a 24-hour rest period.

Temperature derating

Cold reduces capacity (lead-acid: ~1%/°C below 25°C; lithium charging blocked below 0°C by BMS). Heat accelerates aging (battery at 35°C ages ~2× faster than at 25°C). Optimal storage 15–25°C. Below-freezing operation needs self-heating jackets or insulated enclosures.

Battery weight estimation

Approximate weight = total Wh / specific energy. Lead-acid 35 Wh/kg; AGM 40; LFP 110; Li-ion NMC 200. A 5 kWh lead-acid bank weighs 143 kg; same kWh in LFP weighs 45 kg; in Li-ion NMC 25 kg. Critical for portable/mobile applications.