Cell Current Planner

STEP 1

Active material and reference capacity

Everything downstream is normalised to this number. Choose how it is defined, and the tool carries the basis with every later result.

Formula of the material as weighed

Element symbols with integer or decimal subscripts, ( ) and [ ] groups. Write hydrates with · or *, e.g. CuSO4·5H2O.

Ions exchanged per formula unit

ions

Charge per ion

Optional: other end member, to see the alternative mass basis

Theoretical specific capacity Q_th = n·F / (3.6·M)

—mAh g⁻¹

Molar mass M

—g mol⁻¹

Electrons per formula unit n

—e⁻

Charge per formula unit

—mAh mol⁻¹

Basis: per gram of the formula as written. Graphite is 372 mAh g⁻¹ per C₆, not per LiC₆; LiFePO₄ is 170 per LiFePO₄, not per FePO₄.

Specific capacity you already know

mAh g⁻¹

What kind of value it is

What it refers to (material, rate, source)

Reference capacity Q_ref used in every later step

—mAh g⁻¹

Use this when you already have the number: a theoretical value from a paper, a practical value for hard carbon or activated carbon, or a rated value from a datasheet. The tool does not recompute it; it carries the kind and source you state into every current, so a "C/10" on a practical 300 mAh g⁻¹ is never confused with a C/10 on a theoretical 372.

Specific capacitance C_sp

F g⁻¹

Potential window ΔV used for the capacitance

V

Equivalent specific capacity Q = C_sp·ΔV / 3.6

—mAh g⁻¹

Exact only for a linear potential–charge profile (ideal double-layer behaviour) over the same window. For a curved profile the conversion is approximate. Hybrid-capacitor papers usually quote the capacity directly; use the nominal option in that case.

STEP 2

Electrode geometry and active mass

Active material only. The composite mass (with conductive carbon and binder) is never the denominator unless you say so. Coated discs, pressed pellets, binder-free powders and a directly known active mass are all covered.

Geometry

Disc diameter

mm

Mass method

Electrode mass as weighed

mg

Coated disc, pressed pellet, or the powder you loaded.

Tare: bare current collector or container

mg

Same foil and diameter, or the disc before coating. Enter 0 for a pellet or a powder weighed on its own.

Balance readability

Electrode formulation (parts by mass or wt %)

Active material

parts

Conductive carbon

parts

Binder

parts

Active fraction w_act

—

Active-material mass m_act

—mg

Geometric area A

—cm²

Active-material loading

—mg cm⁻²

Composite loading

—mg cm⁻²

Areal capacity q_A (reference basis)

—mAh cm⁻²

Mass uncertainty from balance readability

—%

STEP 3

Current to program

Define the rate in whichever vocabulary your field uses; the other two are calculated from the same reference capacity.

C-rate (1C passes the reference capacity in 1 h)

C ×h⁻¹

Current to program

—mA = —µA

C-rate

—

Specific current j

—mA g⁻¹

Specific current j

—A g⁻¹

Current density i (geometric)

—mA cm⁻²

Nominal half-cycle time

—

Charge per half-cycle at Q_ref

—mAh

Rate basis: —

EC-Lab entry (GCPL)

Current field I_s

—

Cell characteristics: active mass

—

Cell characteristics: molecular weight

—

Cell characteristics: electrons per formula unit

—

Battery capacity EC-Lab should display

—

Sign: EC-Lab treats a positive current as oxidation of the working electrode. In a metal half-cell, a positive-electrode material (LiFePO₄, an organic salt) usually starts with charge, positive current; a negative-electrode material (graphite, hard carbon, Si) usually starts with lithiation or sodiation, negative current. Check that the capacity EC-Lab computes from the cell characteristics equals the value above; a mismatch is nearly always mg versus g or a different electron count.

STEP 4

Rate-capability schedule

One sheet for the whole GCPL programme. Durations assume the full reference capacity on every half-cycle with no constant-voltage hold or rest, so they are upper bounds for the constant-current part and lower bounds for the whole protocol.

Step	Rate	Cycles	Current (mA)	Current (µA)	j (mA g⁻¹)	i (mA cm⁻²)	Half-cycle	Step duration
Total constant-current time (charge + discharge)								—

TOOLBOX

Situations that come up while building the cell

Charge inventory of the metal disc facing your working electrode, and the ratio to the working electrode's areal capacity.

Metal

Foil thickness

µm

Specific capacity of the metal

—mAh g⁻¹

Areal capacity per µm

—mAh cm⁻² µm⁻¹

Areal capacity of the foil

—mAh cm⁻²

Inventory ratio, metal : working electrode

—×

Current density on the metal at the programmed current

—mA cm⁻²

An inventory statement only. The usable capacity of a metal disc is set by its interface (dendrites, dead metal, passivation, the electrolyte), not by the total charge it contains. Densities near room temperature from the RSC periodic table; handbooks differ by up to about 1 % for Na and K.

Li|electrolyte|Li or Na|electrolyte|Na cells: what a current density and a half-cycle time mean in plated charge and metal thickness.

Metal

Current density

mA cm⁻²

Half-cycle time

h

Electrode area

cm²

Charge per half-cycle

—mAh cm⁻²

Equivalent metal thickness moved

—µm

Absolute current to program

—mA

Areal capacities of both electrodes at the same rate, the resulting negative-to-positive ratio, and the mass ratio that would hit a target.

Positive electrode, specific capacity at the rate of interest

mAh g⁻¹

Positive electrode, active loading

mg cm⁻²

Negative electrode, specific capacity at the same rate

mAh g⁻¹

Negative electrode, active loading

mg cm⁻²

Target N/P ratio

—

Li-ion practice is commonly 1.05 to 1.2 to keep graphite above 0 V vs Li⁺/Li. A hybrid capacitor is balanced at the rate it must serve, not at the lowest rate.

Positive areal capacity

—mAh cm⁻²

Negative areal capacity

—mAh cm⁻²

N/P ratio as loaded

—

Negative loading for the target

—mg cm⁻²

Mass ratio m_neg/m_pos for the target

—

In hybrid ion capacitors the device current is normalised to the total active mass of both electrodes. Each electrode then experiences a larger specific current than the device value.

Negative electrode active mass

mg

Positive electrode active mass

mg

Device specific current j_d (per total active mass)

A g⁻¹

Absolute current

—mA

Negative electrode experiences j_neg = j_d(m_neg+m_pos)/m_neg

—A g⁻¹

Positive electrode experiences j_pos = j_d(m_neg+m_pos)/m_pos

—A g⁻¹

Mass ratio m_neg : m_pos

—

This is why adding positive-electrode mass to "match" a rate-limited negative electrode pushes the negative electrode to a harsher current. Read each electrode's half-cell capacity at its experienced current, not at the device current (Surendran, Lal and Shaijumon, ACS Appl. Mater. Interfaces 2021, 13, 52610).

Bulk ohmic drop across a solid polymer or liquid-soaked separator at the programmed current. Interfacial resistances add to this, so the real polarisation is larger.

Ionic conductivity at the operating temperature

S cm⁻¹

Scientific notation is fine: 1e-4

Electrolyte thickness

µm

Area carrying current

cm²

The smaller of electrode and electrolyte areas.

Current

mA

Voltage window of the experiment

V

Bulk resistance R_b = L / (σ·A)

—Ω

Ohmic drop ΔV = I·R_b (estimate, bulk only)

—mV

Fraction of the window

—%

Model estimate. Conductivity must be the value at the cell temperature; a solid polymer electrolyte can change by an order of magnitude between 25 and 60 °C.

The inverse of Step 1: how many electrons (or ions) per formula unit a delivered capacity corresponds to, on the same mass basis as the formula.

Measured specific capacity

mAh g⁻¹

Formula and molar mass

—

Electrons per formula unit x = Q·3.6·M / F

—e⁻ per formula unit

Fraction of the theoretical n

—%

REFERENCE

Equations, conventions and sources

Constants and data

Faraday constant F = 96 485.332 12 C mol⁻¹, exact since the 2019 SI redefinition (F = N_A·e). 1 mAh = 3.6 C exactly, so one mole of electrons is F/3.6 = 26 801.481 mAh.

Standard atomic weights: CIAAW 2024 table. Elements with an interval weight (H, Li, B, C, N, O, Mg, Si, S, Cl, Ar, Br, Tl, Pb) use the CIAAW abridged value (Li 6.94, C 12.011, O 15.999, H 1.0080). The lithium interval is wide (6.938 to 6.997); for Li-rich formulas this contributes up to about 0.1 % to M.

Metal densities near room temperature (RSC periodic table): Li 0.534, Na 0.97, K 0.89, Mg 1.74, Zn 7.134 g cm⁻³.

E1 Molar mass and E2 theoretical specific capacity

M = Σ ν_i · A_r(i) Q_th = n · F / (3.6 · M) [mAh g⁻¹] = 26801.481 · n / M n = (ions per formula unit) × (charge per ion)

Q_th is per gram of the formula as written. State the basis whenever the lithiated and delithiated forms differ in mass by more than your tolerance (graphite: 372 per C₆ versus 339 per LiC₆).

E3 Electrons from a measured capacity, E4 capacitance to capacity

x = Q_meas · 3.6 · M / F Q = C_sp · ΔV / 3.6 [mAh g⁻¹ from F g⁻¹ and V]

E4 is exact only for a linear potential–charge profile over the same window.

E5 Active mass and its uncertainty, E6 geometry and loading

m_act = (m_total − m_tare) · w_act w_act = active parts / total parts u(m_act)/m_act ≈ √2 · r / (m_total − m_tare) A = π d² / 4 L = m_act / A q_A = Q_ref · L / 1000

r is the balance readability used as a proxy for the standard uncertainty of each weighing. Solvent residue, binder loss and punching variability are not included.

E7 Current for a rate, E8 schedule

I = C · Q_ref · m_act j = I / m_act = C · Q_ref i = I / A t_half = 1 / C schedule: duration_k = 2 · N_k / C_k (charge + discharge, capacity = Q_ref, no CV hold, no rest)

"1C" is the current that would pass the reference capacity in one hour; "C/n" passes it in n hours. Q_ref is a choice (theoretical or nominal) and is printed with every current. IEC 61434 writes the same thing as I_t = C_n/1 h.

E9 Metal inventory, E10 symmetric cell, E11 balancing, E12 ohmic drop

Q_M = z · F / (3.6 · M_metal) q_M = ρ · t_f(µm) · 10⁻⁴ · Q_M [mAh cm⁻²] ratio = q_M / q_A symmetric: q = i · t thickness = q / (ρ · Q_M · 10⁻⁴) N/P = q_A,neg / q_A,pos m_neg/m_pos = (N/P)_target · Q_pos / Q_neg j_neg = j_d (m_neg + m_pos)/m_neg R_b = L / (σ · A) ΔV = I · R_b

Vocabulary used on this page

In a metal half-cell the material under test is the working electrode and the metal is the counter and quasi-reference electrode. The working electrode is the positive electrode of that cell even when the material will be a negative electrode in a full cell (graphite, hard carbon, silicon); this page therefore says "working electrode" for half-cells and reserves "positive electrode" and "negative electrode" for full cells. "Anode" and "cathode" are avoided because they swap between charge and discharge.

Specific capacity: per gram of active material. Areal capacity and current density: per geometric electrode area. Specific current: per gram of active material of the electrode carrying the current, except in the hybrid-capacitor convention where it is per total active mass and is labelled as such.

SELF-CHECK

Reference cases

The page recomputes a frozen set of reference values (calculated independently in Python from the same constants) each time it loads. If any case fails, do not trust the numbers above.

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