Calculator
Plotly Graph
This graph shows how resistance changes with conductivity for your geometry.
Example Data Table
These rows show how geometry and conductivity change resistance.
| # | κ (mS/cm) | l (cm) | A (cm²) | R (Ω) | Notes |
|---|---|---|---|---|---|
| 1 | 5.0 | 1.0 | 1.0 | 200 | Dilute salt solution |
| 2 | 12.5 | 1.0 | 1.0 | 80 | Moderate ionic strength |
| 3 | 50.0 | 1.0 | 1.0 | 20 | Concentrated electrolyte |
| 4 | 12.5 | 2.0 | 1.0 | 160 | Spacing doubled |
| 5 | 12.5 | 1.0 | 2.0 | 40 | Area doubled |
Tip: The calculator converts units internally to SI.
Formula Used
The electrical resistance of an electrolyte slab between parallel electrodes is: R = l / (κ · A)
- R is resistance (Ω)
- l is electrode spacing (m)
- A is wetted area (m²)
- κ is conductivity (S/m)
The calculator also reports the cell constant K = l/A (1/m) and conductance G = 1/R = κ·A/l (S).
If you use the molar route, conductivity is estimated by κ = Λm · c, where Λm is molar conductivity and c is concentration.
How to Use This Calculator
- Select an input method: measured κ, or Λm·c.
- Enter electrode spacing l and area A, with units.
- Optionally enable temperature correction and provide T, Tref, and α.
- Click Calculate. Results appear above the form.
- Use Download CSV or Download PDF for records.
Technical Notes
1) Typical conductivity ranges
Ultrapure water can measure below 0.001 mS/cm, while drinking water commonly sits around 0.2–1.5 mS/cm. Seawater is often near 50–60 mS/cm. Battery electrolytes and strong brines may exceed 100 mS/cm. Using these ranges helps you sanity-check computed resistance against the expected ionic strength and temperature. At 25 °C, 1.0 mS/cm corresponds to 0.10 S/m. When κ is extremely low, small geometry errors can dominate the estimate.
2) Geometry drives cell constant
The calculator reports the cell constant K = l/A. A 1.0 cm gap with 1.0 cm² area gives K = 1.0 cm⁻¹ (100 m⁻¹). Doubling spacing doubles K, and doubling area halves K. In practice, probes with K near 1.0 cm⁻¹ suit mid-range samples, while K near 0.1 cm⁻¹ supports higher conductivities. If your cell has K = 10 cm⁻¹, the same sample reads ten times higher resistance.
3) Resistance scaling behavior
With fixed geometry, resistance follows R ∝ 1/κ. For κ = 12.5 mS/cm, l = 1.0 cm, A = 1.0 cm², the ideal resistance is about 80 Ω. If κ drops to 5.0 mS/cm, resistance rises to about 200 Ω. These proportional changes are what the Plotly curve visualizes. Because the relationship is hyperbolic, conductivity gains matter most at low κ. The plotted marker highlights your effective κ after temperature adjustment.
4) Temperature adjustment context
Many aqueous electrolytes show a roughly linear conductivity increase with temperature across narrow windows. An α of 0.020 1/°C implies a 10 °C rise increases κ by about 20%. That same change decreases resistance by about 17% because R depends on 1/κ. Use α when you need comparable reports at a standard reference temperature. For tight specs, measure α experimentally.
5) Molar route interpretation
If you choose Λm·c, conductivity is estimated as κ = Λm·c using SI conversions. For example, Λm = 126.5 S·cm²/mol and c = 0.010 mol/L produce κ ≈ 1.265 S/m, equivalent to 12.65 mS/cm. This approach is useful for quick design estimates before measurements are available, in planning.
6) Practical measurement considerations
Real cells can deviate from the parallel-plate ideal due to electrode polarization, gas bubbles, and nonuniform current paths. Keeping spacing consistent, removing bubbles, and using AC conductivity meters reduce artifacts. For quality checks, track resistance at fixed geometry and temperature; sudden shifts often indicate contamination, depletion, or probe fouling. Repeat readings after mixing, and rinse probes between samples to limit carryover.
FAQs
1) What does the resistance value represent?
It is the bulk ionic resistance between electrodes for the entered spacing and area, assuming uniform current flow and a homogeneous electrolyte. It excludes lead resistance and most electrode-interface effects.
2) Which conductivity unit should I use?
Use the unit your meter reports. The calculator converts S/m, S/cm, mS/cm, and µS/cm to SI internally, so results remain consistent across unit choices.
3) When should I enable temperature correction?
Enable it when comparing readings taken at different temperatures or when reporting at a standard reference like 25 °C. Leave it off if your meter already compensates temperature.
4) Is the molar method accurate for concentrated electrolytes?
It is best for dilute to moderate concentrations where tabulated Λm values and linear assumptions hold. For concentrated systems, activity effects can reduce accuracy; prefer measured conductivity.
5) Why does my measured resistance differ from the calculation?
Differences can come from probe geometry, polarization, bubbles, boundary layers, or incorrect effective area. Check calibration, ensure stable immersion depth, and verify conductivity and temperature inputs.
6) What does the Plotly graph help me see?
It visualizes how resistance changes as conductivity varies around your operating point while holding geometry constant. This makes sensitivity and expected trends easy to communicate.