Calculator
Choose a parameterization, enter values, then calculate. The form uses three columns on large screens, two on small, and one on mobile.
Formula used
The membrane time constant for a first-order RC membrane is:
When using specific membrane parameters per area:
- R is resistance (Ω), C is capacitance (F).
- Rm is specific resistance (Ω·cm²), Cm is specific capacitance (F/cm²).
- Cutoff frequency: fc = 1/(2π τ).
- Step response fraction: 1 − e^{−t/τ}.
How to use this calculator
- Select Specific for biophysical parameters (Rm, Cm), or Lumped for circuit parameters (R, C).
- Enter numeric values and units. In Specific mode, area is optional.
- Optionally enable temperature scaling and provide Q10, Tref, and T.
- Set a step amplitude and a sample time to evaluate V(t).
- Press Calculate. Results appear below the header, above the form.
- Use Download CSV or Download PDF to export the computed summary.
Example data table
These examples illustrate typical orders of magnitude and resulting τ values.
| Example | Inputs | Computed τ | fc (Hz) |
|---|---|---|---|
| Specific membrane | Rm=20000 Ω·cm², Cm=1 µF/cm² | 20 ms | ≈7.96 |
| Lumped whole-cell | R=100 MΩ, C=200 pF | 20 ms | ≈7.96 |
| Faster membrane | R=50 MΩ, C=50 pF | 2.5 ms | ≈63.7 |
Professional article
1) Membrane time constant in electrophysiology
The membrane time constant (τ) describes how quickly a membrane potential approaches a new value after a small perturbation. In the passive RC approximation, the voltage follows an exponential curve with a single characteristic time scale. After one τ, the response reaches about 63.2% of the final step, so τ summarizes speed in one number.
2) Core RC relationship and unit consistency
For a linear compartment, the time constant is τ = R × C. Use ohms for resistance and farads for capacitance to obtain seconds, then convert to milliseconds for reporting. Example: 100 MΩ × 200 pF = 100×10^6 × 200×10^-12 s = 0.020 s, which is 20 ms.
3) Using specific membrane parameters
Biophysical models often specify membrane resistance per area (Rm, Ω·cm²) and capacitance per area (Cm, F/cm²). In that form, the time constant becomes τ = Rm × Cm, and it does not depend on area. A common baseline is Cm ≈ 1 µF/cm², while Rm often ranges from 5,000 to 100,000 Ω·cm².
4) Converting to lumped values with area
If you provide membrane area A, the calculator can report equivalent lumped parameters for circuit intuition. The conversions are R = Rm/A and C = Cm×A, which preserve the same τ. For instance, Rm=20,000 Ω·cm² and A=0.001 cm² give R=20 MΩ and C=1 nF when Cm=1 µF/cm².
5) Temperature scaling and Q10
Ion channel kinetics and membrane resistance can vary with temperature, so controlled scaling improves comparisons. This tool uses R(T)=Rref×Q10^((Tref−T)/10) to adjust resistance before computing τ. With Q10=1.2, moving from 23°C to 33°C scales resistance by 1.2^-1 ≈ 0.833, reducing τ by the same factor.
6) Cutoff frequency as a low-pass summary
A passive membrane behaves like a low-pass filter whose corner frequency is fc=1/(2πτ). Larger τ values produce smaller fc values, meaning the membrane smooths fast fluctuations more strongly. For τ=20 ms, fc≈1/(2×3.1416×0.02)≈7.96 Hz, matching the example table.
7) Step response checkpoints used in experiments
When a step is applied, V(t)=Vstep(1−e^(-t/τ)) for an initially uncharged membrane. Useful checkpoints are 1τ→63.2%, 2τ→86.5%, and 3τ→95.0% of the final value. These percentages help choose sampling windows for current clamp and interpret rise-time in simplified clamp analyses.
8) Practical interpretation and modeling tips
Somatic compartments in many neuron models yield τ values on the order of 5 to 30 ms, while smaller compartments can be 1 to 5 ms. Measured τ can be inflated by series resistance, electrode capacitance, or multi-compartment dynamics that are not strictly single-exponential. Use this calculator to sanity-check units, compare parameter sets, and document results with exports for lab notes and reports.
FAQs
What does the membrane time constant represent physically?
It is the characteristic time for membrane voltage to change in a passive RC model. After one time constant, the voltage has moved about 63% toward its final step.
Is τ affected by membrane area in specific-parameter form?
No. With specific parameters, τ = Rm × Cm, and the area cancels. Area only changes the equivalent lumped R and C values, not their product.
Why does the calculator report a cutoff frequency?
The passive membrane acts like a low-pass filter. The cutoff frequency fc = 1/(2πτ) summarizes how strongly fast voltage fluctuations are attenuated.
What Q10 values are reasonable for temperature scaling?
It depends on preparation and channels, but 1.1 to 1.4 is a common practical range for resistance-like effects. Use Q10=1 to disable scaling.
How do I choose the sample time for the step response?
Pick times like τ, 2τ, and 3τ to see standard rise checkpoints. For fitting, sample densely over roughly 0 to 5τ to capture the curve.
Can τ be larger than expected in recordings?
Yes. Series resistance, electrode filtering, and multiple membrane compartments can slow the observed response. Verify clamp settings and consider fitting multi-exponential models when needed.
Which mode should I use: specific or lumped?
Use specific mode for membrane biophysics parameters (Rm, Cm). Use lumped mode when you already have whole-cell R and C, such as from a simple circuit equivalent.