Membrane Capacitance and Time Constant Calculator
Find a cell membrane's electrical time constant and cutoff frequency from its resistance and capacitance.
⚡ What is the Membrane Time Constant?
The membrane time constant (tau) describes how quickly a cell membrane's voltage responds to a change in current, treating the membrane as a simple parallel resistor-capacitor (RC) circuit. It is defined by tau = Rm x Cm, where Rm is the membrane resistance (how easily current flows through ion channels) and Cm is the membrane capacitance (how much charge the lipid bilayer stores per volt of voltage difference).
Neuroscientists use the membrane time constant to understand how a neuron integrates synaptic inputs over time, predict how quickly a cell's voltage settles after a current injection, and interpret patch-clamp recordings. It is a fundamental parameter in single-compartment and multi-compartment neuron models, alongside the membrane resistance and the space (length) constant that governs how signals decay along dendrites and axons.
A common point of confusion is treating the membrane time constant as a fixed biological property. It is actually a purely electrical quantity, set entirely by Rm and Cm, and both of those change with cell size, ion channel density, and even neuromodulation, meaning tau itself can vary within the same neuron under different physiological conditions.
This calculator computes tau directly from membrane resistance and capacitance, derives the associated cutoff frequency, and plots the classic RC charging curve showing the membrane voltage rising toward its final value after a step current, with the one-tau point (63.2% of final value) marked directly on the chart.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Medium Pyramidal Neuron
Rm = 50 MΩ, Cm = 100 pF
Example 2 — Small Fast-Spiking Interneuron
Rm = 20 MΩ, Cm = 200 pF
Example 3 — Large, High-Resistance Cell
Rm = 100 MΩ, Cm = 80 pF
❓ Frequently Asked Questions
🔗 Related Calculators
What is the membrane time constant?
The membrane time constant, tau = Rm x Cm, describes how quickly a cell membrane's voltage responds to a step change in current, treating the membrane as a simple resistor-capacitor (RC) circuit. It is the time for the membrane voltage to reach 63.2% of its final change.
What is the formula for membrane time constant?
tau = Rm x Cm, where Rm is the membrane resistance and Cm is the membrane capacitance. With Rm in megohms and Cm in picofarads, tau comes out directly in microseconds and is typically reported in milliseconds.
What is a typical membrane time constant for a neuron?
Most mammalian neurons have membrane time constants between about 1 and 50 milliseconds, depending on cell size and membrane properties. Smaller, more compact neurons generally have shorter time constants than large neurons with extensive dendritic membrane area.
What does the cutoff frequency fc mean for a cell membrane?
fc = 1/(2*pi*tau) is the frequency above which the membrane increasingly filters out (attenuates) rapid voltage changes, acting as a low-pass filter. Signals or synaptic inputs that change faster than roughly fc get smoothed out by the membrane's own RC properties.
Why does the membrane behave like an RC circuit?
The lipid bilayer is a thin insulating layer between two conductive solutions, exactly the structure of a parallel-plate capacitor, giving membrane capacitance Cm. Ion channels spanning the membrane provide a path for current to flow, giving membrane resistance Rm. Together they form a parallel RC circuit.
What is 63.2% and why does it appear in the chart?
For any first-order RC charging response, V(t) = Vfinal x (1 - e^(-t/tau)), so at exactly t = tau, the exponent is -1 and V(tau) = Vfinal x (1 - e^-1) = Vfinal x 0.632. This 63.2% mark is a universal signature of one time constant elapsing, independent of the specific Rm and Cm values.
How is specific membrane capacitance related to Cm?
Specific membrane capacitance is remarkably constant across cell types at about 1 microfarad per square centimeter of membrane area. Total membrane capacitance Cm is simply this specific value multiplied by the cell's total membrane surface area, so larger cells generally have larger Cm and, all else equal, a longer time constant.
Does a shorter or longer time constant make a neuron respond faster?
A shorter time constant lets the membrane voltage respond faster to a change in input current, reaching steady state sooner. However, it also means the membrane integrates (sums) synaptic inputs over a shorter time window, a fundamental trade-off between speed and temporal summation in neural signaling.
How does membrane time constant relate to the cable equation?
The membrane time constant tau = RmCm is one of two key parameters (alongside the space constant lambda) in the cable equation, which describes how voltage changes propagate and decay along a neuron's dendrites and axon. Tau governs the temporal decay while lambda governs the spatial decay.
What units does this calculator use?
Membrane resistance Rm is entered in megohms (M-ohm) and membrane capacitance Cm in picofarads (pF), the typical scale for a single cell. The time constant is shown in milliseconds and the cutoff frequency in hertz.