Action Potential Threshold Estimator
Find whether an injected current pushes a neuron's membrane past its firing threshold, and how long that takes, using a passive integrate-and-fire model.
🎯 What is the Action Potential Threshold Estimator?
The action potential threshold estimator predicts whether a constant injected current will ever depolarize a neuron's membrane past its firing threshold, and if so, exactly how long that takes. It uses a passive integrate-and-fire model that treats the membrane as a simple resistor-capacitor (RC) circuit, V(t) = Vrest + I x Rm x (1 - e^(-t/tau)), where tau = Rm x Cm is the membrane time constant.
Neuroscience students use this calculator to build intuition for the relationship between injected current, membrane properties, and spike timing before moving on to the full Hodgkin-Huxley model with its voltage-gated conductances. Electrophysiologists use similar reasoning when choosing a current-clamp stimulus amplitude and duration during patch-clamp recordings, since a stimulus below rheobase will never fire regardless of how long it is applied. Computational neuroscience courses use this exact leaky-integrator formula as the foundation of the widely used integrate-and-fire spiking neuron model.
A common misconception is that any depolarizing current eventually triggers a spike if applied long enough. That is only true if the steady-state depolarization ceiling, I x Rm, exceeds the gap between resting and threshold potential. If it does not, the membrane voltage asymptotically approaches a value below threshold and never crosses it, no matter the duration, this is what "subthreshold" means precisely. Another point of confusion is that doubling the current does not simply halve the time to threshold, because the underlying voltage response is exponential, not linear.
This calculator removes the algebra of solving an exponential equation for time, letting students and researchers immediately see the classification (subthreshold or suprathreshold) and, when applicable, the exact time-to-threshold, with the full charging curve plotted against the threshold line.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Suprathreshold Stimulus Fires a Spike
Vrest=−70 mV, Vth=−55 mV, Rm=50 MΩ, Cm=100 pF, I=0.5 nA
Example 2 — Subthreshold Stimulus Never Fires
Same neuron as Example 1, but a weaker current: Vrest=−70 mV, Vth=−55 mV, Rm=50 MΩ, Cm=100 pF, I=0.2 nA
Example 3 — Fast, Strongly Suprathreshold Stimulus
A smaller, faster neuron with a strong stimulus: Vrest=−65 mV, Vth=−50 mV, Rm=40 MΩ, Cm=80 pF, I=1.0 nA
❓ Frequently Asked Questions
🔗 Related Calculators
What does the Action Potential Threshold Estimator calculate?
It estimates whether a constant injected current will ever depolarize a neuron's membrane past its firing threshold, and if so, exactly how long that takes, using a passive RC (resistor-capacitor) membrane model, V(t) = Vrest + IRm(1-e^(-t/tau)).
What is the formula behind this estimator?
V(t) = Vrest + I x Rm x (1 - e^(-t/tau)), where tau = Rm x Cm is the membrane time constant, I is the injected current, Rm is membrane resistance, and Cm is membrane capacitance. Solving for the time when V(t) equals the threshold potential gives the time-to-threshold.
What does subthreshold mean in this context?
A stimulus is subthreshold when the steady-state depolarization it can produce, I x Rm, added to the resting potential never reaches the threshold potential, no matter how long the current is applied. The membrane voltage approaches its ceiling asymptotically but never crosses threshold, so no action potential fires.
What does suprathreshold mean in this context?
A stimulus is suprathreshold when I x Rm is large enough that Vrest + IRm exceeds the threshold potential. In that case the membrane voltage crosses threshold at a finite time, calculated as t = -tau x ln(1 - (Vth-Vrest)/(IRm)).
Why do I use nanoamps for current and megohms for resistance?
Nanoamps (nA) multiplied by megohms (M-ohm) gives millivolts directly (10^-9 A x 10^6 ohm = 10^-3 V), the standard scale for single-cell patch-clamp current injection and membrane resistance measurements, so no extra unit conversion is needed in the formula.
Is this the same as the full Hodgkin-Huxley action potential model?
No. This is a simplified passive integrate-and-fire approximation using a fixed membrane resistance and capacitance. The full Hodgkin-Huxley model adds voltage-gated Na+ and K+ conductances that actively generate the action potential's rapid upstroke and downstroke once threshold is crossed, see the Hodgkin-Huxley Conductance Calculator for that.
What is rheobase?
Rheobase is the minimum injected current that could ever reach threshold, in this model it is the current at which the steady-state depolarization I x Rm exactly equals Vth - Vrest. At exactly rheobase, the time to threshold predicted by this formula becomes infinite, so practical thresholds require a current somewhat above rheobase.
How does membrane time constant tau affect time-to-threshold?
A shorter tau (smaller Rm x Cm) means the membrane charges faster toward its steady-state voltage for a given current, so time-to-threshold is shorter. A longer tau means the membrane takes longer to reach the same fraction of its steady-state depolarization.
What happens if I increase the injected current far above what is needed to reach threshold?
The steady-state depolarization ceiling I x Rm rises well above threshold, so the exponential charging curve crosses the threshold line much earlier, time-to-threshold decreases toward zero as current increases, though it never reaches exactly zero for a finite current.
Why must the threshold potential be more positive than the resting potential?
This calculator models depolarizing current injection toward a more positive (less negative) threshold, the standard convention for excitatory action potential firing. If the threshold were entered at or below resting potential, the neuron would already be past threshold at rest, which the calculator flags as invalid input.