Calculator
Example Data
| Vrest (mV) | Vth (mV) | Rm (MΩ) | Cm (nF) | I (nA) | t (ms) | Irh (nA) | tc (ms) |
|---|---|---|---|---|---|---|---|
| -70 | -55 | 100 | 0.10 | 0.20 | 2.0 | 0.15 | 2.0 |
| -65 | -50 | 80 | 0.12 | 0.25 | 1.5 | 0.18 | 1.8 |
| -75 | -55 | 120 | 0.09 | 0.18 | 3.0 | 0.14 | 2.2 |
Values are illustrative and vary across cells and preparations.
Formula Used
Treat the membrane as a resistance-capacitance element with time constant
τ = Rm · Cm.
For a constant depolarizing current pulse, the membrane potential approaches a new level:
V(t) = Vrest + I · Rm · (1 − e^(−t/τ))
Threshold is predicted when V(t) ≥ Vth.
Solving for the minimum pulse current gives:
Imin = (Vth − Vrest) / (Rm · (1 − e^(−t/τ)))
Helps compare thresholds across pulse durations using two parameters:
rheobase Irh and chronaxie tc.
I(t) = Irh · (1 + tc/t)
How to Use This Calculator
- Enter Vrest and your chosen Vth in mV.
- Set Rm and Cm using measured or estimated values.
- Choose a depolarizing current and pulse duration.
- Optionally set rheobase and chronaxie for comparisons.
- Press Calculate to view results above the form.
- Use the export buttons to download CSV or PDF reports.
Tip: If RC predicts no crossing, increase current or duration, or adjust Rm/Cm to match your preparation.
Professional Notes on Action Potential Threshold
1) What “threshold” means in practice
Threshold is the membrane potential where inward ionic current becomes regenerative, so a small extra depolarization produces a rapid upstroke. Many neurons show effective thresholds around −55 mV, but values commonly vary by 10–20 mV across cell types, temperature, and channel expression.
2) Why the RC model is useful
The RC pulse model links stimulus current to depolarization through Rm, Cm, and the time constant τ = Rm·Cm. For example, Rm = 100 MΩ and Cm = 0.10 nF give τ ≈ 10 ms. A 2 ms pulse is only 0.2τ, so the voltage rise is far from its steady level, requiring higher current for the same target depolarization.
3) Interpreting “minimum current” output
The reported Imin is the constant pulse current that reaches Vth exactly at pulse end. If your selected current is below Imin, the RC prediction is no crossing at that duration. If it exceeds Imin, the model predicts a crossing before pulse end, providing a safety margin in mV.
4) Strength–duration and stimulation metrics
The Lapicque relation summarizes excitability with rheobase (long‑pulse threshold) and chronaxie (pulse duration where threshold equals 2× rheobase). Typical chronaxie values for excitable tissue often fall near 0.2–2 ms, depending on geometry and membrane kinetics. Shorter pulses increase threshold approximately in proportion to 1/t.
5) Data-driven checks for plausibility
Use ranges as a quick sanity check: Rm often spans ~10–500 MΩ and Cm ~0.01–1 nF for single neurons, producing τ from sub‑millisecond to tens of milliseconds. If τ is extremely small, the RC curve saturates quickly; if τ is large, brief pulses should produce small ΔV unless current is increased.
6) Charge and energy as comparative measures
Charge Q = I·t helps compare protocols with different durations. The capacitive energy estimate E ≈ ½·C·(ΔV)² is not the metabolic cost of spiking, but it can indicate relative electrical “dose” delivered to the membrane capacitor in controlled experiments.
7) Sources of mismatch with real neurons
Real cells include voltage‑gated conductances, adaptation, and distributed morphology, so “threshold” can be dynamic. Hyperpolarizing currents, shunting inhibition, and series resistance can shift effective threshold. Treat model outputs as structured estimates, then validate against recordings.
8) Recommended workflow for experiments
Start with measured Vrest and a candidate Vth, choose Rm and Cm from current clamp or literature, and compute Imin for several pulse widths (for example 0.5, 1, 2, and 5 ms). Compare with Lapicque thresholds to build a strength–duration curve, then refine rheobase and chronaxie from fitted data.
FAQs
1) Is the threshold voltage a fixed number?
Not always. Threshold can shift with temperature, ion concentrations, channel inactivation, and recent spiking. This calculator treats Vth as a chosen reference so you can compare stimulus settings consistently.
2) What does τ tell me about stimulation difficulty?
τ sets how fast voltage rises. If pulse duration is much smaller than τ, the membrane barely charges, so higher current is required. If duration is several τ, the response approaches its steady level.
3) Why do RC and Lapicque predictions differ?
RC depends on Rm and Cm, while Lapicque summarizes excitability using rheobase and chronaxie. They can agree for some cells, but ionic dynamics, geometry, and electrode effects often cause differences.
4) Can I use negative current values?
You can, but negative current hyperpolarizes the membrane in this model and will not reach a depolarizing threshold. For inhibitory or rebound scenarios, additional dynamics would be needed.
5) What units should I use?
Enter mV for voltages, MΩ for resistance, nF for capacitance, nA for current, and ms for time. The calculator converts internally and reports results in the same convenient units.
6) Is the energy output the energy of an action potential?
No. The reported energy is a capacitive estimate based on the final ΔV of the pulse, not the biochemical energy of ion pumping after a spike. Use it mainly for relative comparisons.
7) How do I fit rheobase and chronaxie from data?
Measure threshold current at several pulse durations, then fit I(t) = Irh(1 + tc/t). Irh is the asymptotic long‑pulse threshold, and tc is the duration where threshold equals 2× Irh.