Length Constant Calculator Math

Length Constant Formula:

\[ \lambda = \sqrt{\frac{R_m}{R_i}} \]

Length Constant (λ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is a Length Constant Calculator?

Definition: This calculator computes the length constant (λ) of a neuron's axon or dendrite based on membrane resistance and intracellular resistance.

Purpose: It helps neuroscientists and physiologists understand signal decay in neuronal processes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \lambda = \sqrt{\frac{R_m}{R_i}} \]

Where:

\( \lambda \) — Length constant (meters)
\( R_m \) — Membrane resistance (Ohms·m²)
\( R_i \) — Intracellular resistance (Ohms·m)

Explanation: The length constant represents the distance at which the signal decays to 1/e (about 37%) of its original value.

3. Importance of Length Constant Calculation

Details: The length constant determines how far electrical signals can propagate along neuronal processes without significant decay.

4. Using the Calculator

Tips: Enter the membrane resistance (R_m) in Ohms·m² and intracellular resistance (R_i) in Ohms·m. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical length constant value?
A: In neurons, length constants typically range from 0.1 to 1 mm, but can vary significantly.

Q2: How does diameter affect the length constant?
A: Larger diameter processes have lower R_i, resulting in longer length constants.

Q3: What units should I use?
A: Consistent units are critical - R_m in Ohms·m² and R_i in Ohms·m will give λ in meters.

Q4: What affects membrane resistance?
A: R_m depends on ion channel density and membrane properties.

Q5: How is this related to cable theory?
A: The length constant is a fundamental parameter in cable theory models of neurons.