Electrical Length Calculator: Wavelength and Cable Length

An electrical length calculator converts a physical conductor length into its length as a fraction of a signal’s wavelength, usually expressed in degrees or radians. Enter the cable length and signal frequency, then choose the propagation velocity factor; the calculator returns the electrical length and the corresponding wavelength.

Formula

The electrical length is the physical length divided by the signal wavelength in the medium, multiplied by 360 degrees:

θ = 360° × L / λ = 360° × L × f / (c × VF)

• θ is electrical length in degrees.
• L is physical length in metres (m).
• λ is wavelength in the cable or other medium, in metres (m).
• f is frequency in hertz (Hz); the calculator accepts megahertz (MHz) and converts it to Hz.
• c is the speed of light in vacuum, approximately 299,792,458 metres per second (m/s).
• VF is the velocity factor, a dimensionless fraction describing how fast the signal travels in the medium relative to c.

The calculator also reports the wavelength in the cable: λ = c × VF / f. In radians, the same electrical length is φ = 2πL / λ. Degrees and radians describe the same phase angle using different units.

Worked Example

Using the calculator’s defaults: a 1 m cable, a 100 MHz signal, and a velocity factor of 0.66.

1. Convert frequency: 100 MHz × 1,000,000 = 100,000,000 Hz.
2. Find wavelength in the cable: λ = 299,792,458 × 0.66 / 100,000,000 = 1.9786302228 m, or 1.979 m rounded to three decimal places.
3. Calculate electrical length: θ = 360° × 1 m / 1.9786302228 m = 181.943…°, or 181.94° rounded to two decimal places.

What Electrical Length Means

Electrical length describes how much phase a traveling signal accumulates along a physical path. A cable that is only a metre long can represent many degrees at a high frequency, while the same cable represents fewer degrees at a lower frequency. The result depends on both frequency and how quickly the signal propagates through the cable’s dielectric material.

A quarter wavelength is 90° and a half wavelength is 180°. These lengths matter in transmission-line work because impedance and phase relationships repeat with wavelength. For instance, an ideal half-wave line repeats the load impedance at its input, while a quarter-wave section can transform impedance under specific conditions. These are transmission-line effects, not simply measurements of how long a cable looks.

Electrical length is not the same as the cable’s physical length, nor does it alone tell you whether a cable is a good match for a particular system. It is a phase measure at a specified frequency and propagation velocity.

When to Use the Calculator

Use it when estimating phase delay along a cable, comparing cable length with wavelength, or planning a transmission-line section or antenna feed. It is also useful for checking whether a conductor is electrically short relative to the signal wavelength. For example, a 1 m cable at 100 MHz with VF 0.66 is about 182° long, so treating it as a negligible-length wire would be inappropriate in many RF calculations.

Inputs should describe the signal’s path, not just the surrounding air. For a coaxial cable, use the cable’s specified velocity factor when available. For a different medium or a designed structure such as a microstrip trace, propagation can depend on the material and geometry; a generic cable value may not represent it accurately.

Choosing Inputs and Reading Results

• Length: Enter the physical distance the signal travels. This may differ from a straight-line distance if the cable follows a route.
• Frequency: Use the frequency of interest. A cable has a different electrical length at every frequency.
• Velocity factor: Enter a fraction between 0 and 1 for an ordinary passive medium. A value of 0.66 means the signal travels at about 66% of the speed of light in vacuum.
• Units: The calculator takes metres and MHz. Convert feet to metres by multiplying by 0.3048; convert kilohertz to MHz by dividing by 1,000, and gigahertz to MHz by multiplying by 1,000.

The displayed angle is not restricted to 0°–360°. A result above 360° means the signal accumulates more than one full phase cycle along the path. For example, 450° represents one complete cycle plus another 90°. Reducing an angle modulo 360° can be useful when comparing phase at one frequency, but retain the unreduced value when the number of full wavelengths matters.

Assumptions and Common Mistakes

This calculation assumes a single frequency and a uniform propagation velocity along the entire path. Real cables can have tolerances, connectors, bends, and frequency-dependent electrical properties. The computed value is therefore an ideal estimate based on the inputs, not a measurement of a particular installed cable.

• Using the wrong velocity factor: The value for one cable type may not apply to another. Check the cable specification rather than assuming all coaxial cables have the same VF.
• Mixing units: Substituting a number in feet where metres are expected, or entering 0.1 for 100 MHz, changes the result by a large factor.
• Confusing free-space and cable wavelength: The free-space wavelength is c/f. In a cable it is approximately VF times that value, so it is shorter when VF is below 1.
• Rounding too early: Keep full precision through intermediate steps and round only the displayed answer. Small rounding differences can otherwise affect a later phase calculation.
• Assuming electrical length determines loss or impedance: The phase result does not calculate attenuation, characteristic impedance, mismatch, or connector effects.

For a cable whose velocity factor varies with frequency, use a value appropriate to the frequency being analyzed. For accurate design at high frequencies, consult manufacturer data or use a suitable transmission-line model or measurement; this simple formula cannot account for every cable construction or installation.

Frequently Asked Questions

How do I calculate electrical length?
Divide physical length by wavelength in the medium and multiply by 360°: θ = 360° × L/λ. If you know frequency and velocity factor, use λ = c × VF/f.

What is the difference between physical and electrical length?
Physical length is a distance, such as metres or feet. Electrical length is the phase shift that a signal accumulates over that distance at a particular frequency and propagation velocity, usually expressed in degrees or radians.

Does a cable’s electrical length change with frequency?
Yes. With the cable and velocity factor held constant, electrical length is proportional to frequency. Doubling frequency doubles the calculated phase angle.

What velocity factor should I use?
Use the value specified for the cable or propagation structure at the frequency of interest. If it is unknown, the result is only an estimate; do not treat a typical value for a different cable as exact.

Can electrical length be greater than 360 degrees?
Yes. It counts accumulated phase along the full path, including complete cycles. A value of 360° is one wavelength, and 720° is two wavelengths.

Is a quarter-wave cable always exactly one quarter of its free-space wavelength?
No. It is one quarter of the wavelength in the cable. Since the cable’s velocity factor is usually below 1, its wavelength is shorter than the free-space wavelength at the same frequency.

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in length | Physical length | m | 1 | 0
in freq | Frequency | MHz | 100 | 0
in vf | Velocity factor | fraction of c | 0.66 | 0
out angle | Electrical length | degrees | 360 * length * freq * 1000000 / (299792458 * vf) | 2
out wavelength | Wavelength in cable | m | 299792458 * vf / (freq * 1000000) | 3