Coax Electrical vs Physical Length
l_elec = l_phys × VF
Quick answer
This calculator solves l_electrical = l_physical × VF for Electrical Length. With Physical Length 2.2 m, Velocity Factor 50 %, the result is 1.1 m. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The velocity factor (VF) of a cable is the ratio of the signal propagation speed to the speed of light in vacuum. Because electromagnetic waves travel slower in the cable dielectric than in free space, a cable appears electrically longer than its physical length. The electrical length determines the phase delay and is critical for antenna feed lines, delay matching, phasing harnesses, and impedance matching networks where specific electrical lengths (λ/4, λ/2) are required. VF = 1/√(εr) where εr is the dielectric constant of the insulation material.
Variables
- l_electrical — Equivalent free-space length (m)
- l_physical — Actual cable length (m)
- VF — Velocity factor (0 to 1, dimensionless)
Practical Notes
Common velocity factors: solid polyethylene (RG-58) VF = 0.66, foam polyethylene (LMR-400) VF = 0.85, air-spaced (hardline) VF = 0.92-0.95, PTFE (Teflon) VF = 0.70. For a quarter-wave matching section at 100 MHz (λ = 3 m): physical length = (3/4) × VF = 0.75 × 0.66 = 0.495 m for solid PE coax. VF can be measured with a network analyzer or TDR (time-domain reflectometer).
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| l_elec | Electrical Length | m | mm, cm, m, km |
| l_phys | Physical Length | m | mm, cm, m, km |
| VF | Velocity Factor | — | —, % |
Step by step
- 1. What you know: Physical Length 2.2 m, Velocity Factor 50 %
- 2. The relation: l_electrical = l_physical × VF
- 3. Substitute: l_phys = 2.2 m, VF = 50 %
- 4. Result: Electrical Length = 1.1 m
Worked examples
Minimum range
Given: Physical Length 2.2 mm, Velocity Factor 2.5 %
Result: Electrical Length = 0.055 mm
Low range
Given: Physical Length 2.2 cm, Velocity Factor 25 %
Result: Electrical Length = 5.5 mm
Typical
Given: Physical Length 2.2 m, Velocity Factor 50 %
Result: Electrical Length = 1.1 m
High range
Given: Physical Length 0.22 km, Velocity Factor 0.8
Result: Electrical Length = 0.176 km
Maximum range
Given: Physical Length 2.2 km, Velocity Factor 8
Result: Electrical Length = 17.6 km
Solving for each variable
Solve for Electrical Length
Physical Length 2.2 mm, Velocity Factor 2.5 % → 0.055 mm
Solve for Physical Length
Electrical Length 1 mm, Velocity Factor 2.5 % → 4 cm
Solve for Velocity Factor
Electrical Length 1 mm, Physical Length 2.2 mm → 45.45 %
How Electrical Length changes with Physical Length
| Physical Length (input) | Electrical Length (result) |
|---|---|
| 22 cm | 11 cm |
| 0.55 m | 27.5 cm |
| 1.1 m | 0.55 m |
| 1.65 m | 0.825 m |
| 2.2 m | 1.1 m |
| 3.3 m | 1.65 m |
| 4.4 m | 2.2 m |
| 8.8 m | 4.4 m |
| 15.4 m | 7.7 m |
| 22 m | 11 m |
The same result in other units
| Unit | Value |
|---|---|
| mm | 1100 |
| cm | 110 |
| m | 1.1 |
| km | 0.0011 |
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<p><a href="https://vbatpower.com/formulas/coax-velocity-factor/">Coax Electrical vs Physical Length</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Coax Electrical vs Physical Length?
Use l_electrical = l_physical × VF. With Physical Length 2.2 m, Velocity Factor 50 %, Electrical Length works out to 1.1 m.
What is the formula for Coax Electrical vs Physical Length?
The formula is l_electrical = l_physical × VF. The velocity factor (VF) of a cable is the ratio of the signal propagation speed to the speed of light in vacuum.
How do you find Physical Length when you know the other values?
Rearrange for Physical Length: with Electrical Length 1 mm, Velocity Factor 2.5 %, Physical Length is 4 cm.
How do you find Velocity Factor when you know the other values?
Rearrange for Velocity Factor: with Electrical Length 1 mm, Physical Length 2.2 mm, Velocity Factor is 45.45 %.
What units does Coax Electrical vs Physical Length use?
Electrical Length is shown in mm, cm, m, km. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Wire & Cable formulas →Need more features?
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