symmetrical inductance formulas and interpretation
Symmetrical conductor inductance depends logarithmically on conductor spacing relative to geometric mean radius.
The calculator preserves engineering outputs in H/m and mH/km with compact responsive inputs.
How to use the symmetrical inductance calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
For the supported ideal symmetrical arrangement, inductance per length equals 2 × 10⁻⁷ times the natural logarithm of spacing divided by GMR.
L = (μ₀/2π) ln(D/GMR)- L — Inductance per length
- Series inductance per conductor length (H/m)
- D — Spacing
- Geometric conductor spacing (m)
- GMR — Geometric mean radius
- Effective conductor radius (m)
- μ₀ — Vacuum permeability
- Magnetic constant (H/m)
Conductor-spacing example
Conductor spacing is 1 m and GMR is 0.01 m.
- Spacing
- 1 m
- GMR
- 0.01 m
- L = 2 × 10⁻⁷ ln(100)
- L ≈ 9.21 × 10⁻⁷ H/m
Result: Inductance is about 0.921 mH/km.
Increasing spacing raises inductance logarithmically.
Understanding your results
Interpreting the result
The equation assumes the supported symmetrical geometry and does not include earth-return or complex bundle effects.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.