1.570796e-3
H
1.570796
mH
1,570.796
µH
0.006283
µH/turn²
0.2
m
2,500
turns/m
1.570796e-3
H
1.570796
mH
1,570.796
µH
0.006283
µH/turn²
0.2
m
2,500
turns/m
The Inductance Calculator computes the self-inductance for three common inductor geometries: solenoid, toroid, and coaxial cable. Each geometry has a distinct formula derived from electromagnetic field analysis, allowing you to select the appropriate type and enter its dimensions.
Inductance is a measure of how much magnetic flux linkage a conductor produces per unit of current. It governs energy storage in magnetic fields, filtering behavior in circuits, and the transient response of RL and RLC systems. Choosing the right inductor geometry depends on your application — solenoids for simplicity, toroids for low stray fields, and coaxial for transmission lines.
The inductance of each geometry is derived by calculating the magnetic field (via Ampère's law), the total flux linkage, and dividing by the current:
$$L_{\text{sol}} = \frac{\mu_0 \mu_r N^2 A}{l}$$
A straight coil of N turns, cross-sectional area A, and length l. Best for length ≫ diameter. Simple to wind but has external stray fields.
$$L_{\text{tor}} = \frac{\mu_0 \mu_r N^2 A}{2\pi R}$$
A coil wound on a ring of mean radius R and cross-section A. The field is entirely contained inside the ring — no stray field. Ideal for noise-sensitive applications and transformers.
$$L_{\text{coax}} = \frac{\mu_0 \mu_r l}{2\pi} \ln\frac{b}{a}$$
The inductance per unit length of a coaxial transmission line with inner radius a and outer radius b. The magnetic field exists only in the region between conductors. This is key for impedance calculations in RF and signal transmission.
All three formulas share the factor μ₀μᵣ, showing that a magnetic core amplifies inductance in every geometry. The geometric factors differ because of how the field and flux linkage distribute in each configuration.
Compare the inductance values across geometries for your design constraints. Solenoids are easiest to build but leak flux. Toroids confine all flux internally — better for compact, low-noise designs. Coaxial inductance is typically small (nH to μH per meter) and is a parasitic parameter in cable design affecting signal propagation speed and impedance. Select the geometry that best matches your size, frequency, and EMI requirements.
Inputs
Results
A 100-turn toroid on a ferrite core (μᵣ = 3000, R = 15 mm, A = 1 cm²) gives ~40 mH — suitable for power filtering at audio/mains frequencies.
Inputs
Results
One meter of RG-6 coax has ~0.29 μH inductance — combined with its capacitance, this gives the characteristic 75 Ω impedance.
For the same turns and core material, a toroid with small mean radius can achieve high inductance in a compact package because it confines all flux inside. Solenoids need to be long and thin for the formula to be accurate, often making them larger. Coaxial cables have the lowest inductance — typically fractions of a μH per meter.
In a toroid, the field lines form closed loops entirely within the toroidal core. Outside the torus, the field from different parts of the winding cancels by symmetry. This means no external flux leakage — ideal for sensitive circuits and reducing electromagnetic interference (EMI).
The inductance per unit length (L') and capacitance per unit length (C') of a coaxial cable determine its characteristic impedance: $$Z_0 = \sqrt{L'/C'}$$ and signal velocity: $$v = 1/\sqrt{L'C'}$$. Typical values are 50 Ω or 75 Ω depending on the ratio b/a.
Relative permeability (μᵣ) indicates how much a material amplifies the magnetic field versus vacuum. Air/vacuum: μᵣ = 1. Ferrite: 100–15,000. Silicon steel: 2,000–8,000. Mu-metal: 50,000–100,000. Permalloy: up to 100,000. Higher μᵣ means higher inductance for the same geometry.
These formulas are for single-layer windings. Multi-layer solenoids have higher inductance than predicted due to inter-layer coupling. For accurate multi-layer calculations, use Wheeler's formula or finite-element simulation. The toroid formula works well for uniformly wound multi-layer toroids if you use the average radius.
At low frequencies, the DC inductance value applies. At higher frequencies, skin effect reduces the effective conductor cross-section, parasitic capacitance between turns becomes significant, and core losses (eddy currents, hysteresis) change the effective inductance. Above the self-resonant frequency (SRF), the inductor behaves as a capacitor.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
