inductance

Toroid Inductance Per Turn

Calculate the inductance and core parameters of a toroidal inductor.

The toroid inductance per turn is the quantity of inductance produced by each winding or turn of wire surrounding a toroidal (doughnut-shaped) core. It is dictated by the physical properties of the toroid — including its size, composition, and number of turns.

Knowing toroid inductance per turn is primarily used to calculate and optimize inductance values in electronic circuits. It assists designers and engineers in determining how many turns are needed to reach a specific inductance value for applications such as energy storage, impedance matching, and filtering.

Understanding Toroid Inductance per Turn

Toroidal inductors are electrical elements used for storing energy within a magnetic field. Widely utilized in electronic circuits, they guarantee both low frequencies and significant inductance values.

Advantages of Toroid Inductors

High inductance per unit of turns
High current-carrying capacity
Low noise and interference
High degree of isolation between circuits

Disadvantages of Toroid Inductors

Higher cost compared to other inductor types
Limited availability of suitable core materials
Limited frequency range
May require additional components for proper operation

Applications

Transformer Design
Inductive Components
Power Supply Filtering
RF Circuits
Filtering out high-frequency noise and interference
Voltage and current regulation
Energy storage for later use
Providing a high degree of isolation between circuits

About This Calculator

This online electrical calculator determines the inductance per turn of a toroidal inductor. Toroidal inductors — also known as ring-shaped coil inductors — are frequently used when large inductance is required at low frequencies. They can efficiently manage larger currents due to their increased number of turns.

Formulas

$L = 2 \times N^2 \times \mu_r \times h \times \ln\left(\frac{d_1}{d_2}\right)$

$A_e = \frac{h}{2} \times (d_1 - d_2)$

$L_e = \frac{\pi \times (d_1 - d_2)}{\ln\left(\frac{d_1}{d_2}\right)}$

$V_e = A_e \times L_e$

$\frac{B}{I} = \frac{0.4\pi \times \mu_r \times N}{L_e}$

where:

$L$ = Inductance (H)
$N$ = Number of Turns
$\mu_r$ = Relative Permeability
$h$ = Core Width (m)
$d_1$ = Outer Diameter (m)
$d_2$ = Inner Diameter (m)
$A_e$ = Effective Core Area (m²)
$L_e$ = Effective Core Length (m)
$V_e$ = Effective Core Volume (m³)
$\frac{B}{I}$ = Flux Density per Amp (T/A)

Inputs

Core Width(mm)

Height (width) of the toroid core in millimetres

Outer Diameter(mm)

Outer diameter of the toroid core in millimetres

Inner Diameter(mm)

Inner diameter of the toroid core in millimetres — must be less than outer diameter

Relative Permeability

Relative permeability of the core material — ferrite ≈ 100–10000, iron powder ≈ 10–100

Number of Turns(turns)

Number of winding turns on the toroid

Results

⚠Inner diameter must be less than outer diameter

Inductance—µHInductance of the toroid in microhenries

Effective Core Area—mm²Effective cross-sectional area of the core in square millimetres

Effective Core Length—mmEffective magnetic path length of the core in millimetres

Effective Core Volume—mm³Effective volume of the core in cubic millimetres

Flux Density per Amp—gauss/AFlux density per ampere of current in gauss per amp