Toroid inductance calculator

Enter the number of turns, the core's relative permeability, its effective cross-sectional area in square metres, and the mean magnetic path length in metres. The result is returned in henries, millihenries, and microhenries using the standard magnetic-circuit approximation. It is useful for quick design checks, datasheet comparisons, education, and repeatable automated calculations when the core remains below saturation and behaves close to its stated permeability.

Choose inputs that describe the magnetic core

Start with the total number of turns in the winding, then use the effective magnetic dimensions supplied by the core manufacturer whenever possible. The cross-sectional area is the area carrying magnetic flux through the core, not the window area inside the toroid and not the copper wire area. The mean magnetic path length is the average distance followed by flux around the ring; it is commonly listed as an effective path length on a datasheet. Relative permeability is dimensionless and describes how much more permeable the material is than free space. Use the permeability appropriate to the material, frequency, flux level, and temperature of interest, because a catalog headline value may not represent your operating point. Enter area in square metres and path length in metres. If a datasheet uses square millimetres, multiply by 0.000001 to obtain square metres. If it gives path length in millimetres, multiply by 0.001. Consistent SI units prevent silent scale errors that can otherwise change the answer by factors of thousands or millions.

Understand the equation and returned values

The calculator applies L = μ₀ × μᵣ × N² × A ÷ lₘ. Here μ₀ is the permeability of free space, μᵣ is the core's relative permeability, N is the turn count, A is effective core cross-sectional area, and lₘ is mean magnetic path length. The squared turn term is especially important: doubling the turns produces four times the ideal inductance when every other input remains fixed. Doubling area or relative permeability doubles inductance, while doubling the path length halves it. The response includes inductance in henries, millihenries, and microhenries so you can use the scale most convenient for a schematic or component specification. It also reports the absolute permeability calculated from μ₀μᵣ and echoes the normalized inputs, which makes an automated result easier to audit. Precision controls decimal rounding in each inductance unit, but it does not make uncertain core data more accurate. Keep enough digits for comparison, then round according to the tolerances of the material and winding rather than treating every displayed decimal as physically significant.

Know when the ideal toroid model is appropriate

This calculation assumes a homogeneous, closed, ungapped toroidal core with magnetic flux confined to a uniform effective cross section. It is a useful first estimate for many ferrite and powdered-core designs, but real components depart from that ideal. Permeability may vary with frequency, temperature, manufacturing tolerance, DC bias, and AC flux density. A deliberate or accidental air gap can dominate magnetic reluctance and substantially reduce inductance. At high excitation the core may approach saturation, making inductance nonlinear, while leakage flux and fringing become relevant when geometry is not well represented by one path length and one area. The equation also excludes winding resistance, skin and proximity effects, parasitic capacitance, core loss, and self-resonance. For production design, compare the estimate with the manufacturer's inductance factor or material curves and measure a wound sample under representative conditions. Use this tool to screen dimensions, check unit conversions, explore how turns affect the ideal result, or provide a deterministic baseline. Do not use the output alone to establish current rating, stored-energy safety margins, thermal performance, or high-frequency impedance.