Inductance Formulae
The table below lists some common simplified formulas for calculating the approximate inductance of several inductor constructions.
| Construction |
Formula |
Dimensions |
Notes |
| Cylindrical air-core coil |
|
- L = inductance in henries (H)
- μ0 = permeability of free space = 4 × 10−7 H/m
- K = Nagaoka coefficient
- N = number of turns
- A = area of cross-section of the coil in square metres (m2)
- l = length of coil in metres (m)
|
|
| Straight wire conductor |
|
- L = inductance
- l = cylinder length
- c = cylinder radius
- μ0 = vacuum permeability = nH/cm
- μ = conductor permeability
- p = resistivity
- ω = phase rate
|
exact if ω = 0 or ω = ∞ |
|
- L = inductance (nH)
- l = length of conductor (mm)
- d = diameter of conductor (mm)
- f = frequency
|
- Cu or Al (i.e., relative permeability is one)
- l > 100 d
- d2 f > 1 mm2 MHz
|
|
- L = inductance (nH)
- l = length of conductor (mm)
- d = diameter of conductor (mm)
- f = frequency
|
- Cu or Al (i.e., relative permeability is one)
- l > 100 d
- d2 f < 1 mm2 MHz
|
| Short air-core cylindrical coil |
|
- L = inductance (µH)
- r = outer radius of coil (in)
- l = length of coil (in)
- N = number of turns
|
| Multilayer air-core coil |
|
- L = inductance (µH)
- r = mean radius of coil (in)
- l = physical length of coil winding (in)
- N = number of turns
- d = depth of coil (outer radius minus inner radius) (in)
|
| Flat spiral air-core coil |
|
- L = inductance (µH)
- r = mean radius of coil (cm)
- N = number of turns
- d = depth of coil (outer radius minus inner radius) (cm)
|
|
- L = inductance (µH)
- r = mean radius of coil (in)
- N = number of turns
- d = depth of coil (outer radius minus inner radius) (in)
- accurate to within 5 percent for d > 0.2 r.
|
| Toroidal core (circular cross-section) |
|
- L = inductance (µH)
- d = diameter of coil winding (in)
- N = number of turns
- D = 2 * radius of revolution (in)
|
|
- L = inductance (µH)
- d = diameter of coil winding (in)
- N = number of turns
- D = 2 * radius of revolution (in)
- approximation when d < 0.1 D
|
| Toroidal core (rectangular cross-section) |
|
- L = inductance (µH)
- d1 = inside diameter of toroid (in)
- d2 = outside diameter of toroid (in)
- N = number of turns
- h = height of toroid (in)
|