Series & Parallel Inductor Calculator
Combine inductors with or without coupling and find M, k and the equivalent inductance.
Step-by-step
- Enter valid values to begin.
Ideal inductors with no winding resistance, capacitance or core saturation, at a frequency well below self-resonance. Coupled modes use only L1 and L2 with mutual inductance M = k√(L1L2); aiding means the winding dots are connected so their fluxes add (series) or both currents enter the dotted ends (parallel). k must be below 1 for real windings; k = 1 is an ideal limit and k above 1 is non-physical and flagged. Measured series L values must be taken with the same LCR meter frequency and no DC bias.
Series and Parallel Inductors: When the Flux Talks Between Windings
Core Engineering Principles
Inductors in series add and in parallel combine like resistors, but only if their fields stay out of each other’s way. Put two coils close together and they share flux. The mutual inductance is M = k√(L₁L₂), where k runs from 0 for no coupling up to 1 for every line of flux linking both windings. In series, the fluxes either help or fight. Aiding gives L₁ + L₂ + 2M; opposing gives L₁ + L₂ − 2M. Two 10 µH windings at k = 0.9 read 38 µH aiding and just 2 µH opposing, nearly a factor of twenty apart from a swap of two wires.
That swap is the whole trick in a coupled SEPIC inductor, a common-mode choke or a flyback winding, and it is also how we measure k at the bench. Read the series-aiding and series-opposing inductance with an LCR meter, subtract, divide by four times the geometric mean, and k falls out. The parallel formulas need care: (L₁L₂ − M²) / (L₁ + L₂ ∓ 2M). A k above 1 is a measurement or arithmetic error, never a real part, because it would imply negative leakage inductance. Real windings reach roughly 0.95 to 0.99 with tight winding or a good core.
Parallel: Leq = (L1L2 − M²) / (L1 + L2 ∓ 2M) • k = (Laid − Lopp) / (4√(L1L2)) • E = ½LI²
NEC & Standard References
IEC 62024-1 covers high-frequency inductors of nominal inductance for electronic and telecommunications equipment, including how inductance, self-resonant frequency and rated current are specified. Manufacturer datasheets define the test frequency and DC bias for the inductance you read. IEEE Std 100 and IEC 60050 define self inductance, mutual inductance and the coupling coefficient. Check the dot convention printed on the part before wiring it.1. M = (38 − 2) / 4 = 9 µH.
2. k = 9 / √(10 × 10) = 0.90, which is a sensible value for a bifilar-wound core.
3. Check: (38 + 2) / 2 = 20 µH, which equals L₁ + L₂, so the meter readings agree.
4. Parallel aiding = (100 − 81) / (20 − 18) = 9.5 µH; parallel opposing = 19 / 38 = 0.5 µH.
5. Energy in the series-aiding connection = ½ × 38 µH × 2² = 76 µJ.
- Dot polarity decides everything. A reversed winding turns a 38 µH choke into 2 µH, and the converter may saturate or short.
- Don’t add inductors blindly. Two inductors sharing a core or sitting close together are coupled even if the schematic shows none.
- Opposing windings do not cancel energy storage. Leakage inductance still stores energy and causes switching spikes.
- Bias changes everything. Ferrite inductance drops as current rises, so the real L under load can be well below the meter reading.
- Never trust k above 1. Re-check the meter frequency, lead compensation and L₁ and L₂.