Inductors in Parallel
A group of coils (or inductors) are connected in parallel when one end of all the coils is connected to one common point, and the other end of all the coils is connected to another common point. The source is connected across these two points, so every inductor shares the same voltage while the current divides between the branches.
Use the inductors in parallel calculator to determine the equivalent inductance of a parallel combination. If you want the equivalent inductance of a series circuit instead, where inductances simply add (L = L₁ + L₂ + … + Lₙ), use an inductors-in-series calculator.
Formula for Equivalent Inductance in a Parallel Circuit
When a changing current I flows through a coil, a self-induced e.m.f. appears across it. Using the definition of self-inductance L:
In a parallel connection the total current divides between the branches, so the total current is the sum of the branch currents: I = I₁ + I₂ + … + Iₙ. Differentiating with respect to time and noting that the voltage e is the same across every inductor, the reciprocal of the equivalent inductance equals the sum of the reciprocals of the individual inductances:
Where:
- L — Equivalent parallel inductance (henries, H)
- L₁, L₂, …, Lₙ — Inductances of the individual coils (H)
The SI unit of inductance is the henry (H). One henry is the inductance that produces an e.m.f. of one volt when the current changes at a rate of one ampere per second: 1 H = 1 V·s/A. As with resistors in parallel, the equivalent inductance is always smaller than the smallest individual inductor. Note: this simple formula assumes there is no mutual inductance (magnetic coupling) between the coils.
How to Calculate Total Inductance in a Parallel Circuit
This inductors in parallel calculator has two modes:
- Total Inductance — Enter up to 10 inductor values and the calculator instantly finds the equivalent parallel inductance. New input rows appear as you add more inductors.
- Missing Inductor — Set the desired total inductance and enter the values of all known inductors. The calculator finds the missing inductor needed to reach your target.
Example (Total mode): Three inductors L₁ = 10 mH, L₂ = 20 mH, L₃ = 30 mH connected in parallel:
L = 1 / 183.333 ≈ 5.4545 mH
How to Use the Inductors in Parallel Calculator
- Choose the unit prefix (nH, µH, mH or H) that matches your inductor values.
- Enter the value of each inductor (L1, L2, …). Click Add Inductor to include more — up to 10 in total.
- Read the equivalent parallel inductance in the results panel, together with the step-by-step calculation.
- To work backwards, switch to the Missing Inductor tab, enter your target total inductance and the known inductors, and the calculator solves for the remaining one.
Unit Systems
Inductance is an SI quantity, so it is measured in henries (H) in both the metric (SI) and American engineering systems — there is no separate imperial unit for inductance. The calculator therefore offers the standard decimal prefixes used in electronics:
- nH (nanohenry) — 1 nH = 0.000000001 H, used for very small RF coils and PCB traces
- µH (microhenry) — 1 µH = 0.000001 H, common for RF and switching inductors
- mH (millihenry) — 1 mH = 0.001 H, typical for audio and power inductors
- H (henry) — base SI unit, used for large chokes and transformer windings
Results are always displayed in the most readable form with automatic prefix selection (pH, nH, µH, mH, H) regardless of the input unit.
Frequently Asked Questions
Why is parallel inductance always less than the smallest inductor?
Each additional parallel branch provides another path for current to flow, so the combination opposes changes in current less than any single coil alone. Adding any inductor — no matter how large — always lowers the equivalent inductance, just as adding a resistor in parallel always lowers resistance.
What is the inductance of two equal inductors in parallel?
For two identical inductors L in parallel: L_total = L / 2. More generally, N identical inductors in parallel give L_total = L / N.
Is the formula the same as for resistors?
Yes. Inductors in parallel follow the same reciprocal formula as resistors in parallel (1/L = 1/L₁ + 1/L₂ + …) and as capacitors in series. The only difference is the unit — henries instead of ohms or farads.
Does this account for mutual inductance?
No. The standard parallel formula assumes the coils are magnetically isolated (no coupling). If the inductors share a magnetic field, mutual inductance must be added to the analysis and the equivalent value will differ.
How do I use the "missing inductor" mode?
Switch to the Missing Inductor tab, enter your target total inductance, then add all the inductors you already have. The calculator solves 1/L_missing = 1/L_target − Σ(1/L_known). If the result is impossible (negative), your known inductors already give a lower inductance than the target, so no solution exists.