Formula and Method for Inductors in Series
When two or more inductors are connected end-to-end in a single current path with no shared magnetic field, their inductances simply add: L_total = L1 + L2 + L3 + ... + Ln, the inductive counterpart of resistors in series. This calculator also accounts for mutual inductance (M) between two coils that are magnetically coupled — for example, wound on the same core — where the total either increases (series-aiding) or decreases (series-opposing) depending on how their magnetic fields interact.
How the calculation works
Enter each inductor's value and pick a common unit. With no coupling, the calculator sums L1, L2, and L3 directly. If L1 and L2 are magnetically coupled, enter their mutual inductance M and choose whether the windings are aiding (fields reinforce) or opposing (fields cancel). The tool then applies L_total = L1 + L2 + L3 ± 2M, using + for aiding and − for opposing, and reports the coupling coefficient k = M / √(L1 × L2), which must stay between 0 and 1 for any physically realizable pair of coils.
Common mistakes
- Assuming all series inductors just add: that's only true when there is no shared magnetic flux. Two coils wound on the same core or transformer leg need the ±2M correction.
- Mixing up aiding and opposing: series-aiding (fields reinforce, flux adds) increases total inductance; series-opposing (fields cancel) decreases it. Reversing one coil's leads flips which case applies.
- Entering an impossible mutual inductance: M can never exceed √(L1 × L2) — that would imply a coupling coefficient greater than 1, which has no physical meaning.
Real-world applications
- Combining standard inductors on a breadboard or PCB to reach a total inductance value that isn't available off the shelf.
- Modeling transformer leakage inductance, where two windings on a shared core are coupled and the aiding/opposing sign matters.
- Designing filter chokes and crossover networks in audio and RF circuits, where series inductance sets the cutoff frequency.
- Estimating total loop inductance in wiring harnesses or PCB traces routed close together.
Frequently Asked Questions
How do you calculate total inductance for inductors in series?
Add the individual inductances directly: L_total = L1 + L2 + L3 + ... + Ln, as long as none of the inductors share a magnetic field. For example, three inductors of 10 mH, 15 mH, and 5 mH in series give a total of 30 mH.
Why are inductors in series different from resistors in series?
The addition rule looks the same (L_total = the sum of each L, just like R_total = the sum of each R), but inductors can also interact through mutual inductance if their magnetic fields overlap — resistors have no equivalent effect. When two coupled coils are in series, the total becomes L1 + L2 ± 2M instead of just L1 + L2.
What is the difference between series-aiding and series-opposing inductors?
In series-aiding, the coils are connected so their magnetic fields reinforce each other, adding 2M to the sum (L_total = L1 + L2 + 2M). In series-opposing, the fields cancel, subtracting 2M (L_total = L1 + L2 − 2M). Swapping the connection at either coil's terminals switches between the two cases.
What is the maximum possible mutual inductance between two coils?
Mutual inductance cannot exceed the geometric mean of the two inductances: M ≤ √(L1 × L2). This corresponds to a coupling coefficient k = M/√(L1×L2) of at most 1 (perfect coupling); real-world coils typically have k well below 1 unless they share a tightly wound common core.
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
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General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |