You're Building an RF Filter and Need to Know the Total Inductance of Your Coil Network
Inductors store energy in magnetic fields. Like capacitors, inductors combine in series and parallel, but the rules are opposite to capacitors and the same as resistors. Inductors in series add; inductors in parallel use reciprocal formulas. Understanding inductance combinations is essential for RF filters, LC circuits, power supplies, and impedance matching networks.
What This Calculator Does
This calculator computes total inductance for inductors arranged in series, parallel, or combinations. You provide individual inductor values, and it instantly calculates the total inductance. It also works in reverse: if you need a specific total inductance and know some component values, it can find the missing inductor. It handles multiple units (henries, millihenries, microhenries, nanohenries) and shows practical example combinations.
How to Use This Calculator
Series Inductors: Enter the values of inductors connected end-to-end (one after another). The calculator shows the total as a simple sum. Series inductors add directly.
Parallel Inductors: Enter the values of inductors connected with their terminals together. The calculator shows the total using the reciprocal formula.
Mixed Series/Parallel: For complex circuits, enter groups of series inductors (calculating their total), then combine those totals in parallel (or vice versa).
All values can be in henries (H), millihenries (mH), microhenries (µH), or nanohenries (nH). The calculator converts automatically.
The Formula Behind the Math
For inductors in series (like resistors in series):
L_total = L₁ + L₂ + L₃ + ...
Inductances simply add. This is because inductors in series have their magnetic fields add together (assuming they're not magnetically coupled).
For inductors in parallel (like resistors in parallel):
1 / L_total = 1 / L₁ + 1 / L₂ + 1 / L₃ + ...
Or equivalently:
L_total = 1 / (1/L₁ + 1/L₂ + 1/L₃ + ...)
For two inductors in parallel:
L_total = (L₁ × L₂) / (L₁ + L₂)
Worked Example:
Design an RF circuit with three inductors: 10 µH, 20 µH, and 30 µH.
Series arrangement:
L_total = 10 + 20 + 30 = 60 µH
Series inductances add directly.
Parallel arrangement:
1/L_total = 1/10 + 1/20 + 1/30
1/L_total = 6/60 + 3/60 + 2/60 = 11/60
L_total = 60/11 ≈ 5.45 µH
The parallel total is smaller than any individual inductor.
Series-Parallel (two groups in parallel):
Group 1: 10 µH and 20 µH in series = 10 + 20 = 30 µH
Group 2: 30 µH alone
Total: 1 / (1/30 + 1/30) = 1 / (2/30) = 15 µH
Our calculator does all of this instantly, but now you understand exactly what it's computing.
Resonant Circuits (LC Circuits)
An inductor and capacitor form a resonant circuit. The resonant frequency is:
f₀ = 1 / (2π × √(L × C))
At resonance, the inductive reactance (X_L = 2πfL) equals the capacitive reactance (X_C = 1/(2πfC)), and they cancel. The circuit has minimum impedance for series circuits or maximum for parallel circuits. Radio receivers use LC circuits to select specific broadcast frequencies. By varying L or C, you tune the frequency. Larger L or C → lower frequency. Smaller L or C → higher frequency.
RF Filters and Impedance Matching
In RF (radio frequency) circuits, inductors and capacitors form filters that pass certain frequencies and block others. An inductor-capacitor network can match the impedance of one circuit to another, maximizing power transfer. The exact combination and values depend on the target frequency and impedances. Network analyzers measure the response to verify design.
Power Supply Circuits
Inductors in power supplies (especially switching regulators) store energy during part of the switching cycle and release it during another part. This smooths current and reduces noise. Multiple inductors can be combined to achieve desired inductance while distributing current (parallel inductors in parallel windings). Proper inductance ensures smooth output voltage and current.
Magnetic Coupling and Transformers
Real inductors placed near each other are magnetically coupled: the magnetic field of one induces current in the other. This coupling is often undesired (interference) but is intentionally used in transformers. A transformer consists of two inductors wound on the same core, with coupling coefficient k close to 1. The transformer ratio is the square root of the inductance ratio.
Tips and Things to Watch Out For
Series and parallel rules are the same for inductors and resistors (opposite to capacitors). Series adds, parallel uses reciprocals. This is a critical point to remember when designing circuits.
Magnetic coupling between inductors affects the formula. If two inductors are in close proximity, their magnetic fields interact (mutual inductance). The total inductance is not simply the sum or reciprocal-you must account for coupling. The more closely wound they are, the stronger the coupling effect.
Inductor DC resistance. Real inductors have some resistance in the coil wire. This DC resistance acts like a series resistor and affects circuit performance. Higher frequency or more turns increases resistance. Litz wire (many small strands insulated individually) reduces this in RF coils.
Frequency-dependent inductance. At very high frequencies, parasite effects (capacitance between turns, skin effect in the conductor) can change inductance. For precise RF work, inductance must be measured at the operating frequency.
Core material affects inductance. Air-core inductors have lower inductance but better linearity. Iron-core or ferrite-core inductors have higher inductance and different frequency responses. Core saturation at high currents reduces inductance nonlinearly.
Frequently Asked Questions
Why do inductors in series add while capacitors in series use reciprocals?
Inductors in series have their magnetic fields add (voltage divides). Capacitors in series have their charge the same but voltages divide. The voltage dividing in capacitors is why reciprocals apply. The opposite effect in inductors causes them to add like resistors.
What's the relationship between inductance and frequency?
Inductive reactance is X_L = 2πfL. Higher frequency or higher inductance means higher reactance (more opposition to current). Inductors block high frequencies and pass low frequencies.
How do I calculate the inductance of a coil?
For a cylindrical air-core solenoid: L = µ₀ × N² × A / l, where N is turns, A is cross-sectional area, l is length, and µ₀ is permeability of free space (4π × 10⁻⁷). For more complex shapes or cores, use an online calculator or measure with an LCR meter.
What's mutual inductance?
When two inductors are magnetically coupled (close together), the changing current in one induces voltage in the other. This mutual inductance is M = k × √(L₁ × L₂), where k is the coupling coefficient (0 to 1). Transformers use k ≈ 1 (tight coupling).
What happens when you open or close a circuit with an inductor?
Inductors oppose changes in current. When a circuit is closed, current ramps up, not instantly. When opened, the inductor tries to maintain current, creating a voltage spike (back-EMF). This can damage components. Diodes or snubber circuits protect against these spikes.
How is inductance related to energy storage?
Energy stored in an inductor is E = ½LI². Larger inductance or higher current means more stored energy. When the circuit is suddenly interrupted, this energy is released, potentially as sparks or voltage spikes.
Related Calculators
Use our Capacitor Calculator to design LC resonant circuits that depend on both capacitor and inductor values. The Ohm's Law Calculator helps analyze RL circuits and determine time constants. The Wavelength Calculator helps with RF circuits and resonant frequencies. For more electrical concepts, explore our Decibel and Resistor Color Code Calculators.