Inductance Calculator
Compute inductance for common coil geometries (solenoid or toroid) or solve for required turns.
Calculation Steps
Practical Guide
Inductance Calculator: Solenoids & Toroids Made Simple
This guide explains what the inductance calculator is doing under the hood, how to choose the right coil model, and how to sanity-check results. You’ll see the exact equations used for solenoids and toroids, what assumptions they rely on, and how small design choices (turns, core, geometry) move inductance by a lot.
Quick Start
If you’re here from Google, you probably want a fast, trustworthy inductance number. Follow these steps to avoid the most common errors.
- 1 Select what you want to solve for: Inductance (L) or Number of turns (N).
- 2 Choose your coil type: Solenoid (long straight coil) or Toroid (ring core).
- 3 Enter the core’s relative permeability \( \mu_r \). Use \( \mu_r \approx 1 \) for air-core, or a datasheet value for ferrite/iron.
-
4
Provide the geometry:
- Solenoid: coil radius \(r\) and coil length \(\ell\).
- Toroid: core cross-section area \(A\) and mean path length \(\ell_m\).
- 5 If solving for \(L\), enter the number of turns \(N\). If solving for \(N\), enter your target inductance \(L\).
- 6 Check the result units (H, mH, or μH) and review quick stats like area and inductance per turn².
- 7 Sanity-check: does the magnitude match typical parts? (Rules of thumb below.)
Tip: Inductance scales with \(N^2\). If your result looks off by ~4×, you may have doubled/halved turns somewhere.
Watch the assumptions: The solenoid formula assumes a “long” coil (length several times diameter). Short coils can read high in theory but lower in practice due to fringing.
Choosing Your Method
Inductance depends heavily on geometry and magnetic path. The calculator offers two standard models—use the one that matches your field path.
Method A — Long Solenoid (straight coil)
Use this when your coil is wound on a straight bobbin, tube, or air former, and the magnetic field is mostly inside the coil.
- Great for air-core inductors and straight-core chokes.
- Easy to estimate quickly from radius & length.
- Matches many introductory EM and circuits problems.
- Assumes uniform internal field; short coils & wide spacing reduce accuracy.
- Ignores leakage/fringing and winding thickness.
Method B — Toroid (ring core)
Use this when the field follows a closed loop through a doughnut-shaped core (ferrite/iron powder toroid).
- Very accurate for toroids because flux is well-contained.
- Low EMI and leakage; common in power electronics.
- Datasheets often provide \(A\) and \(\ell_m\).
- Requires mean path length, not just outer diameter.
- Core saturation and gaps need extra modeling.
Which one do I pick? If your winding looks like a spring on a straight tube → solenoid. If it wraps around a ring core → toroid.
What Moves the Number the Most
These are the dominant “levers” in inductance. Changing any one of them can shift results by orders of magnitude.
Inductance scales as \(N^2\). Doubling turns multiplies \(L\) by 4. Halving turns cuts \(L\) to 1/4.
Air-core coils have \(\mu_r \approx 1\). Ferrite may be 200–5000. A high-\(\mu_r\) core is the fastest way to raise \(L\).
Larger coil/core area increases flux linkage. For solenoids, \(A=\pi r^2\), so radius has a squared effect.
Longer path reduces inductance (flux spreads out). Shortening a solenoid while keeping turns the same increases \(L\), but also increases fringing.
Thick multi-layer windings and wide turn spacing lower effective coupling. The calculator assumes tight winding.
If current drives the core toward saturation, effective \(\mu_r\) drops and inductance falls. Air gaps intentionally lower \(L\) but raise linear current range.
Worked Examples
Below are two realistic, fully worked cases that match the calculator’s equations. You can plug these values into the tool to verify the same results.
Example 1 — Air-Core Solenoid, Solve for Inductance
- Coil type: Solenoid
- Turns: \(N = 200\)
- Radius: \(r = 0.01\ \text{m}\) (1 cm)
- Length: \(\ell = 0.05\ \text{m}\) (5 cm)
- Relative permeability: \(\mu_r = 1\) (air)
Interpretation: This magnitude is typical for a small air-core choke. If you need several mH without adding many turns, you’ll almost always need a magnetic core.
Example 2 — Ferrite Toroid, Solve for Turns
- Coil type: Toroid
- Target inductance: \(L = 2.0\ \text{mH} = 0.002\ \text{H}\)
- Core area: \(A = 1.5\times10^{-4}\ \text{m}^2\)
- Mean path length: \(\ell_m = 0.12\ \text{m}\)
- Relative permeability: \(\mu_r = 2000\)
Interpretation: A high-\(\mu_r\) toroid needs far fewer turns for the same \(L\). Always check saturation current in the datasheet—2 mH at low current can drop at high current if the core saturates.
Common Layouts & Variations
Real inductors come in many shapes and materials. The calculator focuses on the two most common analytical models; use this table to map your real build to the right inputs and expectations.
| Configuration | Typical Use Case | How to Model | Pros / Cons |
|---|---|---|---|
| Air-core solenoid | RF inductors, sensors, low-loss coils | Solenoid with \(\mu_r=1\) | Pros: no saturation, low hysteresis. Cons: larger size for same \(L\). |
| Ferrite rod / straight core | Chokes, small signal inductors | Solenoid with datasheet \(\mu_r\) | Pros: large \(L\) boost. Cons: \(\mu_r\) varies with frequency & bias. |
| Toroidal ferrite/iron powder | Power inductors, EMI filters | Toroid using \(A\) and \(\ell_m\) | Pros: tight flux, low EMI. Cons: winding is slower; can saturate. |
| Gapped core (toroid or E-core) | Energy storage inductors | Use lower effective \(\mu_r\) | Pros: higher linear current range. Cons: lower \(L\) per turn. |
| Short solenoid / pancake coil | Wireless power, coils near metal | Solenoid as a rough estimate | Pros: compact. Cons: fringing makes simple theory optimistic. |
Frequency matters: Datasheet \(\mu_r\) is not constant; ferrite permeability drops with frequency and DC bias. The calculator assumes a constant \(\mu_r\).
Specs, Logistics & Sanity Checks
The calculator gives a clean physics estimate. Before you commit to a design or order parts, verify these practical items.
Core Datasheet Must-Knows
- Material type (ferrite vs iron powder vs laminated steel)
- \(\mu_r\) at your operating frequency
- Effective area \(A_e\) and path length \(\ell_e\)
- Saturation flux density \(B_\text{sat}\)
- Loss curves vs frequency & temperature
Winding Realities
- Wire gauge and fill factor (space for turns)
- Single-layer vs multi-layer (multi-layer lowers accuracy)
- Spacing/insulation thickness between turns
- Skin & proximity effects at high frequency
- Lead length adds small inductance too
Sanity Check Ranges
Use these to see if your result is in the right ballpark:
- Small air-core coils: ~1–500 μH
- Ferrite toroids, tens of turns: ~0.5–20 mH
- Power inductors: choose \(L\) so ripple current meets spec
- If \(L\) changes a lot with current → saturation risk
If your calculated inductance seems too high for a given core size, check for a unit slip: area in cm² vs m² and length in cm vs m are the two most common mistakes.