Inductance Calculator — Instantly calculate inductance, number of turns, core permeability, or coil length for solenoids and air-core coils. Enhanced, interactive design. Mobile-optimized, SEO-rich, and privacy-first. All calculations run instantly in your browser—no data leaves your device.
How to Use the Inductance Calculator
- Select Calculation Type
Choose what you want to calculate: Inductance (L), Number of Turns (N), Coil Length (l), or Core Permeability (μ).
- Enter Your Data
Input the required values for your chosen calculation. Ensure you use standard SI units: Henries (H), meters (m), and square meters (m²).
- See Real-Time Results
The calculated result, the specific formula used, and a clear explanation will appear instantly in the result card as you type.
- Copy or Clear
Use the “Copy” button to save the full result for your notes, or click “Clear” to reset the calculator for a new problem.
Advantages & Limitations of the Inductance Calculator
Advantages
- Comprehensive: Solves for all four key variables of the solenoid inductance formula.
- Instantaneous: Results appear in real-time as you input data.
- Educational: Always displays the active formula, reinforcing the physics concepts.
- 100% Private: All calculations are client-side; no data is sent or stored.
- Fully Responsive: A clean, modern interface that works flawlessly on any device.
Limitations
- Solenoid Formula Only: Specifically designed for straight, single-layer solenoids. Not applicable for toroids or other coil shapes.
- SI Units Required: Does not auto-convert from common units like millimeters (mm) or microhenries (µH).
- Ideal Conditions: Assumes an ideal solenoid where the length is significantly greater than the radius.
- No Advanced Magnetics: Does not calculate magnetic field strength (B) or inductive reactance (XL).
The Ultimate Inductance Calculator: A Guide to Coils, Permeability, and Magnetic Fields
Alongside resistors and capacitors, inductors are one of the three fundamental passive components in electronics. An inductor is essentially a coil of wire, and its defining property is inductance. This property describes the tendency of the electrical conductor to oppose a change in the electric current flowing through it. This opposition is a result of the magnetic field that is generated by the current.
To make the design and analysis of these crucial components straightforward, we have developed a powerful and versatile Inductance Calculator. This tool is an essential resource for electronics students, engineers, amateur radio enthusiasts, and DIY hobbyists. It’s built around the fundamental formula for the inductance of a solenoid, allowing you to instantly solve not just for inductance, but also for the number of turns, coil length, or core permeability. This comprehensive guide will delve into the physics of inductance, dissect the key formula, and explore the many practical applications where this calculator is an indispensable aid.
What is Inductance? The Core Concepts
Whenever an electric current flows through a wire, it generates a magnetic field around it. If you wind that wire into a coil, you concentrate this magnetic field in the center, or core, of the coil. If the current changes, the magnetic field also changes. According to Faraday’s law of induction, a changing magnetic field induces a voltage (or electromotive force, EMF) in the coil.
Crucially, Lenz’s law dictates that this induced voltage will be in a direction that *opposes* the initial change in current. This opposition is what we call inductance (L).
- Inductance is the property of a circuit element that opposes changes in current.
- It is measured in Henries (H), named after the American scientist Joseph Henry.
- One Henry is the inductance in which a change of one Ampere per second results in an induced voltage of one Volt.
- Like the Farad, the Henry is a large unit, so inductance is commonly measured in millihenries (mH, 10⁻³ H) and microhenries (µH, 10⁻⁶ H).
The Solenoid Inductance Formula: The Heart of the Calculator
While inductance is a property of any conductor, it is most pronounced and predictable in a component specifically designed to have it: an inductor, or coil. The most common form is the solenoid, which is a cylindrical coil of wire. The formula for the inductance of an ideal solenoid is the foundation of our Inductance Calculator.
L = (μ * N² * A) / l
Let’s break down each component of this crucial equation:
- Inductance (L): The value we want to find, in Henries (H).
- Permeability (μ): This is a measure of how easily a magnetic field can be established in the material inside the coil (the “core”). It is measured in Henries per meter (H/m). Permeability is often expressed as `μ = μ₀ * μᵣ`:
- μ₀ is the permeability of free space, a universal constant equal to approximately 1.2566 × 10⁻⁶ H/m. Our calculator defaults to this “air core” value.
- μᵣ is the relative permeability of the core material. For air or a vacuum, it’s 1. For ferromagnetic materials like iron, it can be in the thousands, which dramatically increases the inductance.
- Number of Turns (N): This is the total number of times the wire is wrapped around the core. Inductance is proportional to the *square* of the turns, making this a very influential factor. Doubling the turns quadruples the inductance.
- Cross-Sectional Area (A): This is the area of the coil’s core, in square meters (m²). A wider coil has a higher inductance.
- Coil Length (l): This is the length of the coil, in meters (m). A longer coil (for the same number of turns) has a lower inductance because the magnetic field is less concentrated.
A Multi-Functional Design Tool
The true power of this calculator lies in its ability to be a design tool. By rearranging the core formula, it allows you to solve for any of the key physical parameters required to achieve a desired inductance.
- Solving for Number of Turns (N = √((L * l) / (μ * A))): This is perhaps the most common use case. If you need an inductor of a specific value (L) and have a core of a certain size (A, l) and material (μ), this mode tells you exactly how many times to wind the wire.
- Solving for Coil Length (l = (μ * N² * A) / L): If you have a set number of turns and want to achieve a specific inductance, this mode tells you how long the coil needs to be.
- Solving for Permeability (μ = (L * l) / (N² * A)): This mode allows you to work backward. If you have an unknown core material, you can wind a coil of known dimensions (N, A, l), measure its inductance (L), and then use the calculator to determine the permeability of the core.
Practical Applications and Use Cases
Inductors are everywhere in electronics, and this calculator is essential for anyone working with them.
From the simplest filters to the most complex power systems, the ability to accurately determine the properties of a coil is fundamental. The Inductance Calculator provides the power to design, analyze, and understand these essential components with ease and precision.
Frequently Asked Questions About the Inductance Calculator
Permeability is a material’s ability to support the formation of a magnetic field. It is often given as a relative permeability (μᵣ), which is a factor relative to the permeability of a vacuum (μ₀ ≈ 1.257 × 10⁻⁶ H/m). To get the absolute permeability (μ) for the calculator, you must multiply the two: `μ = μ₀ * μᵣ`. For an air-core coil, you can use the default value, as the relative permeability of air is approximately 1.
Not directly in this formula. The ideal solenoid formula assumes a thin sheet of current and doesn’t account for wire diameter. In the real world, a thicker wire will slightly increase the coil’s overall diameter (affecting Area) and limit how many turns you can fit into a given length, but the formula itself does not have a term for wire gauge.
This calculator is specifically for straight solenoids. A toroid (a donut-shaped coil) is more efficient at containing its magnetic field and uses a different formula: `L ≈ (μ * N² * A) / (2 * π * r)`, where `r` is the major radius of the toroid. This tool should not be used for toroidal inductors.
The formula used here is for an ideal solenoid, which assumes the length of the coil is significantly larger than its radius (typically length > 10 × radius). This ensures that the magnetic field inside is uniform and “end effects” can be ignored. For short, wide coils, more complex formulas are needed to get a highly accurate result, but this calculator provides an excellent approximation for most common inductors.
You must convert all values to their base SI units before entering them. The easiest way is using scientific notation:
• 1 µH = 1e-6 H
• 1 mm = 0.001 m
• 1 cm² = 0.0001 m²
Forgetting to convert units is the most common source of error when using this formula.
Yes, 100%. This is a client-side tool, which means all calculations happen on your computer, within your web browser. No data you enter is ever sent to, processed by, or stored on our servers. Your privacy is fully guaranteed.
Absolutely. This is a completely free resource provided for educational and practical purposes. There are no fees, subscriptions, or sign-ups required to use its full functionality.