Inductor Design Calculator
Calculate core inductance, number of turns, cross-sectional area, or magnetic path length using the standard magnetic circuit formula. Verify with detailed step-by-step calculations and realistic engineering charts.
⚡ Free Tool · No Signup · Instant Results
Inductor Design Calculator
Calculations are based on standard magnetic circuit formulas assuming ideal conditions. Actual results may vary due to core saturation, flux leakage, and tolerances.
The equation assumes a linear magnetic material and negligible air gap. Real inductors may vary due to core saturation and manufacturing tolerances.
How to Use Inductor Design Calculator
Designing an inductor using a magnetic core involves selecting the physical size, turns count, and core materials. This solver lets engineers design magnetic circuits quickly. Follow these step-by-step instructions to model your inductors:
- Step 1: Select the variable to calculate. Choose the target parameter from the top dropdown (Inductance, Turns, Core Area, or Path Length).
- Step 2: Enter permeability value. Input the absolute permeability (μ) of your selected core material in H/m.
- Step 3: Enter number of turns. Input the total turn count (N) wrapped around the magnetic core.
- Step 4: Enter core area. Input the cross-sectional core area (A) and choose between square meters (m²), square centimeters (cm²), or square millimeters (mm²).
- Step 5: Enter magnetic path length. Input the core's mean path length (l) and select the appropriate length unit (m, cm, mm).
- Step 6: Press Calculate. Click the Calculate button to resolve the equation.
- Step 7: Review results and unit conversions. Study the computed value and the converted formats displayed in the outputs.
How to Calculate Inductor Design Calculator
Determining the properties of magnetic circuits depends on how magnetic flux is guided through the core material. The core's geometry (cross-sectional area A and path length l) combined with its material permeability (μ) and winding turns (N) dictates the overall inductance. The core equations and parameters are explained below:
Magnetic Circuit Inductance Formula
Where the design variables represent:
- L: Inductance in Henries (H)
- μ: Absolute permeability of the core material in Henries per meter (H/m)
- N: Number of winding turns
- A: Cross-sectional area of the core in square meters (m²)
- l: Mean magnetic path length of the core in meters (m)
Step-by-Step Engineering Calculation Example
To demonstrate this formula, let's verify a design with these core parameters:
- Permeability (μ): 0.001 H/m
- Turns (N): 150 turns
- Core area (A): 2 cm2
- Magnetic path length (l): 10 cm
Step 1: Convert units to base SI units
Convert area from square centimeters to square meters:
A = 2 cm2 = 2 × 10-4 m2 = 0.0002 m2
Convert length from centimeters to meters:
l = 10 cm = 0.1 m
Step 2: Apply the inductance formula
L = (μ × N2 × A) ÷ l
L = (0.001 × 1502 × 2 × 10-4) ÷ 0.1
L = (0.001 × 22500 × 0.0002) ÷ 0.1
L = 0.0045 ÷ 0.1
L = 0.045 H
Step 3: Convert the final inductance into common units
L = 0.045 H
L = 0.045 × 1,000 = 45 mH
L = 0.045 × 1,000,000 = 45000 μH
Final Answer:
The total inductance is exactly 0.045 H (which is equal to 45 mH or 45000 μH).
Real-Life Scenario: Power Supply Filter Inductor
In switch-mode power supplies (SMPS), a filter inductor is used to smooth out high-frequency current ripple. Suppose an engineer is designing a buck converter filter inductor targeting an inductance of 45 mH to filter a 100 kHz switching ripple. By selecting a high-permeability manganese-zinc (MnZn) ferrite core with a permeability of 0.001 H/m, a core area of 2 cm² (2 × 10-4 m²), and wrapping 150 turns of copper wire, the designer achieves the required 45 mH within a magnetic path length of exactly 10 cm (0.1 m). This matches our calculations and ensures low ripple currents in the power supply.
Inductor Design Calculator Chart
This reference chart displays pre-calculated inductance values across various turn counts, core areas, magnetic path lengths, and permeability levels. Winding and core dimensions are presented in standard electrical units for quick lookups.
| Turns (N) | Core Area (cm²) | Path Length (cm) | Permeability (H/m) | Inductance (mH) |
|---|---|---|---|---|
| 100 | 1.0 cm² | 5.0 cm | 0.0020 H/m | 40.00 mH |
| 150 | 1.5 cm² | 8.0 cm | 0.0010 H/m | 42.19 mH |
| 200 | 2.0 cm² | 10.0 cm | 0.0030 H/m | 240.00 mH |
| 50 | 0.5 cm² | 3.0 cm | 0.0015 H/m | 6.25 mH |
| 80 | 1.2 cm² | 6.0 cm | 0.0025 H/m | 32.00 mH |
| 120 | 2.5 cm² | 12.0 cm | 0.0008 H/m | 24.00 mH |
| 300 | 4.0 cm² | 15.0 cm | 0.0012 H/m | 288.00 mH |
| 250 | 3.0 cm² | 10.0 cm | 0.0022 H/m | 412.50 mH |
| 180 | 1.8 cm² | 9.0 cm | 0.0018 H/m | 116.64 mH |
| 500 | 5.0 cm² | 20.0 cm | 0.0005 H/m | 312.50 mH |
Note: All calculations in the table are rounded to two decimal places. Real-world values depend on core material properties, core saturation limits under bias current, and temperature characteristics.
Inductor Design Calculator Frequently Asked Questions
The primary formula used for designing an inductor is based on the magnetic circuit equation L = (μ × N² × A) / l. In this equation, L is the inductance in Henries, μ represents the absolute permeability of the core material in Henries per meter, N is the total number of wire turns, A is the core's cross-sectional area in square meters, and l is the magnetic path length in meters.
The number of turns required for an inductor depends on your target inductance, the permeability of the core material, the core's cross-sectional area, and its magnetic path length. It is calculated using the rearranged formula N = √((L × l) / (μ × A)). Increasing the number of turns increases the inductance quadratically, meaning doubling the turns yields four times the inductance.
Yes, the core material significantly affects inductance through its magnetic permeability (μ). Ferromagnetic core materials, such as ferrites, iron powder, and laminated steel, have much higher permeability than air or vacuum. By concentrating the magnetic flux lines inside the core, these materials can increase the inductance of a coil by thousands of times for the same physical size.
The standard SI unit for inductance is the Henry (H). Since one Henry is a very large amount of inductance for most electronic circuits, smaller sub-units are widely used. These include the millihenry (mH, representing one-thousandth of a Henry) and the microhenry (µH, representing one-millionth of a Henry). Inductor design equations require converting all these units to Henries.
The magnetic path length (l) of an inductor is the mean distance that the magnetic flux lines travel around the closed loop of the core. For simple geometries like a toroidal ring core, it is the circumference calculated at the mean diameter. For rectangular or E-cores, it is the sum of the center-line lengths of each leg of the magnetic circuit path.
Yes, this equation can theoretically be applied to air-core inductors by setting the permeability (μ) to the permeability of free space (μ₀ ≈ 1.257 × 10⁻⁶ H/m). However, because air-core inductors do not confine the magnetic flux within a solid core, significant flux leakage occurs, making empirical formulas like Wheeler's equation much more accurate for real-world air-core designs.