Solenoid Inductance Calculator
Calculate coil inductance, magnetic field strength, and stored energy.
About solenoid inductance
A solenoid is a helical coil that stores energy in a magnetic field when electric current flows through its turns. For a long, tightly wound coil whose length is large compared with its diameter, inductance is approximated by L = μ₀μᵣN²A/l. In this expression, μ₀ is the permeability of free space, μᵣ is the core's relative permeability, N is the number of turns, A is the circular cross-sectional area, and l is the coil length. This calculator derives area from the entered diameter and reports inductance in henries. The same geometry determines the approximate magnetic flux density inside the solenoid: B = μ₀μᵣNI/l. More turns, more current, or a core with higher permeability increases the field, while a longer winding reduces it. Once inductance is known, the ideal energy stored by the field is U = ½LI². These relationships are useful when estimating electromagnets, relays, actuators, laboratory coils, and introductory inductor designs. The long-solenoid equation is an engineering approximation. Real coils have fringing fields near their ends, winding gaps, wire resistance, parasitic capacitance, and frequency-dependent core losses. Ferromagnetic permeability also changes with field strength and can collapse near magnetic saturation. For short coils, high-frequency circuits, precision filters, or designs operating near saturation, use measured core data and a more detailed field model. Enter all dimensions in metres and current in amperes. Use relative permeability 1 for air, vacuum, and approximately non-magnetic cores. A manufacturer may provide an effective permeability for a ferrite or powdered-iron core; that effective value is generally more useful than a generic material maximum. The output is best treated as an ideal baseline that supports comparison and early design decisions, not as a replacement for prototype measurement. Keep units consistent because centimetres or millimetres entered as metres can change the result by orders of magnitude. Also confirm whether a stated diameter refers to the magnetic core, winding mean, or outside coil dimension. Careful measurement makes comparisons between candidate geometries much more meaningful.
Solenoid inductance examples
| Inputs | Results | Use |
|---|---|---|
| l 0.10 m, d 0.02 m, N 500, I 2 A, μᵣ 1 | L 0.987 mH, B 12.57 mT | Air-core laboratory coil |
| l 0.20 m, d 0.04 m, N 1000, I 1 A, μᵣ 100 | L 0.790 H, B 0.628 T | Idealized magnetic core |
| l 0.05 m, d 0.01 m, N 200, I 0.5 A, μᵣ 1 | L 78.96 μH, B 2.513 mT | Small air-core coil |
How to calculate solenoid inductance
- Measure the wound coil length and outside magnetic diameter in metres.
- Enter the total turn count and operating current.
- Use 1 for an air core or enter the core's effective relative permeability.
- Select Calculate and review inductance, field strength, and stored energy.
Frequently asked questions
What is solenoid inductance?
Inductance describes how strongly a coil opposes a change in current by storing magnetic energy. Its SI unit is the henry.
Why does the number of turns get squared?
Each turn contributes magnetic flux and links flux produced by the other turns. That combined linkage makes ideal inductance proportional to N squared.
What relative permeability should I use for air?
Use a relative permeability of 1 for an air-core solenoid. Vacuum is also exactly 1, while ordinary non-magnetic materials are very close.
Does this include wire resistance?
No, the model calculates ideal magnetic properties only. Copper resistance and heating require wire length, gauge, and temperature data.
Is the formula accurate for short coils?
Accuracy decreases when coil length is comparable to its diameter because end fringing becomes important. A correction factor or numerical field model is preferable for short coils.