Model magnetic fields inside solenoids for designs. Enter turns, length, radius, and relative permeability easily. See results above, then export with one click today.
This calculator uses the permeability of free space μ0 = 4π × 10-7 T·m/A and the relative permeability μr.
Notes: The long-solenoid model is best when L ≫ R and you are away from the ends. The finite model estimates axial field and is still an idealization.
| Model | I (A) | N | L (m) | R (m) | z (m) | μr | B (mT) |
|---|---|---|---|---|---|---|---|
| Long | 1.0 | 500 | 0.25 | — | — | 1.0 | 2.513 |
| Finite | 1.0 | 500 | 0.25 | 0.02 | 0.00 | 1.0 | 2.498 |
| Finite | 1.0 | 500 | 0.25 | 0.02 | 0.10 | 1.0 | 2.278 |
This tool estimates the magnetic flux density B produced by a solenoid using idealized electromagnetic models. Enter current, turns, and geometry to get B in Tesla, mT, μT, and Gauss. Many small coils land in the mT range at practical currents.
The long-solenoid approximation uses B = μ0 μr (N/L) I. It works best when L ≫ R and the point of interest is well inside the winding, away from both ends. It is ideal for quick sizing because it scales linearly with turns per meter and current.
Because real coils are finite, the field drops near the ends and changes with axial position. The finite model computes B(z) on the symmetry axis using radius R, length L, and position z from the coil center. It captures end effects better than the long model.
Length, radius, and position accept common units and are converted internally to meters. Keep inputs consistent with your physical coil and avoid unrealistic combinations, such as very short coils with huge turn counts. When comparing to a Hall sensor, record the probe location carefully, since small offsets matter.
The factor μr approximates how a core changes magnetic response. Air is near μr≈1, while ferromagnetic materials can be much higher at low fields. In practice, cores saturate (often around ~1–2 T), so large μr inputs can overpredict at high current.
Engineering work commonly uses mT, while background fields are often μT. Earth’s magnetic field is roughly 25–65 μT, so many coils exceed it near the winding. Gauss still appears in some references: 1 T = 10,000 G. Reporting multiple units helps match instruments.
Magnetic field increases with current, but resistive heating rises as P = I^2R. For higher current, check wire gauge, coil resistance, cooling, and duty cycle. Strong fields can attract steel objects and disturb sensitive sensors. Ramp current gradually and verify temperature rise.
Solenoids are used in relays, actuators, valves, magnetic lenses, and lab fixtures. Validate by measuring at the coil center with a calibrated Hall sensor, then repeat at a known offset z. If results differ, verify dimensions, sensor alignment, current accuracy, and nearby ferromagnetic materials.
Use the long model for quick inside-field estimates when the coil is much longer than its radius and you are away from the ends. Use the finite model when you need the axial field near ends or at a specific position z.
μr approximates how a core material changes the magnetic response compared with free space. Air is about 1. Ferromagnetic materials can be much larger at low fields, but effective μr drops as the core approaches saturation.
Using the center as z=0 makes the finite-solenoid formula symmetric and reduces sign mistakes. Positive and negative z positions yield the same magnitude on-axis for a centered coil, so you can focus on distance from the center.
Not directly. This calculator covers the long-solenoid inside estimate and the finite on-axis field. Off-axis fields need numerical integration or specialized solvers. For quick approximations, sample several near-axis points and compare to your measurements.
Common causes include inaccurate coil dimensions, sensor misalignment, current measurement error, and end effects when using the long model. Nearby ferromagnetic objects or a core also change the field. Use the finite model and measure the exact sensor position z.
The calculator has no physical current limit, but your coil does. Determine safe current from wire gauge, coil resistance, insulation, and cooling. Check temperature rise during operation and consider duty cycle. Heating grows with I^2, so increases can become severe quickly.
Compare your result to Earth’s field (roughly 25–65 μT) and typical small solenoids (often a few mT at moderate currents). Measure at the center with a Hall sensor, then at one offset distance to confirm the trend with z.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.