Estimate field strength for coils and experiments. Switch between center and on-axis calculations instantly today. Use consistent units, then save outputs in seconds easily.
This calculator provides two commonly used solenoid magnetic-field models. Choose the one that best matches your geometry and measurement location.
| Model | I (A) | N | L (m) | µr | R (m) | x (m) | B (T) |
|---|---|---|---|---|---|---|---|
| Ideal | 2.00000 | 800 | 0.400000 | 1.00000 | 0.0200000 | 0 | 0.005026548 |
| Finite | 1.50000 | 1200 | 0.300000 | 1.00000 | 0.0150000 | 0 | 0.002250721 |
| Finite | 3.00000 | 600 | 0.250000 | 200.000 | 0.0200000 | 0.0500000 | 0.4432890 |
Values are illustrative and depend on winding density, core material, and measurement location.
This tool estimates magnetic flux density B produced by a current‑carrying solenoid. It supports an ideal “long solenoid” approximation and a geometry‑aware finite, on‑axis model. Outputs appear in tesla, millitesla, microtesla, and gauss, making it easy to match lab sensors and datasheets.
Field magnitude scales with current I, turns N, and inverse length 1/L. For example, doubling I doubles B, and doubling N doubles B. Shorter coils have higher turns‑per‑meter n = N/L, increasing the central field.
The ideal model uses B = μ0 μr (N/L) I. It works best when the solenoid is long compared with its radius and you care about the field near the center. In that region, edge effects are small and the field is close to uniform.
The finite model estimates B(x) on the solenoid axis using coil radius R and position x measured from the center. It predicts reduced field near the ends and a smooth transition outside the winding. This helps when your sensor sits off‑center or you are mapping a profile.
Many bench solenoids produce microtesla to tens of millitesla, depending on geometry and current. Earth’s magnetic field is roughly tens of microtesla, so readings near that level may be dominated by background unless you shield or subtract it. Small electromagnets with iron cores can exceed 0.1 T at modest currents.
The factor μr approximates how a magnetic core concentrates flux. Air‑core coils use μr ≈ 1. Ferromagnetic materials can have much larger effective values, but the relationship is not constant because of saturation and hysteresis. Treat μr as an engineering estimate unless you have measured data.
Always convert length and radius to meters internally, then interpret results with your sensor’s range. Hall probes often read in mT or G, while magnetometers may read in µT. Uncertainty comes from winding non‑uniformity, temperature‑dependent resistance (changing current), and fringe fields near edges.
Use the ideal model for quick sizing of coils, power supplies, and safety margins. Use the finite model to plan sensor placement, estimate gradients, and compare against measured axial scans. The CSV and PDF exports support lab notebooks, reports, and repeatable parameter sweeps.
Use the ideal model for long coils and center measurements. Use the finite model when coil radius matters or your sensor is near an end or at a specific axial position.
x is the distance along the axis measured from the solenoid’s center. Set x = 0 for the center. Positive or negative values move toward opposite ends, changing the predicted on‑axis field.
Edge effects occur because the winding does not extend infinitely. Magnetic field lines spread outward near the coil ends, so the axial component becomes smaller than the central, nearly uniform region.
For air‑core coils, use μr = 1. For cores, start with a typical datasheet value, then refine using measurement. Effective μr depends on geometry, gaps, and saturation, so treat it as approximate.
No. The finite expression here is for the solenoid axis only. Off‑axis fields require more advanced models or numerical methods. For quick checks, you can measure with a probe at the desired location.
Length, radius, and position accept m, cm, mm, in, and ft. Results are shown in tesla with automatic conversions to millitesla, microtesla, and gauss for convenient comparison.
Differences can come from non‑uniform winding, current ripple, nearby ferromagnetic objects, sensor calibration, and core saturation. Try measuring current directly, moving away from metal surfaces, and using the finite model when geometry is short.
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.