Magnetic Field of a Solenoid Calculator

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.

Choose ideal for long solenoids; finite for geometry-aware on-axis field.
Use 1 for air-core; higher for magnetic cores (approximate).
Needed only for the finite solenoid model.
x = 0 is coil center; positive toward one end.
Formula Used

This calculator provides two commonly used solenoid magnetic-field models. Choose the one that best matches your geometry and measurement location.

Ideal long solenoid (near center)
B = μ0 μr (N / L) I
Where μ0 = 4π×10−7 H/m, μr is relative permeability, N is turns, L is length (m), and I is current (A).
Finite solenoid (on-axis at position x)
B(x) = (μ0 μr N I / 2) · [ (x+L/2)/√(R²+(x+L/2)²) − (x−L/2)/√(R²+(x−L/2)²) ]
R is solenoid radius (m). x is axial position measured from the center (m). This model estimates the field along the axis of a uniformly wound coil.
How to Use This Calculator
  1. Select a model: ideal for long coils, finite for on-axis points.
  2. Enter current, turns, solenoid length, and relative permeability.
  3. If using the finite model, also enter radius and axial position.
  4. Press Calculate Magnetic Field to view results above the form.
  5. Use Download CSV or Download PDF to save outputs.
Example Data Table
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.

Article

1) What this solenoid field calculator delivers

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.

2) Inputs that control field strength

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.

3) Ideal long‑solenoid model and where it fits

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.

4) Finite solenoid model for axial positions

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.

5) Typical numbers to sanity‑check results

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.

6) The role of core material and relative permeability

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.

7) Units, measurement, and uncertainty

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.

8) Practical uses in design and experiments

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.

FAQs

1) Which model should I choose?

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.

2) What does x mean in the finite model?

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.

3) Why does the field drop near the ends?

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.

4) How do I pick a value for μr?

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.

5) Can this calculator predict off‑axis fields?

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.

6) What units are supported and how are results reported?

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.

7) Why are my measured values different from the estimate?

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.

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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.