Solenoid Magnetic Flux Density (Tesla) & Air-Core Coil Inductance Calculator

Compute solenoid magnetic field B = μ₀μrNI/L and inductance L = μ₀μrN²A/L.

Internal Magnetic Flux Density (B)
11.78 mT
Solenoid Inductance (L) 481.91 μH
Magnetic Field in Gauss 117.81 Gauss
Magnetomotive Force (N·I) 750 A·turns
Inputs
turns
Total number of wire turns wound on the solenoid.
mm
Solenoid axial winding length in millimeters.
mm
Solenoid mean diameter in millimeters.
A
Excitation current flowing through the winding in Amperes.
μ_r
Core relative magnetic permeability μ_r (1.0 air core).
Results & Graph
Internal Magnetic Flux Density (B)
11.78 mT
Solenoid Inductance (L)
481.91 μH
Magnetic Field in Gauss
117.81 Gauss
Magnetomotive Force (N·I)
750 A·turns

Internal Magnetic Flux Density (B)

Graph 1 • Number Of Turns N Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 mT 9.5 mT 19.1 mT 50%: 5.89 mT 5.9 50% 75%: 8.84 mT 8.8 75% 100%: 11.78 mT 11.8 100% 125%: 14.73 mT 14.7 125% 150%: 17.67 mT 17.7 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Internal Magnetic Flux Density (B) 11.78 mT Solenoid Inductance (L) 481.91 μH Magnetic Field in Gauss 117.81 Gauss Magnetomotive Force (N·I) 750 A·turns
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Internal Magnetic Flux Density (B)11.78 mTSolenoid Inductance (L)481.91 μHMagnetic Field in Gauss117.81 GaussMagnetomotive Force (N·I)750 A·turns
Summary: A 250-turn solenoid (80 mm long, 25 mm diameter) at 3 A generates 11.78 mT (117.8 Gauss) and has inductance 481.91 μH.
Summary: A 250-turn solenoid (80 mm long, 25 mm diameter) at 3 A generates 11.78 mT (117.8 Gauss) and has inductance 481.91 μH.
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Formula & Mathematical Methodology: Solenoid Flux & Inductance Physics & Engineering Equation

BTesla = μ₀ × μr × N × I / Length
LHenries = μ₀ × μr × N² × Area / Length
B_Tesla = μ₀ × μ_r × N × I / Length; L_Henries = μ₀ × μ_r × N² × Area / Length
  • numberOfTurnsN: Number Of Turns N (turns)
  • coilLengthMm: Coil Length Mm (mm)
  • coilDiameterMm: Coil Diameter Mm (mm)
  • currentAmps: Current Amps (A)
  • relativePermeabilityMur: Relative Permeability Mur (μ_r)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Solenoid Flux & Inductance

Compute solenoid magnetic field B = μ₀μrNI/L and inductance L = μ₀μrN²A/L.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: B_Tesla = μ₀ × μ_r × N × I / Length; L_Henries = μ₀ × μ_r × N² × Area / Length.
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Solenoid Flux & Inductance via B_Tesla = μ₀ × μ_r × N × I / Length; L_Henries = μ₀ × μ_r × N² × Area / Length.

Frequently Asked Questions

What equation powers the Solenoid Magnetic Flux Density (Tesla) & Air-Core Coil Inductance Calculator?

It evaluates B_Tesla = μ₀ × μ_r × N × I / Length; L_Henries = μ₀ × μ_r × N² × Area / Length using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Electrical & RF Engineering

Solenoid Magnetic Flux Density (Tesla) & Air-Core Coil Inductance Calculator: inputs, method, and how to read the result

Compute solenoid magnetic field B = μ₀μrNI/L and inductance L = μ₀μrN²A/L.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Number Of Turns N: Total number of wire turns wound on the solenoid.
  • Coil Length Mm: Solenoid axial winding length in millimeters.
  • Coil Diameter Mm: Solenoid mean diameter in millimeters.
  • Current Amps: Excitation current flowing through the winding in Amperes.

What the calculation includes

With the default values shown, Internal Magnetic Flux Density (B) is 11.78 mT. The calculation follows Solenoid Flux & Inductance Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Number Of Turns N from 250 turns to 275 turns changes Internal Magnetic Flux Density (B) from 11.78 mT to 12.96 mT. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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