Solenoid Force Calculator

The Solenoid Force Calculator computes electromagnetic pull force using Maxwell stress tensor (F = B²A/2µ₀) for solenoid actuators and electromagnets. Features interactive force-vs-gap SVG chart, coil design parameters, core material selection (soft iron, silicon steel, ferrite), saturation detection, and thermal rating. Free, no signup required.

Presets

Core Material

Coil Parameters

Number of Turns

Current (A)

Coil Length (m)

Coil Radius (m)

Core Cross-Section Area (m²)

Air Gap (mm)

Wire Gauge (AWG)

Duty Cycle (%)

🔥 High power dissipation! Consider duty cycle reduction.

Results

Holding Force

9.993 N (1.02 kgf)

Magnetic Field (B)

167.6 T

Magnetic Flux (Φ)

0.00005012 Wb

Flux Density

0.5012 T

MMF (Magnetomotive Force)

800 A·t

Total Reluctance

1.596e+7 A·t/Wb

Coil Resistance

3.056 Ω

Power Dissipation

12.22 W

Force vs. Air Gap

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What is a Solenoid Force Calculator?

A solenoid force calculator computes the electromagnetic pull force of solenoid actuators and electromagnets using the Maxwell stress tensor equation: F = B²A/(2µ₀), where B is the flux density in the air gap and A is the core cross-section area. The calculator accounts for core material permeability, magnetic circuit reluctance, and saturation effects. The interactive force-vs-gap chart shows how force varies non-linearly with air gap distance — a critical design parameter for relays, valves, locks, and actuators.

How to Use This Calculator

Enter coil parameters: number of turns, current, coil dimensions
Select a core material (soft iron, silicon steel, ferrite) or choose a preset application
Set the air gap distance to calculate the pull force at that gap
View the force-vs-gap curve to understand how force varies with stroke
Check for saturation and thermal warnings to ensure safe operating conditions

Frequently Asked Questions

How is solenoid pull force calculated?

Solenoid pull force is calculated using the Maxwell stress tensor: F = B²A/(2µ₀). First, compute the MMF (N×I), then the total reluctance of the magnetic circuit (core + air gap). The flux Φ = MMF/R gives the flux density B = Φ/A. Force depends on B² so it increases dramatically as the air gap closes.

Why does solenoid force increase as the air gap decreases?

The air gap has much higher reluctance than the core (µr ≈ 1 vs 5000). As the gap closes, total reluctance drops rapidly, increasing flux density. Since force depends on B², it follows an approximate 1/gap² relationship, creating the characteristic non-linear force-stroke curve.

What is magnetic saturation and how does it affect force?

Magnetic saturation occurs when the core material reaches its maximum flux density (e.g., 1.5 T for soft iron, 2.0 T for silicon steel). Beyond saturation, increasing current produces diminishing returns in flux and force. This calculator detects saturation and warns when B exceeds the material's limit.