Introduction

Solenoids are widely used in industrial automation, smart locks, medical devices, vending machines, automotive systems, and countless other applications. One of the most important parameters when designing or selecting a solenoid is its force output.

Engineers often ask:

• How much force can a solenoid generate?

• How do you calculate solenoid force?

• What factors affect electromagnetic force?

• How can force be increased without enlarging the solenoid?

This guide explains the principles behind solenoid force calculation, the key formulas involved, and practical considerations for custom solenoid design.

What Is Solenoid Force?

Solenoid force is the electromagnetic pulling or pushing force generated when electrical current flows through a coil.

When voltage is applied to a solenoid coil, an electromagnetic field is created. This magnetic field attracts the movable plunger (armature), producing mechanical motion.

The generated force depends on:

• Coil current

• Number of wire turns

• Core material

• Air gap

• Magnetic circuit design

• Stroke length

The force is usually measured in:

• Newtons (N)

• Pounds-force (lbf)

• Kilograms-force (kgf)

Unit Conversion

Basic Solenoid Force Formula

The theoretical force generated by a solenoid can be estimated using:

[
F = \frac{(N \times I)^2 \times \mu \times A}{2g^2}
]

Where:

From this formula we can observe:

Force increases when:

✓ More coil turns

✓ Higher current

✓ Larger magnetic area

✓ Better magnetic material

Force decreases when:

✗ Air gap increases

✗ Current decreases

✗ Poor magnetic materials are used

Why Air Gap Is Critical

The air gap has the largest influence on force.

Because force is inversely proportional to the square of the gap distance:

[
F \propto \frac{1}{g^2}
]

If the air gap doubles:

• Force becomes only 25%

If the gap triples:

• Force becomes only 11%

Example

This is why most solenoids generate their maximum force when the plunger is fully pulled in.

Step-by-Step Solenoid Force Calculation Example

Assume a custom tubular solenoid has:

• Coil turns (N) = 800

• Current (I) = 0.5 A

• Pole area (A) = 0.0001 m²

• Air gap (g) = 0.001 m

• Relative permeability (μ) ≈ 4π×10⁻⁷ × 1000

Step 1: Calculate Ampere Turns

[
NI = 800 \times 0.5
]

[
NI = 400
]

Step 2: Square the Result

[
(NI)^2 = 160000
]

Step 3: Apply Formula

Substituting all values into the force equation provides an estimated electromagnetic force.

Actual results vary due to:

• Magnetic saturation

• Eddy current losses

• Friction

• Manufacturing tolerances

Therefore, simulation and testing are always recommended.

Simplified Engineering Rule

For practical engineering projects, many designers use the following estimation method:

Small Solenoid

• Force: 1N – 10N

• Stroke: 1mm – 5mm

Medium Solenoid

• Force: 10N – 50N

• Stroke: 5mm – 15mm

Large Solenoid

• Force: 50N – 300N

• Stroke: 10mm – 30mm

Heavy-Duty Solenoid

• Force: 300N+

• Custom design required

Relationship Between Stroke and Force

One common mistake is assuming force remains constant throughout the stroke.

In reality:

As the plunger moves away from the core:

• Air gap increases

• Magnetic flux decreases

• Force drops significantly

Typical Force Curve

For this reason, engineers should specify:

• Starting force

• Holding force

• End-of-stroke force

When requesting a custom solenoid.

How to Increase Solenoid Force

If higher force is required, engineers can optimize several design parameters.

Increase Coil Turns

More turns generate a stronger magnetic field.

Benefits:

• Higher force

Trade-off:

• Increased resistance

• Larger coil size

Increase Current

According to the formula:

[
F \propto I^2
]

Doubling current can theoretically increase force fourfold.

Trade-off:

• Higher temperature rise

• Increased power consumption

Reduce Air Gap

Reducing the gap often provides the largest force improvement.

Benefits:

• Significant force increase

Trade-off:

• Limited stroke length

Improve Core Material

Common materials include:

• Low carbon steel

• Pure iron

• Silicon steel

• Specialized magnetic alloys

High-permeability materials improve magnetic efficiency.

Increase Pole Area

A larger magnetic contact area allows more magnetic flux.

Benefits:

• Higher force

Trade-off:

• Larger overall dimensions

Continuous Duty vs Intermittent Duty

Force calculations must consider duty cycle.

Continuous Duty Solenoid

Operating continuously for long periods.

Requires:

• Lower current density

• Better heat dissipation

Intermittent Duty Solenoid

Operates for short cycles.

Advantages:

• Higher peak force

• Smaller package size

Many industrial applications use intermittent-duty custom solenoids to maximize force output.

Why Simulation Is Better Than Manual Calculation

Modern custom solenoid manufacturers use finite element analysis (FEA) software to predict force accurately.

Simulation provides:

• Magnetic flux distribution

• Force curves

• Temperature rise

• Saturation analysis

• Stroke performance

Compared to manual formulas, FEA delivers much more realistic results.

Common engineering software includes:

• ANSYS Maxwell

• COMSOL Multiphysics

• JMAG

• Opera Electromagnetic

Information Needed for Custom Solenoid Force Calculation

To accurately calculate force, manufacturers typically require:

Electrical Parameters

• Voltage

• Current

• Duty cycle

Mechanical Parameters

• Required force

• Stroke length

• Installation space

Environmental Conditions

• Temperature range

• Humidity

• Vibration level

Performance Requirements

• Response time

• Operating frequency

• Lifetime expectation

Providing complete specifications enables engineers to design the most efficient custom solenoid solution.

Why Work with a Professional Custom Solenoid Manufacturer?

Calculating force is only the first step in solenoid development.

A professional custom solenoid manufacturer can provide:

• Electromagnetic simulation

• Prototype development

• Coil optimization

• Thermal analysis

• Life-cycle testing

• Mass production support

This ensures the final product delivers reliable force performance while meeting cost and manufacturing targets.

Conclusion

Solenoid force depends on several interacting factors, including coil turns, current, magnetic permeability, pole area, and especially air gap distance. While theoretical formulas provide a useful starting point, actual force performance should always be verified through simulation and testing.

For custom applications such as industrial automation, smart locks, medical devices, automotive systems, and vending machines, working with an experienced custom solenoid manufacturer is the most effective way to achieve the desired force, stroke, efficiency, and reliability.

Whether you need a miniature actuator or a high-force industrial solenoid, accurate force calculation is the foundation of successful custom solenoid design.