How to use this calculator
- Enter coil ampere-turns. Set turns and current at the operating condition, not only the cold coil rating.
- Enter pole and gap. Use effective pole diameter and the working air gap at the stroke position you care about.
- Set core properties. Enter approximate core path length, relative permeability, leakage factor and saturation flux density.
- Check saturation. If utilization exceeds 100%, the result is capped by the entered saturation limit and needs better B-H data.
How it works
This first-pass model treats the solenoid as a simple magnetic circuit. The
ampere-turns N I drive flux through an air gap plus a finite core
reluctance:
B_raw = mu0 · N · I / (g + l_core / mu_r)
The calculator then applies the leakage factor and caps the result at the entered saturation flux density:
B_eff = min(B_raw · k_l, B_sat)
Force comes from magnetic pressure on the pole face:
F = B_eff² · A / (2 · mu0)
Use this for screening an actuator, latch or relay before you commit to a coil and core geometry. For a known measured pole flux density, the electromagnet holding force calculator is the cleaner workflow.
Worked example
Verified against the live calculator
Suppose a solenoid has 800 turns at 2 A, a
12 mm pole, 1 mm air gap, 50 mm core path,
effective mu_r = 1000, 70% leakage factor and
1.6 T saturation.
Ampere-turns are 1600 A·turn. The effective magnetic path is
0.001 + 0.05/1000 = 0.00105 m, giving raw flux density of about
1.915 T. After leakage, the effective field is about
1.340 T, below saturation.
Pole area is pi x 0.012² / 4 = 1.131e-4 m². Magnetic pressure is
about 0.714 MPa, so pull force is about 80.8 N.
Frequently asked questions
How do you calculate solenoid pull force?
This calculator estimates gap flux density from ampere-turns and magnetic path length, then uses magnetic pressure: F = B^2 * A / (2 * mu0). It applies leakage and saturation limits before calculating force.
Why does air gap matter so much?
Air has very low permeability, so most of the magnetomotive force is spent across the air gap. Small increases in gap can sharply reduce flux density and pull force.
What should I use for leakage factor?
Use 50% to 80% for a rough first pass. Open magnetic paths, large gaps and small armatures need lower values. Closed, well-aligned pole pieces with good steel contact can use higher values.
Is this valid for a moving solenoid plunger?
It is a static first-pass screen at the entered gap. Real plunger force changes with stroke, geometry, saturation, coil temperature and armature shape, so final actuator selection should use test data or FEA.
Method & assumptions
- Static force only. It does not model plunger acceleration, coil heating, eddy currents or inductance rise time.
- The core path is collapsed into one effective length and one effective relative permeability.
- Leakage/fringing is handled as a simple percentage derating, not a field solution.
- Flux density is capped at the entered saturation limit. Real saturation follows the material B-H curve.