Solenoid Force Calculator

Inputs

Coil turns (N)

Total turns in the winding.

Coil current (I)

Current through the coil.

Pole diameter (d_p)

Effective circular pole-face diameter.

Air gap (g)

Working air gap between pole face and armature.

Core path length (l_c)

Approximate ferromagnetic path length in the core and armature.

Relative permeability (mu_r)

First-pass effective core permeability. Real steel varies strongly with B.

Leakage factor (k_l)

Percent of ideal gap flux retained after leakage/fringing. Use lower values for open geometries and large gaps.

Saturation flux density (B_sat)

Approximate usable saturation limit for the core material.

Default result

Estimated pull force(F)

80.85N

Pass

18.18 lbf

Also computed

Equivalent static mass(m_eq)8.245kg

Effective flux density(B_eff)1.34T

Raw gap flux density(B_raw)1.915T

Saturation utilization(B/B_sat)83.78%

Ampere-turns(NI)1,600A·turn

Pole area(A)113.1mm²

Gap dominates this first-pass force estimate. Use the curve to see how quickly pull force falls as stroke or clearance increases.

Method notes 3 notes

Magnetic circuit uses B_raw = mu0*N*I/(g + l_core/mu_r), then applies the leakage factor and saturation cap.
Pull force uses F = B_eff^2*A/(2*mu0) at the pole face.
Real solenoid force depends on plunger shape, stroke, fringing, coil heating, steel B-H curve and dynamics; validate final designs with test or FEA.