Please enter all required numeric values.
Formulas & Mathematical Logic
Step 1: Ampere-turns = N × I. This combines coil turns and current into magnetic excitation.
Step 2: Force = (N × I)² × 4 × π × 10^-7 × A / (2 × g²). This estimates ideal magnetic pulling force.
Step 3: Pounds-force = 0.224808942443 × Force. This converts newtons into pounds-force.
Practical meaning: force rises with current, turns and area, but drops sharply as the air gap increases.
Step-by-Step Example
Example values: current = 2 A, turns = 500, area = 0.0004 m², gap = 0.002 m.
Ampere-turns = 500 × 2 = 1000.
Force = 1000² × 4 × π × 10^-7 × 0.0004 / (2 × 0.002²).
Force = about 62.832 N.
Force in pounds = 62.832 × 0.224808942443 = about 14.125 LBS.
Practical meaning: reducing the air gap can increase force dramatically, but real core saturation and heat must be checked.
About This Calculator
Estimate solenoid pull force before building the coil and plunger assembly.
This CalcBoy calculator uses current, turns, pole area and air gap to estimate ideal electromagnet force.
The Solenoid Electromagnet Force Calculator is useful for quick actuator, relay, valve, latch and lifting electromagnet estimates. A solenoid creates a magnetic field when current flows through the coil. That field pulls a ferromagnetic plunger or armature toward the core. The strength of the force depends heavily on ampere-turns, magnetic area and especially the air gap.
Best UseSolenoid actuators, electromagnets, magnetic locks, relays and plunger mechanisms.
Key InputsCurrent, coil turns, magnetic area and air gap distance.
Design BenefitQuickly compare how gap, current or turns affect pulling force.
Safety ReminderReal force may be lower due to core saturation, leakage flux, friction and heating.
This calculator uses an ideal magnetic force equation. It is excellent for early design comparison, but real solenoids include losses that the simple formula does not fully model. Core material, plunger shape, magnetic path, coil heating, duty cycle, wire resistance, spring load and mechanical friction all affect the final measured force.
Quick tip: the air gap is the most sensitive input. If the gap doubles, force can drop by roughly four times in the ideal equation.
For practical actuator design, use the calculator result as a starting point, then test the actual solenoid under load. Check coil temperature, current draw, plunger movement, duty cycle and supply voltage. If high force is needed, reduce the air gap, increase effective pole area, use a better magnetic core material, or increase ampere-turns while staying within safe thermal limits.
Frequently Asked Questions
What is solenoid force?
It is the magnetic pulling force produced by a coil and core that attracts a plunger or armature.
Why does air gap affect force so much?
The formula contains gap squared in the denominator, so a small increase in gap can greatly reduce force.
Can I use this for a real solenoid actuator?
Yes, for early estimation. Real designs should also check saturation, spring load, friction, heat and stroke position.
What units should area and gap use?
This calculator uses square meters for area and meters for gap to preserve the original SI-based formula.
Does more turns always increase force?
More turns can increase force, but it also increases coil resistance, size and heat depending on wire gauge and current.
Does this include core saturation?
No. Core saturation is not included, so the real force may be lower at high current or small core area.