Magnetic Force Calculator
Use the gradient model for a magnetic moment in a changing field. Use the pressure model for an effective air-gap field and pole area.
Example Data Table
This example uses the field-gradient method and empirical drag coefficients.
| Input | Example value | Unit | Purpose |
|---|---|---|---|
| System mass | 12 | kg | Sets gravitational weight. |
| Magnetic moment | 2.4 | A·m² | Defines dipole strength. |
| Field gradient | 55 | T/m | Creates gradient-based lift. |
| Speed | 4 | m/s | Sets drag magnitude. |
| Drag coefficients | 0.28 and 0.04 | N·s/m and N·s²/m² | Models electromagnetic braking. |
Formula Used
The calculator supports two lift estimates. Select the model that best matches your measured system.
The gradient equation treats the magnetic moment and field gradient as aligned. The pressure equation assumes an effective air gap, a usable pole area, and limited leakage. Drag coefficients are empirical values.
How to Use This Calculator
- Choose the field-gradient or magnetic-pressure lift method.
- Enter mass and local gravity in SI units.
- For gradient mode, enter magnetic moment or magnetization with volume.
- For pressure mode, enter flux density and effective pole area.
- Add speed and drag coefficients from trusted measurements.
- Select Calculate Forces and review lift, drag, power, and support ratio.
- Download the values as CSV or save the print view as PDF.
Magnetic Lift and Drag Force Basics
Magnetic lift appears when a magnetic system experiences an upward force. The force can come from a field gradient. It can also come from magnetic pressure across an air gap. Lift must exceed the system weight for upward acceleration. Equal lift and weight create vertical balance. This calculator evaluates both useful lift models.
Gradient-Based Lift
A magnetic dipole in a changing field experiences force. The simplified relation is F = μ(dB/dz). Here, μ is magnetic moment. The term dB/dz is the vertical magnetic field gradient. A positive gradient is treated as upward. Larger moments and steeper gradients increase lift. This approach suits magnets, actuators, lab assemblies, and field studies. It is an approximation. Real force depends on field geometry, material behavior, alignment, and saturation.
Pressure-Based Lift
Magnetic pressure provides another practical estimate. The relation is F = B²A/(2μ₀). In this expression, B is air-gap flux density. A is effective pole area. The constant μ₀ is the permeability of free space. This model works best when the air gap is small and leakage is controlled. Pole shape, fringing, and core properties can change the real result. Use conservative margins when designing load-bearing equipment.
Electromagnetic Drag
Moving conductors near magnetic fields can generate eddy currents. Those currents resist motion. The resistance becomes magnetic drag. It uses Fd = c₁v + c₂v². The linear term is useful at lower speeds. The quadratic term models stronger speed effects. Both coefficients are empirical. Obtain them from tests, simulations, or validated design data. The drag force always acts opposite the chosen motion direction.
Power and Motion
Drag consumes mechanical power. The calculator uses P = Fd v. This power becomes heat or electrical loss in most systems. Net vertical force equals lift minus weight. Dividing net vertical force by mass gives vertical acceleration. A support ratio above one indicates available upward force. A ratio of one indicates static support. A ratio below one means the system cannot hover without other forces.
Using Reliable Inputs
Use SI units throughout. Convert magnet volume from cubic centimeters carefully. Measure the field gradient near the operating location. Do not assume a peak field equals a useful gradient. For pressure calculations, use the effective pole area rather than external magnet dimensions. Choose drag coefficients from measured force-speed data whenever possible. Repeat calculations across the full speed range. Check temperature, alignment, vibration, and changing air gaps. These factors often control real performance.
Design Checks
Compare calculated lift with worst-case weight, not nominal weight. Include payload changes and safety margins. Review the required gradient or flux density shown by the result. Values beyond material limits signal an impractical concept. Check drag power against thermal capacity. A system may lift correctly but overheat during sustained motion. Treat this calculator as an engineering estimate. Confirm critical designs with detailed field analysis and physical testing. Check measurements before committing to final hardware.
Frequently Asked Questions
1. What does magnetic lift mean?
Magnetic lift is the upward force produced by a magnetic field interaction. It can counter system weight. The exact mechanism depends on field geometry, materials, current, distance, and magnetic alignment.
2. Which lift model should I select?
Choose the gradient model when you know magnetic moment and field gradient. Choose the pressure model for an air-gap estimate with flux density and effective pole area. Use measured results to confirm either model.
3. Can magnetic moment be calculated from magnetization?
Yes. Use μ = M × V, where M is magnetization in amperes per meter and V is volume in cubic meters. The calculator converts entered cubic centimeters before using this relation.
4. Why is the field gradient important?
A uniform field mainly causes torque on a dipole. A changing field can create net force. A steeper vertical gradient usually produces larger gradient-based lift for the same magnetic moment.
5. What creates magnetic drag?
Relative motion can induce eddy currents in conductive material. Their magnetic field opposes the motion that created them. This produces braking force and converts mechanical energy into heat or electrical loss.
6. Why does the calculator use two drag coefficients?
The linear term can represent low-speed damping. The quadratic term captures stronger speed-dependent effects. Together they provide a flexible empirical estimate when a full electromagnetic simulation is unavailable.
7. What does a support ratio above one show?
A ratio above one means calculated lift exceeds weight. The system has positive net vertical force under the entered conditions. Real designs still need margin for field changes, misalignment, temperature, and load variation.
8. Can the drag force be negative?
The calculator reports drag magnitude as positive. Physically, its direction is opposite the chosen motion direction. Reverse the travel direction in a vector model to reverse the drag-force sign.
9. Is the pressure model exact?
No. It is an idealized air-gap estimate. Fringing, material saturation, pole shape, gap size, and leakage can change the actual force. Use finite-element analysis or testing for critical work.
10. How should I measure drag coefficients?
Measure opposing force across several steady speeds. Fit the data to Fd = c₁v + c₂v². Repeat measurements at operating temperatures and air gaps for a more dependable model.
11. Is this calculator enough for a final design?
Use measured inputs and confirm results through careful testing.