Example Data Table
| Material |
Volume |
Density |
χv |
B |
dB/dz |
Expected Use |
| Pyrolytic graphite |
1 cm³ |
2200 kg/m³ |
-4.5E-4 |
0.6 T |
600 T/m |
Strong classroom levitation estimate |
| Bismuth |
0.5 cm³ |
9780 kg/m³ |
-1.66E-4 |
2 T |
1200 T/m |
Compact diamagnetic sample check |
| Water |
0.1 cm³ |
1000 kg/m³ |
-9.05E-6 |
10 T |
1400 T/m |
High field demonstration estimate |
Formula Used
The calculator uses the SI magnetic permeability of free space:
μ₀ = 4π × 10⁻⁷ H/m
Sample volume conversion:
V = volume in cm³ × 10⁻⁶
Mass from density when direct mass is empty:
m = ρV
Weight force:
W = mg
Direct diamagnetic lift force magnitude:
Fχ = |χv| V B |dB/dz| / μ₀
Lift ratio:
R = Fχ / W
Required magnetic field-gradient product:
B(dB/dz)required = μ₀mg / (|χv|V)
Required gradient at a known field:
(dB/dz)required = B(dB/dz)required / B
A lift ratio above one means magnetic lift exceeds weight. A ratio above the selected safety factor gives a stronger design target.
How To Use This Calculator
- Enter the material name for clear result labeling.
- Enter sample volume in cubic centimeters.
- Enter density, unless you want to provide direct mass.
- Enter volume susceptibility in SI units. Diamagnetic values are negative.
- Enter magnetic field strength in tesla.
- Enter the vertical field gradient in tesla per meter.
- Add a gap estimate to calculate field change across the gap.
- Choose a safety factor for practical design allowance.
- Press the calculate button and review the result above the form.
- Use CSV or PDF buttons to download the calculated report.
Understanding Direct Diamagnetic Levitation
Direct diamagnetic levitation happens when a material is pushed away from a stronger magnetic field. The effect is weak, but it is real. A diamagnetic sample has negative volume susceptibility. That value makes the magnetic force point toward lower field strength. If the upward force is greater than weight, the sample can float without contact.
Why The Calculator Helps
This calculator compares magnetic lift with gravitational weight. It uses volume, mass, susceptibility, magnetic field, and vertical field gradient. These values control the force balance. The tool also estimates the required gradient for levitation. That makes it useful for planning demonstrations, checking magnet designs, and comparing materials.
Important Physics Meaning
The key term is B times dB/dz. A high field alone is not enough. A strong gradient is also needed. Small gaps, sharp pole shapes, and layered magnet arrays can create larger gradients. Stable levitation may need support from geometry, because Earnshaw related limits still matter for many magnetic systems. Diamagnetic materials are special because their response can create passive stability in suitable field shapes.
Using Results Carefully
A lift ratio above one means lift equals or exceeds weight. A ratio above the selected safety factor gives a more practical target. The safety factor helps cover imperfect alignment, uncertain susceptibility, and field measurement errors. The net acceleration result shows how strongly the sample would rise or fall before reaching an equilibrium point.
Practical Design Notes
Use measured field data when possible. Magnet supplier values may not match your exact gap. Susceptibility is unitless in SI form, but some tables use cgs units. Convert values before entry. Volume should represent the part inside the strong field region. Mass can be entered directly, or estimated from density and volume. Pyrolytic graphite, bismuth, and water are common examples. Strong magnets can be hazardous. Keep electronics, watches, cards, and medical implants away. Wear eye protection when working with brittle magnets. This calculator gives an engineering estimate, not a certification for a laboratory setup.
Limits And Next Steps
For final hardware, confirm forces with experiments. Map the field at several heights. Check side forces and tilt. Use guards for magnets. Repeat calculations after every design change. Document results for safer reviews too.
FAQs
1. What is direct diamagnetic levitation?
It is levitation caused by the repulsion of a diamagnetic material from a stronger magnetic field. The upward magnetic force must exceed the sample weight.
2. Why is susceptibility entered as a negative value?
Diamagnetic materials have negative volume susceptibility. The calculator uses its magnitude for force size, while the negative sign reminds users of the repulsive response.
3. What does B times dB/dz mean?
It is the magnetic field-gradient product. Diamagnetic lift depends on both field strength and how quickly the field changes with height.
4. Can any material levitate this way?
No. Strong diamagnetic materials work best. Weak materials need very high fields, very steep gradients, or extremely small sample masses.
5. Why does the calculator include a safety factor?
The safety factor covers measurement errors, alignment issues, sample shape effects, and field-map uncertainty. A higher value gives a more cautious design target.
6. Is a lift ratio above one always stable?
No. It means lift can exceed weight. Stable levitation also depends on field geometry, side forces, and how the sample reacts to displacement.
7. What units should susceptibility use?
Use dimensionless SI volume susceptibility. Values from cgs references may need conversion before entry, or the result can become wrong.
8. Can this replace laboratory testing?
No. It is an estimate for planning and comparison. Final levitation setups should be checked with measured fields, safe handling, and controlled experiments.