Enter toroid parameters
Use mean radius for quick design checks, or radial mode for inner and outer core geometry.
Formula used
For an ideal toroid, Ampere's law gives the magnetic field around the closed circular path inside the core.
H(r) = N × I / (2πr)The magnetic flux density follows from permeability.
B(r) = μ0 × μr × H(r) = μ0 × μr × N × I / (2πr)When cross-sectional area is known, flux and inductance can also be estimated.
Φ = B × A L ≈ μ0 × μr × N² × A / (2πrmean)These equations assume a closed magnetic path, small fringing, steady current, and nearly uniform core area. Radial mode highlights how field strength drops as radius increases.
How to use this calculator
- Choose mean radius mode for quick estimates, or radial mode for geometry-based analysis.
- Enter turns, current, relative permeability, radius values, and cross-sectional area.
- Select units that match your design sheet or lab measurements.
- Press Calculate field to show the result above the form.
- Review flux density, field strength, flux, inductance, and stored energy.
- Use the export buttons to save results as CSV or PDF.
Example data table
| Example | Turns | Current (A) | μr | Radius (cm) | Area (cm²) | B (mT) | H (A/m) | Flux (µWb) |
|---|---|---|---|---|---|---|---|---|
| Air core lab coil | 180 | 1.20 | 1 | 6.00 | 4.50 | 0.72 | 572.96 | 0.324 |
| Ferrite sensor ring | 320 | 0.35 | 2,000 | 2.50 | 1.80 | 1,792.00 | 713.01 | 3.226e+5 |
| Iron powder choke | 95 | 2.80 | 75 | 1.80 | 6.00 | 221.67 | 2,351.96 | 1.330e+5 |
Frequently asked questions
1. What does this calculator solve?
It estimates magnetic field strength, flux density, magnetomotive force, flux, inductance, and stored energy for ideal toroidal coils using your design inputs.
2. Why does the field change with radius?
Ampere's law makes the field inversely proportional to radius. The inner edge of a toroid carries stronger field than the outer edge.
3. What is relative permeability?
Relative permeability compares a material's magnetic response with free space. Higher values usually increase flux density and inductance for the same current.
4. Does the calculator work for air-core toroids?
Yes. Set relative permeability to 1. That gives the ideal air-core field and lets you compare it with high-permeability materials.
5. Why can outside field show nearly zero?
An ideal toroid confines most flux inside the core path. Real coils leak some field, but the ideal model treats external flux as negligible.
6. How accurate is the inductance estimate?
It is a first-order estimate using mean magnetic path length and uniform area. Real cores may differ because of gaps, saturation, leakage, and fringing.
7. Which radius should I enter?
Use mean radius for quick design work. Use inner, outer, and evaluation radius when you want field values at a specific core location.
8. Can I use this for saturation checks?
Yes, as a screening step. Compare calculated flux density with the core material's saturation flux density from its datasheet.