Helmholtz Coil Field Calculator

Estimate coil field, spacing, and heating instantly. Review exact values, ideal values, units, and conversions. Useful for lab setups needing stable magnetic field control.

Calculated Results

Exact center field: -
Exact center field in gauss: -
Ideal Helmholtz field: -
Spacing deviation: -
Uniformity indicator: -
Coil pair ampere-turns: -
Estimated resistance: -
Voltage drop: -
Power dissipation: -
Target-field current: -

Exact field uses the two-coil center-field equation for identical circular coils. Ideal field assumes classic Helmholtz spacing where separation equals coil radius.

Calculator Inputs

For the most uniform central field, use spacing equal to radius. Leaving relative permeability at 1 suits air-core laboratory coils.

Example Data Table

Turns Current (A) Radius (m) Spacing (m) Relative Permeability Exact Center Field (mT)
100 1.50 0.10 0.10 1.00 1.349
150 2.50 0.12 0.12 1.00 2.518
200 3.00 0.15 0.15 1.00 3.595

Formula Used

Exact center field for two identical circular coils:

B = μ0 × μr × N × I × R² / (R² + (s/2)²)^(3/2)

Ideal Helmholtz field when spacing equals radius:

BH = (4/5)^(3/2) × μ0 × μr × N × I / R

Electrical estimates:

V = I × Rcoil, and P = I² × Rcoil

Here, μ0 is the permeability of free space, μr is relative permeability, N is turns per coil, I is current, R is coil radius, and s is center-to-center spacing between the two coils.

How to Use This Calculator

  1. Enter turns per coil and the coil current.
  2. Choose the correct units for current, radius, spacing, and field.
  3. Input coil radius and the separation between coil centers.
  4. Keep relative permeability at 1 for air-core coils.
  5. Optionally enter target field and coil-pair resistance.
  6. Press Calculate Field to display results above the form.
  7. Use the export buttons to save the calculated summary as CSV or PDF.

Frequently Asked Questions

1. What does a Helmholtz coil do?

It generates a nearly uniform magnetic field near the midpoint between two identical circular coils. This is useful for calibration, sensor testing, and controlled magnetic experiments.

2. Why is spacing equal to radius important?

That spacing minimizes field curvature near the center. It creates the classic Helmholtz condition, improving uniformity across a small central working volume.

3. Is the field equation exact here?

The displayed exact center field is exact for the midpoint on the common axis of two identical circular coils. It does not map off-axis field variations.

4. When should relative permeability differ from 1?

Use values above 1 only when the field region contains magnetic material that changes permeability. Standard air-core laboratory coils usually use 1.

5. What unit is gauss compared with tesla?

One tesla equals 10,000 gauss. Small laboratory coil fields are often reported in millitesla, microtesla, or gauss for convenience.

6. Why include resistance, voltage, and power?

They help estimate supply requirements and thermal load. Higher current increases field strength, but it also raises heating and operating cost.

7. Can this calculator solve for current needed?

Yes. If you enter a target field, it estimates the current needed using the exact center-field model for your chosen geometry and permeability.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.