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Magnetic Flux Density Converter

Convert magnetic flux density between Tesla, milliTesla, microTesla, Gauss, and nanoTesla for sensor and motor applications.

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Formula

1T=104G=103mT=106muT1 T = 10⁴ G = 10³ mT = 10⁶ mu T

How It Works

This calculator converts between Tesla, Gauss, millitesla, microtesla, and nanotesla for magnetics engineers, sensor designers, and physicists working with magnetic fields. Per SI Brochure (BIPM), the Tesla is the SI unit of magnetic flux density: 1 T = 1 Wb/m^2 = 1 V·s/m^2 = 1 kg/(A·s^2). The CGS unit Gauss relates as 1 T = 10,000 G exactly. Magnetic fields span 15 orders of magnitude: nanotesla for geomagnetic surveys (Earth's field = 25-65 uT varying with location per NOAA WMM), millitesla for Hall sensors (1-100 mT operating range), and Tesla for MRI machines (1.5-7 T clinical, up to 45 T research per IEEE/NSF). The magnetic permeability of free space mu_0 = 4*pi × 10^-7 H/m exactly (2019 SI).

Worked Example

Problem

A Hall-effect current sensor measures motor phase current using a 5 mm air gap. Calculate required field for 100 A measurement with a sensor having 2.5 mV/mT sensitivity.

Solution
  1. Field from wire: B = mu_0 × I / (2*pi*r) = 4*pi*10^-7 × 100 / (2*pi*0.0025) = 8 mT at 2.5 mm from center
  2. Convert to Gauss: 8 mT = 80 G = 8000 uT
  3. Hall sensor output: V = 2.5 mV/mT × 8 mT = 20 mV
  4. Required ADC resolution for 0.1 A accuracy: 20 mV / 1000 steps = 20 uV/step (14-bit ADC at 3.3 V = 200 uV/step - marginal)
  5. Improve by: ferrite concentrator (10x gain = 80 mT), or closer spacing, or higher sensitivity sensor (5 mV/mT)
  6. EMC consideration: stray fields from motor magnets (10-50 mT) may saturate sensor - add magnetic shielding

Practical Tips

  • ✓Earth's field per NOAA World Magnetic Model: 25-65 uT (0.25-0.65 G) depending on location. Horizontal component ~20 uT (compass reference), vertical 40-60 uT. Smartphones measure this with 3-axis magnetometers (resolution ~0.1 uT)
  • ✓Hall sensor ranges per Allegro/Melexis datasheets: linear sensors 10-200 mT typical, latching switches 5-50 mT operate/release. Saturation occurs at 200-500 mT. For > 500 mT, use magnetoresistive (AMR/GMR) sensors
  • ✓Safe exposure per ICNIRP guidelines: static fields < 2 T for general public, < 8 T for occupational. MRI scanners use 1.5-3 T clinical (7 T research). Permanent magnets rarely exceed 0.5 T at surface (5000 G)

Common Mistakes

  • ✗Confusing Tesla (flux density B) with Weber (total flux Phi) - they are different quantities related by Phi = B × A. A 0.5 T field over 0.01 m^2 = 5 mWb total flux. Motor design uses both: B for saturation limits, Phi for voltage calculation
  • ✗Forgetting 1 T = 10,000 G conversion - using wrong factor gives 10,000x error. Gauss is common in permanent magnet specs (NdFeB surface field 3000-5000 G = 0.3-0.5 T), Tesla is SI standard
  • ✗Misinterpreting Hall sensor sensitivity units - some specify mV/mT, others mV/G (10x different). A 2.5 mV/mT sensor = 0.25 mV/G. Always verify units before calculating expected output voltage

Frequently Asked Questions

Per SI: B (Tesla) = mu_0 × mu_r × H where H (A/m) is driving field, mu_0 = 4*pi × 10^-7 H/m exactly, mu_r is relative permeability (1 for air, 1000-10000 for ferrite). In air: B(T) = 1.257 × 10^-6 × H(A/m). B includes material response; H is independent of medium.
Per IEEE magnetics society: Gauss remains in permanent magnet industry datasheets (NdFeB, SmCo specs), motor design (air gap flux in kG), and magnetic recording (coercivity in Oe). Conversion: 1 T = 10,000 G = 10 kG. SI prefers Tesla, but legacy tools and references use CGS units.
Per JEDEC and military standards: most ICs tolerate < 10 mT (100 G) without performance impact. Hall sensors saturate at 200-500 mT. Magnetic storage (HDD, tape) may be affected above 5-10 mT. CRT displays (legacy) are sensitive to > 0.5 mT. Keep magnets away from sensitive electronics.
Earth: 25-65 uT (0.25-0.65 G) per NOAA. Small DC motor surface: 10-100 mT (100-1000 G), 1000x stronger. This is why motors interfere with magnetometers - a motor 10 cm away creates ~1 mT field, overwhelming Earth's 50 uT. Use magnetic shielding or distance for compass accuracy.

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