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Hall Effect Voltage & Sensor Calculator

Discovered by Edwin Hall in 1879, the Hall effect occurs when a current-carrying conductor is placed in a perpendicular magnetic field, causing Lorentz forces to deflect charge carriers transversely.

Longitudinal electrical current flowing through the sensor in Amperes.

Perpendicular magnetic field strength in Tesla (1 T = 10,000 Gauss).

Thickness of conductor along magnetic field direction in millimeters.

Charge carrier volumetric density in /m³ (Semiconductor ≈ 10²¹; Copper ≈ 8.5×10²⁸).

Polarity of dominant charge carriers.

Calculated Result
-7489.8109 mV

Hall Voltage (V_H)

Hall Voltage (V_H)

-7489.8109 mV (-7.4898 V)

Hall Coefficient (R_H)

-0.0062415 m³/C

Majority Carrier Type

Electrons (n-type / negative VH)

Carrier Density (n)

1.00e+21 /m³

Slab Thickness

0.5 mm (500 µm)

Calculation Breakdown

  1. 1. Compute Hall Coefficient R_HR_H = 1 / (q · n) = 1 / (1.602×10⁻¹⁹ C · 1.00e+21 m⁻³) = -0.0062415 m³/C
  2. 2. Thickness Conversiont = 0.5 mm = 0.0005 m
  3. 3. Calculate Hall Voltage V_HV_H = (I · B · R_H) / t = (0.5 A · 1.2 T · -0.0062415) / 0.0005 m = -7489.8109 mV

Hall Voltage vs Magnetic Field (Tesla)

Interactive visualization based on your current inputs

VH (mV)
-12.5-9.1-5.7-2.41.00.2 T0.5 T1.0 T1.5 T2.0 TField B (Tesla)VH (mV)

What Is the Hall Effect Voltage & Sensor Calculator?

The Hall effect describes the production of a voltage difference across an electrical conductor transverse to an electric current and an applied magnetic field.

How Does the Hall Effect Voltage & Sensor Calculator Work?

Moving charges experience Lorentz force F = q(v × B), steering carriers toward one side of the slab until an opposing electrostatic field balances magnetic deflection.

Hall Effect Voltage & Sensor Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

V_H = \frac{I \cdot B}{n \cdot q \cdot t} = \frac{R_H \cdot I \cdot B}{t}, \quad R_H = \pm \frac{1}{n \cdot q}

Hall voltage equals current times B-field over carrier density times elementary charge q times slab thickness t.

How to Use the Hall Effect Voltage & Sensor Calculator

  1. Input the bias current through the sensor.
  2. Specify the applied magnetic field in Tesla.
  3. Enter the semiconductor wafer thickness in mm.
  4. Specify the carrier density and majority carrier type.

Step-by-Step Example Calculation

Silicon Hall Sensor (0.5A, 1.2T, 0.5mm)

Input Values:

currentAmps:0.5
magneticFieldTesla:1.2
thicknessMm:0.5
carrierDensityPerM3:1.0e21
carrierType:electrons
Worked Steps: In an n-type semiconductor with n = 10²¹ /m³, an applied 1.2 T field generates a measurable -7.49 mV Hall voltage.

Understanding Your Result

Hall Voltage (mV): Measurable transverse potential difference.

Hall Coefficient (RH): Intrinsic material constant in m³/C.

Sign Interpretation: Identifies whether electrons or holes dominate transport.

Factors That Affect the Result

  • Directly proportional to current and magnetic field; inversely proportional to slab thickness and carrier density.

When Should You Use This Calculator?

  • Brushless DC motor commutation, non-contact current transformers, semiconductor wafer Hall mobility testing.

Assumptions & Limitations

  • Assumes uniform magnetic field and single carrier dominant band transport without quantum Hall regime effects.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Classical Drude-Lorentz Hall effect formulation using elementary charge q = 1.602×10⁻¹⁹ C.

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