Hall Voltage Calculator: Solve Current, Field, Density, or Thickness

Hall Voltage Formula and Rearrangements for the Hall Effect

The calculator uses the standard ideal Hall-effect relation for a single dominant carrier type.

Formula: V H = (I B) / (n q t)

where:

• V_H is the Hall voltage in volts (V).
• I is the current through the sample in amperes (A).
• B is the magnetic flux density in tesla (T).
• n is the charge carrier density in m⁻³.
• q is the magnitude of charge of each carrier in coulombs (C). For electrons this is approximately 1.602 × 10⁻¹⁹ C.
• t is the sample thickness, meaning the dimension across which the Hall voltage is measured, in meters (m).

Rearranging the same Hall-voltage equation lets you solve for the missing quantity directly:

• Solve for current: I = VH n q t / B
• Solve for magnetic field: B = VH n q t / I
• Solve for carrier density: n = I B / (q t VH)
• Solve for thickness: t = I B / (n q VH)

The calculator performs these rearrangements automatically. Choose the variable you want to find, provide the remaining values in SI units, and the page evaluates the corresponding expression so you can move between a measured Hall signal and the physical conditions that produced it.

How to Use This Hall-Effect Calculator

To use this Hall voltage calculator, select the quantity you want to compute and fill in the known values for the others. All inputs are in SI units:

• Current I: amperes (A).
• Magnetic field B: tesla (T).
• Carrier density n: m⁻³.
• Thickness t: meters (m).
• Charge magnitude q: coulombs (C); the calculator uses the elementary charge if you leave the field blank.

After you calculate, the result tells you how strong the transverse Hall signal is for the conditions you entered. A larger voltage means the sideways electric field had to grow more to balance the magnetic force on the moving carriers. In the ideal formula, higher current or magnetic field pushes the Hall voltage up, while higher carrier density or greater thickness pushes it down.

For real measurements, the absolute Hall voltage may be small enough that unit mistakes matter more than the formula itself. If your result looks far too large for a thin sample in a modest field, recheck whether you entered tesla rather than millitesla, meters rather than millimeters, and the carrier density in m⁻³ rather than cm⁻³.

Worked Example: Hall voltage for a doped silicon slab

This Hall-voltage example uses a doped silicon slab 1 mm thick, carrying 20 mA in a 0.3 T magnetic field. Using an electron carrier density of 1 × 10²¹ m⁻³ and the elementary charge q = 1.602 × 10⁻¹⁹ C, the calculator can estimate the Hall voltage.

1. Convert thickness to meters: t = 1 mm = 1 × 10⁻³ m.
2. Write down the known values: I = 0.02 A, B = 0.3 T, n = 1 × 10²¹ m⁻³, q = 1.602 × 10⁻¹⁹ C, and t = 1 × 10⁻³ m.
3. Use the Hall relation: VH = I B / (n q t).
4. Compute the denominator: n q t = (1 × 10²¹) × (1.602 × 10⁻¹⁹) × (1 × 10⁻³).
5. First multiply n and q: (1 × 10²¹) × (1.602 × 10⁻¹⁹) = 1.602 × 10².
6. Now include t: 1.602 × 10² × 10⁻³ = 1.602 × 10⁻¹ = 0.1602.
7. Compute the numerator: I B = 0.02 × 0.3 = 0.006.
8. Divide: V_H = 0.006 / 0.1602 ≈ 0.0374 V = 37.4 mV.

The calculator returns approximately 3.74 × 10⁻² V, or 37.4 mV, for these inputs. That scale is typical of a small laboratory Hall signal: easy to miss if the wiring or unit conversions are wrong, but straightforward to detect with the right meter range. If the sample were made twice as thick while everything else stayed fixed, the Hall voltage would drop by half. If the carrier density were ten times lower, the Hall voltage would rise tenfold.

Those scaling rules are exactly why Hall measurements are useful for semiconductor characterization. Thin samples, strong magnetic fields, and low carrier densities create the largest signals, while thicker samples or heavily doped materials produce smaller voltages that can be harder to measure cleanly.

Hall-voltage parameter effects: current, field, density, charge, and thickness

The table below summarizes how each Hall-voltage input behaves when everything else is held fixed.

Note that the sign of the Hall voltage depends on the charge carriers and the orientation of the magnetic field and current. The calculator uses the magnitude of the charge |q|, so it reports the size of the Hall response rather than the sign convention of a particular experiment.

Assumptions and limitations for Hall-voltage estimates

The Hall relation in this calculator is an ideal textbook model, so it is best used for estimates and cross-checks rather than as a full device simulator. Keep these Hall-effect assumptions and limitations in mind:

• Uniform magnetic field: The formula assumes that B is uniform across the active cross section of the sample. In fringe fields or near magnet edges, the actual Hall voltage may differ.
• Single carrier type: The expression V_H = I B / (n q t) assumes that conduction is dominated by one type of charge carrier, either electrons or holes. Mixed conduction or compensation changes the effective Hall response.
• Simple geometry: The calculator treats the sample as a rectangular bar with a well-defined thickness and current distribution. Patterned Hall plates, thin films, or devices with guard rings may need geometry factors or numerical modeling.
• Steady-state current: Transient effects and high-frequency operation are ignored. The model is most accurate for DC or slowly varying currents.
• Linear material response: It is assumed that material properties such as carrier density and mobility do not change with applied field or current over the range considered. Strong heating or very large fields can invalidate this.
• SI units only: All entries and results are in SI. If you work in cm, gauss, or other units, convert to meters and tesla before using the calculator.

Real measurements can also include contact offsets, misalignment between the current path and the magnetic field, and temperature-dependent changes in conductivity. Those effects do not invalidate the calculator; they just mean the closed-form result is a first estimate rather than the final word.

How the Hall effect creates the transverse voltage

In a Hall-voltage measurement, current flows through a conductor or semiconductor while a magnetic field is applied perpendicular to that current. The moving electrons or holes are forced sideways by the magnetic field, and charge begins to pile up on one side of the sample. That separation builds an electric field across the thickness of the material, and the resulting potential difference is the Hall voltage.

In a typical Hall bar, the current runs along the long axis, the magnetic field points through the face of the sample, and the Hall probes read the transverse voltage. The size of that voltage depends on the current, field, carrier density, sample thickness, and carrier charge, which is why the calculator can be used both for forward estimates and for solving the inverse problem from a measured signal.