The strength of magnetic fields is usually measured with calibrated Hall probes, which operate based on the Hall effect.
If a thin conductor or semiconductor is placed in a magnetic field $\vec{B}$ and a current flows through it perpendicular to the field lines, the electrons are deflected by the Lorentz force perpendicular to both the field and their direction of motion. This deflection continues until the repelling electric field $\vec{E}$ between all charges $Q$ completely compensates the Lorentz force. In this equilibrium we have:
$$
F_\mathrm{el} = F_\mathrm{L}
$$
Substituting the expressions gives:
$$
QE = QvB
$$
Now assume that the part of the conductor in the magnetic field has length $l$. With $v = l/t$ and $I = q/t$ we obtain:
$$
QE = IBl
$$
The total charge $Q$ can be expressed using the electron density $n$ (electrons per cubic meter) and the conductor’s volume $V$:
$$
Q = nVe = ndlbe
$$
Here, $d$ is the thickness and $b$ is the width of the conductor. Using this relation and $E = U/b$, we can solve for the Hall voltage:
$$
U_\mathrm{H} = \frac{IB}{ned}
$$
The Hall voltage increases with higher current and magnetic flux density, but is inversely proportional to the electron density and the thickness of the conductor. For this reason, semiconductors with fewer free electrons are often better suited than good conducting metals. However, the resulting Hall voltages are usually very small and must be amplified with voltage amplifiers to provide a usable signal.
The Hall constant, which depends on the material, is defined as:
$$
\boxed{A_\mathrm{H} = \frac{1}{ne}}
$$
In this form, the Hall voltage is written as:
$$
\boxed{U_\mathrm{H} = A_\mathrm{H}\frac{IB}{d}}
$$
The sign of the Hall constant depends on whether the current is carried predominantly by electrons (as in metals) or by holes (as in some semiconductors). In practice, Hall constants are difficult to determine and show significant variation, since tiny impurities and temperature fluctuations can strongly affect the measured value.
Example:
For copper, the typical value of the Hall constant is $-5.3 \cdot 10^{-11}\,\mathrm{m^3/C}$. A thin conductor with a thickness of 1 mm is placed in a strong magnetic field of 1.5 T. A current of 15 A flows through the wire. The resulting Hall voltage is approximately 1.19 mV.