Compute the Hall coefficient from carrier concentration, determine the carrier type (electron / hole) from its sign, and compute the Hall voltage. All calculations 100% on your device.
1 · Hall coefficient from carrier concentration
RH = 1 / (n · q) — q = −e for electrons (n-type), +e for holes (p-type).
Carrier type
Unitm³/C
2 · Carrier concentration from the Hall coefficient
n = 1 / (RH · q) — the RH sign determines the carrier type.
Carrier type
Unitm⁻³
3 · Hall voltage
VH = RH · I · B / d
FormulaVH = RH·I·B/d
Brief theory
RH = EH / (j · B) = 1 / (n · q)
The Hall effect occurs when electric current flows through a conductor in a perpendicular magnetic field: charge carriers are deflected by the Lorentz force and pile up on one side, producing a measurable Hall electric field EH and Hall voltage VH.
The Hall coefficient sign is the most important information: negative means the dominant carriers are electrons (n-type), positive means holes (p-type). This is how the Hall effect is used to characterize semiconductors.
Verified example: copper with n = 8.47×10²⁸ m⁻³ has RH = −7.369×10⁻¹¹ m³/C. For 1 A current, 1 T field, and 1 mm thickness, its Hall voltage is −73.690 nV (negative sign = electrons). For comparison, silver: −1.0651×10⁻¹⁰ m³/C; intrinsic silicon: −6.2415×10² m³/C (much larger because it has few carriers); intrinsic germanium: −2.6006×10⁻¹ m³/C.
Material preset values (Cu, Ag, Si, Ge) are typical concentrations at room temperature, not exact constants — actual values depend on purity, temperature, and doping.
Material
typical n (m⁻³)
RH (m³/C)
Copper (Cu)
8.47×10⁾²
−7.369×10⁻¹¹
Silver (Ag)
5.86×10⁾²
−1.0651×10⁻¹⁰
Intrinsic silicon (Si)
1.0×10¹⁸
−6.2415×10²
Intrinsic germanium (Ge)
2.4×10¹⁹
−2.6006×10⁻¹
Frequently Asked Questions (FAQ)
What is the Hall effect?
The Hall effect is the appearance of a transverse electric voltage (Hall voltage, V_H) across a current-carrying conductor placed in a magnetic field perpendicular to the current. Charge carriers are deflected by the Lorentz force, pile up on one side of the sample, and produce a measurable Hall electric field E_H.
What is the Hall coefficient formula?
The Hall coefficient is given by R_H = E_H / (j · B) = 1 / (n · q), where E_H is the Hall electric field (V/m), j the current density (A/m²), B the magnetic induction (T), n the charge carrier concentration (m⁻³), and q the charge per carrier: q = −e for electrons, q = +e for holes, e = 1.6022×10⁻¹⁹ C.
Why is the Hall coefficient sign important?
The R_H sign indicates the dominant charge carrier type: negative means electrons (n-type semiconductor), positive means holes (p-type). Example: copper has R_H = −7.369×10⁻¹¹ m³/C (negative → electrons), while a hole example with n = 2.0×10¹⁶ m⁻³ gives R_H = 3.1208×10² m³/C (positive). This is why the Hall effect is used to characterize semiconductors.
How do I calculate the Hall voltage?
Use V_H = R_H · I · B / d, where I is the current (A), B the magnetic field (T), and d the sample thickness (m). Verified example: copper (R_H = −7.369×10⁻¹¹ m³/C) with I = 1 A, B = 1 T, d = 1 mm gives V_H = −73.690 nV. Second example: doped silicon with n = 1.0×10²¹ m⁻³ (R_H = −6.2415×10⁻³ m³/C) with I = 10 mA, B = 0.5 T, d = 1 mm gives V_H = −31.208 mV.
What is the difference between n-type and p-type carriers in the Hall effect?
In n-type material the dominant carriers are negatively charged electrons (q = −e), so R_H is negative; in p-type the dominant carriers are holes that behave like positive charges (q = +e), so R_H is positive. This calculator uses the q matching the selected carrier type.
Why is the Hall coefficient of metals so small?
Because R_H = 1/(n·q) is inversely proportional to carrier concentration: metals have n around 10²⁸–10²⁹ m⁻³, so R_H is only on the order of 10⁻¹⁰ m³/C (copper: −7.369×10⁻¹¹ m³/C). In contrast, intrinsic silicon with n = 1.0×10¹⁶ m⁻³ has R_H = −6.2415×10² m³/C — much larger.
What is the unit of the Hall coefficient?
The SI unit of the Hall coefficient is m³/C (cubic meters per coulomb). This is consistent with both forms of the formula: from 1/(n·q) we get 1/(m⁻³·C) = m³/C, and from E_H/(j·B) we get (V/m)/((A/m²)·T) = m³/C.
What is the charge carrier concentration of copper?
The typical value for copper at room temperature is n ≈ 8.47×10²⁸ m⁻³ (one free electron per atom), giving R_H = −7.369×10⁻¹¹ m³/C. This is a typical value, not an exact constant — the actual value depends on purity and temperature.
Are the material preset values (Cu, Ag, Si, Ge) exact?
No. The preset values are typical carrier concentrations at room temperature for illustration and quick checks. A sample’s actual value depends on purity, temperature, and doping (for semiconductors, doping changes n by many orders of magnitude). For serious measurements, measure your sample’s R_H, then compute n from mode 2 of this calculator.
What is the relationship between the Hall coefficient and Hall mobility?
Hall mobility is defined as μ_H = |R_H| · σ, where σ is the electrical conductivity (S/m). So if you know R_H from this calculator and the material’s conductivity, the carrier mobility can be computed directly. The R_H sign still tells you the carrier type.
We use cookies and third-party services (including Google AdSense) to personalize content, analyze traffic, and serve relevant ads. By clicking "Accept", you consent to our use of cookies as described in our Privacy Policy.
Report an issue
2 taps, no typing needed — diagnostics are sent automatically.