Magnetic Field of a Straight Wire Calculator — Biot-Savart Ampere
Calculate the magnetic flux density at any distance from a long straight current-carrying conductor using the Ampere's law result.
A
m
B = μ₀ · I / (2π · r) — circles the wire by the right-hand rule
- 1
μ₀ × I
0.000001257 × 10 = 0.000012566 - 2
2π × r
2π × 0.05 = 0.31415927 - 3
Magnetic field B
μ₀·I ÷ (2π·r) = 0.000012566 ÷ 0.31415927 = 0.00004000Field circles the wire in closed loops; magnitude halves every time the distance doubles.
How does this calculator work?
A long straight wire carrying current I produces a circular magnetic field B = μ₀·I / (2π·r) at perpendicular distance r. The field halves every time you double the distance (1/r dependence). μ₀ = 4π×10⁻⁷ T·m/A. Enter current in amperes and distance in metres to get B in tesla, mT, μT, and gauss.
Formula
How this is calculated
A long straight conductor carrying current I produces a magnetic field that forms closed circular loops centred on the wire. Applying Ampere's law to a circular path of radius r coaxial with the wire gives the field magnitude B = μ₀ · I / (2π · r), where μ₀ = 4π × 10⁻⁷ T·m/A is the permeability of free space. The field direction follows the right-hand rule: curl the fingers of the right hand in the direction the field circles the wire, with the thumb pointing in the direction of conventional current.
The field falls off as 1/r — doubling the distance halves the field. For a wire carrying a household current of 10 A, the field 5 cm away is B = (4π × 10⁻⁷ × 10) / (2π × 0.05) ≈ 40 μT, which is comparable to Earth's geomagnetic field (~50 μT). At 1 mm the field would reach 2 mT. The XY plot shows the 1/r decay from 20 % to 500 % of the input distance.
This result assumes an infinitely long, straight wire and a medium with permeability μ₀ (air or vacuum). For a wire of finite length, or when the observation point is very close to a bend or termination, the full Biot-Savart integral must be used. For a coil or solenoid see the related calculators.
Frequently asked questions
A point charge produces a field that spreads in three dimensions, giving 1/r². An infinite straight wire is a one-dimensional source, so the field spreads in only two dimensions (cylindrically), giving 1/r. A magnetic dipole, extending only over a finite volume, falls off as 1/r³.
The field forms closed circles around the wire. If current flows upward, the field circles anticlockwise when viewed from above — right-hand rule: point the right thumb along the current, and the curled fingers show the field direction. This calculator gives the magnitude only.
Enter current in amperes and distance in metres; the result comes in tesla. For practical wire-level fields (typically 1 μT – 1 mT) the calculator also shows microtesla, millitesla, and gauss (1 T = 10⁴ G ≈ 20 000 times Earth's field).
TG we-Calculate Editorial Team. (2026). Magnetic Field of a Straight Wire Calculator — Biot-Savart Ampere [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/magnetic-field-of-straight-current-carrying-wire-calculator
TG we-Calculate Editorial Team. "Magnetic Field of a Straight Wire Calculator — Biot-Savart Ampere." TG we-Calculate. 2026. https://we-calculate.com/calculator/magnetic-field-of-straight-current-carrying-wire-calculator.
TG we-Calculate Editorial Team, "Magnetic Field of a Straight Wire Calculator — Biot-Savart Ampere," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/magnetic-field-of-straight-current-carrying-wire-calculator
@misc{wecalculate_magnetic_field_of_straight_current_carrying_wire_calculator, title = {Magnetic Field of a Straight Wire Calculator — Biot-Savart Ampere}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/magnetic-field-of-straight-current-carrying-wire-calculator}}, year = {2026}, note = {TG we-Calculate} }
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