Biot-Savart Magnetic Field Calculator
The Biot-Savart law relates an electric current to the magnetic field it creates. Its most common application is the field surrounding a long, straight, current-carrying wire, where the field circles the wire and weakens with distance. This relationship is essential for cable routing, electromagnetic interference analysis, and laboratory magnet design. Enter the current in amperes, the perpendicular distance from the wire, and optionally the permeability for a magnetic medium; this calculator returns the magnetic flux density in tesla, the value in microtesla, and the equivalent in gauss.
Biot-Savart formula (long straight wire)
mu_0 = 1.25663706212e-6 H/m
Magnetic field = (mu * I) / (2 * pi * r)
1 tesla = 1,000,000 microtesla
1 tesla = 10,000 gauss
mu is the permeability of the surrounding medium in henries per metre, I is the current in amperes, and r is the perpendicular distance from the wire in metres. The result is the magnetic flux density in tesla.
Magnetic field context
- The long-wire result assumes an infinitely long, straight, thin conductor; it is accurate close to a long wire.
- The field falls off as one over the distance, so it halves when the distance doubles.
- Use the permeability of free space for air and vacuum; multiply by relative permeability for magnetic materials.
- One tesla equals 10,000 gauss and 1,000,000 microtesla; the Earth's field is around 50 microtesla.
- For coils and loops, the full Biot-Savart integral or Ampere's law applies instead of this simplified form.
Biot-Savart law: frequently asked questions
What is the Biot-Savart law?
The Biot-Savart law gives the magnetic field produced by a steady electric current. For an infinitely long straight wire it simplifies to B = (mu_0 x I) / (2 x pi x r), where mu_0 is the permeability of free space, I is the current, and r is the perpendicular distance from the wire.
What is the permeability of free space?
The permeability of free space, mu_0, is approximately 1.25663706212 x 10^-6 henries per metre (or tesla metres per ampere). Since the 2019 SI redefinition it is a measured quantity very close to the older exact value of 4 pi x 10^-7.
Does this assume an infinite straight wire?
Yes. This calculator uses the standard result for an infinitely long, straight, thin wire, which is an excellent approximation when the distance from the wire is small compared with the wire's length. Loops and finite segments need the full integral form of the law.
How does the field change with distance?
For a long straight wire the field falls off as one over the distance. Doubling the distance from the wire halves the magnetic field. This inverse relationship is weaker than the inverse-square fall-off seen for point sources.
What direction does the field point?
The magnetic field forms concentric circles around the wire. Point the right thumb in the direction of conventional current and the fingers curl in the direction of the field. The field is everywhere tangent to these circles.
Official sources
- NIST Fundamental Physical Constants: vacuum magnetic permeability.
- NIST: SI units (tesla, ampere).
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.