Magnetic Field Calculators

Biot-Savart Law Calculations for Engineers & Researchers

Accurate static magnetic field calculation based on the Biot–Savart law — no meshes, no FEM approximations.

Biot–Savart law No FEM / no grids Engineering accuracy Instant recompute
What this calculator does

This service computes magnetic fields generated by current-carrying conductors directly from the Biot–Savart law using real source geometry and user-defined observation points. No mesh-based solvers or numerical field approximations are used.

What you can calculate
  • Frames and current loops
  • Coils and solenoids
  • Helical and spiral windings
Key features
  • Strict Biot–Savart formulation
  • No grids, interpolations, or FEM approximations
  • High accuracy for engineering and scientific use
  • Support for spatial transformations of the source
  • Fast recalculation when parameters change
Output

For each observation point you obtain the field components Bx, By, Bz and the field magnitude |B|.

Further discussion & learning

If you’d like to discuss magnetic field calculations, assumptions, or numerical methods with other physicists and engineers, you may find Physics Forums helpful.

Analytic formulas
Helix
Helical conductor

The current path is represented as a helical curve described by the following parametric equations: 𝑥=𝑟*cos(𝑡), 𝑦=𝑟*sin(𝑡), 𝑧=𝑘*𝑟*𝑡 where: r is the radius, t is the angular parameter, k is the tangent of the helix pitch angle relative to the base of the cylinder on which the spiral is wound (analogous to y = kx). If k > 0, the helix is right-handed.If k < 0, the helix is left-handed. If k = 0, the helix degenerates into a circular loop. The magnetic field is computed using the Biot–Savart–Laplace law. The calculation is reduced to a single integral, which is evaluated using the Simpson method.

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Analytic formulas
Double Cylinder
Coaxial inner &amp; outer radii

The model is represented as two current-carrying ribbons with opposite current directions, wound into circular loops and nested inside one another. An elementary current element is a circular ribbon of width dh. The magnetic field is computed using the Biot–Savart–Laplace law. The calculation is reduced to a double integral: an integral over the circumference, and an integral over the cylinder height h. One of the integrals has an analytical solution, while the second is evaluated using the Simpson method. This method can be applied to the calculation of solenoids and permanent magnets, which are represented as current ribbons.

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Analytic formulas
Rectangular Frame
Thin rectangular loop

The model is represented as a rectangular current loop, where the current element is modeled as an infinitesimal straight line segment. The magnetic field is computed using the Biot–Savart–Laplace law. The calculation is reduced to single integrals, which have analytical solutions. As a result, the final expressions are given in terms of elementary functions.

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Analytic formulas
Rectangular Frame Ribbon
Finite thickness

The model is represented as a current-carrying ribbon formed into a rectangular loop. Each differential current element is a thin rectangular ribbon segment of width dc. The magnetic field is computed using the Biot–Savart–Laplace law. The calculation reduces to a double integral: one integral over the rectangular contour and one over the ribbon width C. Both integrals admit analytical solutions, so the resulting field expressions are written entirely in terms of elementary functions.

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Analytic formulas
Archimedes Spiral
Planar spiral (XY plane)

The model is a planar Archimedean spiral in the XY plane defined by r(t) = a + s·t/(2π). t is the angular parameter, a is the initial radius, s is the distance between turns, r(t) is the radial function. The magnetic field is computed using the Biot–Savart–Laplace law. The calculation reduces to a single integral over t, evaluated numerically using Simpson’s method.

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Analytic formulas
Helmholtz Rings
Coaxial rings (z-axis)

The model is represented as two circular current ribbons carrying currents in the same direction. The rings are positioned along the z-axis and separated symmetrically by a distance of r/2 in the positive and negative directions. Parameters: r — ring radius; w — ribbon width The magnetic field is computed using the Biot–Savart–Laplace law. An elementary current element is a circular ribbon of width dw. The calculation is reduced to a double integral: an integral over the circumference, and an integral over the ribbon width w. One of the integrals has an analytical solution, while the other is evaluated using the Simpson method.

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General solution
General Curve
Arbitrary current path

Compute the magnetic field of a current flowing along an arbitrary space curve x(t), y(t), z(t) using the Biot–Savart–Laplace law. The curve is entered as parametric functions and their derivatives; the field is evaluated numerically for a single point or along a line of points.

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Recently Used Configurations

Your last 6 calculated configurations on this device.