Calculate the magnetic field strength around a current-carrying wire using the Biot-Savart law. Supports straight wires, loops, and solenoids with visual field diagrams.
The Magnetic Field of a Wire Calculator computes the magnetic flux density (B field) around current-carrying conductors using fundamental electromagnetic equations. It supports three configurations: infinite straight wire, circular loop, and solenoid — covering the most common scenarios in electrical engineering and physics. That makes it useful for quick checks on coil strength, wiring fields, and lab-scale electromagnet setups.
For a straight wire, the magnetic field forms concentric circles and decreases inversely with distance (B = μ₀I / 2πr). For a circular loop, the field at the center is B = μ₀I / 2R. For a solenoid, the interior field is nearly uniform at B = μ₀nI. These relationships, derived from the Biot-Savart law and Ampère's law, are foundational in electromagnetism.
Enter the current, conductor geometry, and distance to compute field strength in Tesla, Gauss, and milliTesla. The calculator also shows force between parallel wires, field direction using the right-hand rule, and energy density of the magnetic field. It is a quick way to compare a wire field against familiar magnetic values.
Use this calculator when you need a field-strength estimate from a simple current geometry without doing the derivation or unit conversion by hand. It is useful for electromagnetics coursework, coil intuition, and quick comparisons with Earth-field or lab-scale values where the geometry is simple but the units are not. That keeps the geometry check fast when you just need the magnitude.
Straight Wire: B = μ₀I / (2πr). Circular Loop Center: B = μ₀I / (2R). Solenoid: B = μ₀nI, where n = N/L (turns per meter). μ₀ = 4π × 10⁻⁷ T·m/A. Force between parallel wires: F/L = μ₀I₁I₂ / (2πd).
Result: B = 40.0 μT
A straight wire carrying 10 A creates a field at 5 cm distance of B = (4π×10⁻⁷ × 10) / (2π × 0.05) = 4.0 × 10⁻⁵ T = 40 μT. This is comparable to Earth's magnetic field strength.
The Biot-Savart law provides the fundamental relationship for calculating magnetic fields from arbitrary current distributions: dB = (μ₀/4π) × (I dℓ × r̂)/r². For a straight wire, integration yields B = μ₀I/(2πr). For a loop and solenoid, different integration paths give their respective standard formulas.
This law is the magnetic equivalent of Coulomb's law for electric fields. Combined with the principle of superposition, it can compute the field from any current distribution, though complex geometries often require numerical methods.
Magnetic field calculations are essential in transformer design, motor engineering, magnetic shielding, and electromagnetic compatibility (EMC). Engineers use these formulas to ensure fields don't interfere with sensitive electronics, to design inductors and electromagnets, and to predict forces in actuator systems.
In power systems, the fields around high-voltage lines are regulated for public safety. In medical devices, precise field calculations ensure MRI image quality and patient safety. In particle physics, bending magnets use solenoid fields to steer charged particles.
The range of magnetic fields in engineering spans many orders of magnitude: Earth's field is ~50 μT, a refrigerator magnet ~5 mT, a loudspeaker magnet ~1 T, an MRI scanner ~3 T, and a superconducting research magnet up to 45 T. Understanding this scale helps engineers choose appropriate materials and designs.
A current-carrying wire creates a magnetic field in concentric circles around it. The field strength decreases with distance from the wire (1/r for a straight wire). The direction follows the right-hand rule: thumb in current direction, fingers curl in field direction.
μ₀ is the permeability of free space, equal to 4π × 10⁻⁷ T·m/A (approximately 1.257 × 10⁻⁶). It relates the magnetic field to the current that produces it. In materials, the total permeability is μ = μᵣμ₀, where μᵣ is the relative permeability.
Earth's magnetic field is approximately 25-65 μT (0.25-0.65 Gauss) at the surface, depending on location. It's about 30 μT at the equator and 60 μT near the poles. The calculator helps you compare wire fields to Earth's field.
Parallel wires carrying current in the same direction attract each other. Parallel wires carrying current in opposite directions repel. The force per unit length is F/L = μ₀I₁I₂ / (2πd).
1 Tesla = 10,000 Gauss. Tesla is the SI unit; Gauss is the CGS unit. Earth's field is about 0.5 Gauss = 50 μT. An MRI machine produces 1.5-3 T. A refrigerator magnet is about 5 mT.
Inside a long solenoid, the contributions from each turn add constructively along the axis and cancel at the edges. The resulting field is nearly uniform and parallel to the axis: B = μ₀nI. This breaks down near the ends where the field drops to about half.