Magnetic Field Calculator

A magnetic field is a region of space where a moving electric charge experiences a force. Field strength is measured in Tesla (T) or the smaller unit Gauss (G), where 1 T = 10,000 G. The formulas for calculating magnetic field strength depend on the geometry of the current source.

Key formulas:

Straight wire (Biot-Savart): B = (μ₀ × I) ÷ (2π × r)

Center of a circular loop: B = (μ₀ × I) ÷ (2 × R)

Interior of a solenoid: B = μ₀ × n × I

What each variable means:

• B: magnetic field strength (Tesla)
• μ₀: permeability of free space = 4π × 10⁻⁷ T·m/A (approximately 1.2566 × 10⁻⁶)
• I: current in Amperes (A)
• r: perpendicular distance from the wire in meters (m)
• R: radius of the circular loop in meters
• n: number of turns per meter in the solenoid (turns/m)

Worked example — solenoid: A solenoid has 500 turns, is 0.25 m long, and carries 2 A of current.

n = 500 ÷ 0.25 = 2,000 turns/m B = (4π × 10⁻⁷) × 2,000 × 2 = 5.03 × 10⁻³ T = 5.03 mT

Reference values:

• Earth’s magnetic field: ~25–65 μT (0.000025–0.000065 T)
• Refrigerator magnet: ~5 mT
• MRI machine: 1.5–3 T
• Strongest continuous lab magnet: ~45 T
• Neutron star surface: ~10⁸ T

Applications: Electric motors, generators, MRI machines, particle accelerators, and electromagnetic brakes all rely on precise magnetic field calculations.