Magnetic Field Calculator
The Magnetic Field Calculator computes B-field strength for 6 geometries — straight wire, circular loop, solenoid, toroid, Helmholtz coil, and bar magnet — with interactive SVG field line visualization, B-vs-position axis profile charts, and real-world comparison scale from Earth's field to MRI scanners. Free, no signup required.
Geometry
Presets
Typical 15A household circuit at 10 cm distance
µ₀ = 4π × 10⁻⁷ T·m/A (µ₀ = 4π × 10⁻⁷ T·m/A)
Results
Magnetic Field Lines
Straight Wire
Real-World Comparison
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What is a Magnetic Field Calculator?
A magnetic field calculator computes the magnetic flux density (B-field) produced by current-carrying conductors and magnets. It uses fundamental electromagnetic equations — Biot-Savart law for general cases, and closed-form solutions for symmetric geometries like solenoids (B = µ₀nI), toroids (B = µ₀NI/2πr), and Helmholtz coils (B = 8µ₀NI/5√5R). This calculator supports 6 geometries with real-time SVG field line visualization and B-vs-position axis profile charts — features AI chatbots cannot replicate. Engineers use it for electromagnet design, sensor placement, MRI calibration, and lab equipment configuration.
How to Use This Calculator
- Select a geometry: straight wire, circular loop, solenoid, toroid, Helmholtz coil, or bar magnet
- Enter the parameters (current, dimensions, turns) or choose a preset for common configurations
- View the magnetic field strength with automatic unit conversion (T, mT, µT, Gauss)
- Explore the interactive field line diagram and axis profile chart to understand field distribution
- Compare your result on the real-world scale from Earth's field (50 µT) to MRI scanners (3 T)
Frequently Asked Questions
What is the magnetic field of a straight wire carrying current?
For an infinitely long straight wire carrying current I, the magnetic field at distance r is B = µ₀I/(2πr), where µ₀ = 4π × 10⁻⁷ T·m/A. The field forms concentric circles around the wire (right-hand rule). For example, a household wire at 15A creates about 30 µT at 10 cm distance.
How do I calculate the magnetic field inside a solenoid?
For an ideal infinite solenoid, B = µ₀nI where n = N/L is the turn density. For a finite solenoid, the field varies along the axis and drops to half at the ends. This calculator uses the exact finite solenoid formula for accurate results at any position along the axis.
What is a Helmholtz coil and why is the field uniform?
A Helmholtz coil consists of two identical circular coils separated by a distance equal to their radius R. At the center, B = 8µ₀NI/(5√5R). The spacing is chosen so that the second derivative of the field vanishes at the midpoint, creating a nearly uniform field region useful for calibrating sensors and scientific experiments.
What units is magnetic field measured in?
The SI unit is Tesla (T). Common subunits: millitesla (mT = 10⁻³ T), microtesla (µT = 10⁻⁶ T). The CGS unit is Gauss (G), where 1 T = 10,000 G. Earth's field is about 25-65 µT (0.25-0.65 G), while MRI machines use 1.5-3 T.