Magnetic Field Of Straight Current Carrying Wire Calculator - Find the field around a wire from current and distance, with the right-hand-rule direction.

The magnetic field of straight current carrying wire calculator gives the magnetic field strength B produced by a current I flowing through a long straight conductor at a perpendicular distance r. It applies the Biot-Savart result B = (µ₀ · I) / (2π · r) and shows how the field circles the wire.

Whenever charge moves it sets up a magnetic field. A straight wire carrying a steady current is the simplest case to study, and its field is what makes electromagnets, motors, and transformers work. The pattern is easy to picture: the field lines are not straight like the wire, they wrap around it in closed loops.

Knowing the field magnitude and direction near a wire matters for wiring layout, electromagnetic compatibility, and lab work where a stray field can affect sensitive instruments. A mains cable, a busbar, or a coil winding all start from this same basic result, so getting the single-wire case right is the foundation for everything more complicated.

This tool skips the algebra and the constant µ₀ so you can answer a practical question quickly: how strong is the field a given distance from a conductor that carries a given current? The answer comes straight from the Biot-Savart law integrated along an infinitely long line. Because the geometry is so regular, the result depends on just two quantities, which makes it a useful sanity check before reaching for a numerical field solver.

When the same current is wound into a coil the field is stronger and more uniform, which you can size with the solenoid magnetic field calculator.

The calculator evaluates the Biot-Savart expression for a straight wire and reports the result in tesla, with the gauss equivalent shown alongside.

• I (current): Current in amperes (A) flowing through the wire.
• r (distance): Perpendicular distance from the wire in metres (m).
• µ₀ (vacuum permeability): A constant equal to 4π×10⁻⁷ T·m/A that sets how strongly a current makes a field in free space.

The derivation starts from the Biot-Savart law, which says each tiny piece of current contributes a small field. Adding up every piece of an infinitely long straight wire gives the tidy 1/r formula above. The factor 2π appears because the circular symmetry lets most of the components cancel, leaving only the field that points around the wire.

For a finite wire the calculator adds the corrected expression B = (µ₀ · I · L) / (4π · r · √(r² + (L/2)²)) = (µ₀ · I)/(2π·r) · L/√(L² + 4r²), which reduces to the long-wire value as the length L grows. When L is many times larger than r the two expressions agree to within a fraction of a percent.

The result in tesla is shown alongside its gauss equivalent (1 T = 10,000 G) so you can compare against published field values directly. Microtesla (µT) is handy for small fields near household wiring, where the numbers are only a few tens of microtesla.

According to Wikipedia - Biot-Savart law, the magnetic field around a long straight wire is B = µ₀I / 2πr.

Each wire makes the field above, and the magnetic force between wires calculator shows how two such fields make parallel wires attract or repel.

The magnetic field of straight current carrying wire calculator rests on a few simple ideas that explain why the formula looks the way it does.

A charge placed in this circular field feels a sideways push that the Lorentz force calculator quantifies from charge, velocity, and field.

The magnetic field of straight current carrying wire calculator takes three numbers and returns the field, so the steps are short.

1. 1 Enter the current: Type the wire current I in amperes; use 0 only to confirm a zero field. For alternating current, use the RMS value to get the RMS field.
2. 2 Set the distance: Enter the perpendicular distance r from the wire to the point of interest in metres. Remember r is the shortest distance to the line of the wire, not the distance along it.
3. 3 Add the wire length if finite: Leave wire length at 0 for the long-wire formula, or enter L to see the finite-wire correction on the perpendicular bisector. Use this when the wire is comparable to or shorter than r.
4. 4 Read the result: Read the field in tesla and its gauss equivalent, plus the right-hand-rule direction. The finite-wire field is shown separately so you can see how much the short-wire correction matters.

Before finding the field you usually set the current with a resistor, which the Ohm's law calculator relates to voltage and resistance.

It avoids hand errors with µ₀ and powers of ten, and it makes the tesla-to-gauss conversion immediate. Multiplying by 10,000 in your head is where mistakes slip in, especially at the microtesla scale.

Showing the finite-wire correction next to the long-wire value helps you see when the simpler formula is good enough. If the two readings are within a percent of each other you can safely use the long-wire shortcut; if they differ, the geometry matters.

Having the direction stated by the right-hand rule alongside the magnitude means you leave with the full picture: not just how strong the field is, but which way it points, which is what you need for force or induction problems that build on this result. It also keeps the units honest, since tesla and gauss are easy to mix up once numbers get small.

Two inputs drive the answer, and a few practical limits decide when the formula stops being accurate.

• • The formula assumes a straight wire in free space; nearby ferromagnetic material such as iron distorts the field and can make it much stronger or change its direction.
• • It ignores the wire's own radius, so it is not valid at distances smaller than the conductor thickness. Right at the surface you should use the radius as the minimum r.

According to Encyclopaedia Britannica - Magnetic Field, a steady current produces a magnetic field whose direction is set by the right-hand rule.

The Biot-Savart law is the general source of this result, and the Biot number calculator applies the same law to other conductor shapes.