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Physics

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Physics

Biot-Savart Law Calculator.

Calculates the magnetic field produced by a current-carrying wire segment at a point in space using the Biot-Savart law.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Enter the current in amperes.

  2. 2

    Enter the length of the wire segment in meters.

  3. 3

    Enter the perpendicular distance from the wire to the point in meters.

  4. 4

    Enter the angle between the current direction and the line from the segment to the point in degrees.

  5. 5

    The calculator computes the magnetic field using the Biot-Savart law.

(4e-7 * current * length * sin(angle * pi / 180)) / (4 * pi * distance * distance)

Frequently asked questions

What is the Biot-Savart law?

It describes the magnetic field generated by a steady current. For a small wire segment, the field is proportional to the current, length, and sine of the angle, and inversely proportional to the square of the distance.

What units does the result use?

The magnetic field is in teslas (T). For typical currents and distances, values are often in microteslas (µT) or milliteslas (mT).

Can I use this for a long straight wire?

This calculator is for a finite segment. For an infinitely long wire, use the formula B = μ₀I/(2πr). For a finite segment, the result is an approximation that improves as the segment is small relative to the distance.

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Magnetic field (B)

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How it works

Calculates the magnetic field produced by a current-carrying wire segment at a point in space using the Biot-Savart law.

  1. Enter the current in amperes.
  2. Enter the length of the wire segment in meters.
  3. Enter the perpendicular distance from the wire to the point in meters.
  4. Enter the angle between the current direction and the line from the segment to the point in degrees.
  5. The calculator computes the magnetic field using the Biot-Savart law.

Formulas

The math behind this calculator, written out so you can verify the result.

Biot-Savart Law for a finite segment

B = (μ₀ I L sin θ) / (4π r²)

This gives the magnetic field at a point due to a short straight wire segment of length L carrying current I, at distance r, with angle θ between the current direction and the line

Real-world use cases

Where this calculation shows up in everyday life.

Educational demonstrations

Helps students understand how magnetic field strength varies with current, distance, and angle.

Example: Compare fields at different distances from a wire.

Design of electromagnets

Estimate the field contribution from a short coil segment when designing solenoids or magnetic sensors.

Example: Approximate the field near a small loop.

Physics problem solving

Quickly verify textbook problems involving finite current elements.

Example: Check a homework problem with given parameters.

Tips and common mistakes

Tips

  • Use consistent units: meters for length and distance, amperes for current.
  • The angle should be between 0° and 180°; the sine is positive in this range.
  • For small segments, the result approximates the field from a differential element.
  • Remember that the field direction is perpendicular to both the current and the radius vector.

Common Mistakes to Avoid

  • Forgetting to convert degrees to radians when using sine.
  • Using the full wire length when the point is far away; the approximation improves for short segments.
  • Confusing distance r with the length of the wire.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.