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Magnetic Force Calculator

Find the magnetic force on a charged particle.

How it is calculated

The tool applies the Lorentz force on a moving charge, F = |q| × v × B × sin θ. Here q is the charge in coulombs (C), v the speed in metres per second (m/s), B the magnetic flux density in tesla (T) and θ the angle in degrees between the velocity and the field. The charge is taken as its absolute value, so the sign of the charge only decides the direction of the force, which this tool does not show. If the angle is left blank it uses 90°, the maximum case. The force is printed in newtons in scientific notation with four decimals. Zero force appears at 0° and 180°.

Worked example

A particle with the charge of a proton, q = 1.602e-19 C, moves at v = 3e6 m/s through a field of B = 0.5 T, with the velocity at θ = 30° to the field. First q × v × B = 1.602e-19 × 3e6 × 0.5 = 2.403e-13. Then sin 30° = 0.5, so F = 2.403e-13 × 0.5 = 1.2015 × 10⁻¹³ N. At 90° the same particle would feel twice as much, 2.4030 × 10⁻¹³ N.

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Common mistakes

  • Typing the angle in radians. The field expects degrees, so 1.57 means 1.57° (almost no force) rather than 90°.
  • Measuring the angle from the field's perpendicular instead of from the field direction. The formula uses sin θ with θ between v and B, so parallel motion gives zero force, not the maximum.
  • Entering the charge in elementary charges or microcoulombs. The field is in coulombs; a single electron is about 1.602e-19 C, not 1.
  • Entering a field in gauss. One gauss is 1e-4 tesla, so 5000 G must be typed as 0.5 T.
  • Expecting a negative result for a negative charge. The tool uses the absolute value of q and gives the size of the force only, not its direction.

About this calculator

This calculator finds the magnetic (Lorentz) force on a moving charged particle: F = q · v · B · sinθ, where q is the charge, v is its velocity, B is the magnetic field strength, and θ is the angle between the velocity and field vectors. The force is zero when the charge moves parallel to the field and maximum when it moves perpendicular to it, and it always acts perpendicular to both v and B (found via the right-hand rule).

Physics students and electrical engineers use this relationship to understand how charged particles curve in magnetic fields — the basis of cyclotrons, mass spectrometers, particle accelerators, and the Hall effect used in many current sensors.

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Comments (1)

  • Editorial team

    The force is always perpendicular to the velocity, so it bends the path without changing the speed. For a charge moving at right angles to the field, set the result equal to m v squared over r and you can solve for the radius of the circular path, which is a handy follow-up for particle problems. Which particle or device are you modelling, and does the radius you get look physically sensible?

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