Magnetic field strength from force on a moving charge
A charge moving through a magnetic field experiences a force perpendicular to both its velocity and the field. The force magnitude depends on charge magnitude, speed, field magnitude, and the sine of their angle.
This calculator solves only the scalar magnitude equation. A single force magnitude does not by itself establish the complete magnetic-field vector; direction requires vector geometry and the right-hand rule.
How to calculate magnetic field magnitude
- Enter force magnitude: Use the magnetic contribution to force in newtons.
- Enter particle data: Provide non-zero charge in coulombs and positive speed in m/s.
- Enter the vector angle: Use an angle strictly between 0° and 180°.
- Calculate and interpret: Read field magnitude in teslas and determine direction separately.
Formula and variables
Use force in newtons, charge in coulombs, speed in m/s, and the angle between velocity and magnetic field in degrees to obtain teslas.
B = F/(|q|v|sin θ|)- B — Magnetic field magnitude
- Magnitude of the magnetic flux density (T)
- F — Magnetic force magnitude
- Force attributable to the magnetic field (N)
- |q| — Charge magnitude
- Absolute electric charge of the particle (C)
- v — Speed
- Particle speed (m/s)
- θ — Angle
- Angle between velocity and magnetic-field vectors (degrees)
Elementary charge moving perpendicular to a field
A charge of 1.602176634 × 10⁻¹⁹ C moving at 1.0 × 10⁶ m/s experiences 1.0 × 10⁻¹³ N at 90°.
- Force
- 1.0 × 10⁻¹³ N
- Charge
- 1.602176634 × 10⁻¹⁹ C
- Speed and angle
- 1.0 × 10⁶ m/s, 90°
- B = 10⁻¹³/(1.602176634 × 10⁻¹⁹ × 10⁶ × 1)
Result: B ≈ 0.6241509 T.
At 90°, the sine factor is one and the magnetic force magnitude is maximal for the specified q, v, and B.
Understanding your results
A tesla result is a field magnitude
The displayed result is nonnegative even when a signed charge is entered, because charge sign changes force direction rather than field magnitude.
- At 90°, sin θ = 1.
- At 0° or 180°, magnetic force is zero and this inverse equation cannot determine B.
- Negative charge reverses force direction.
- Electric and other forces must be separated from the magnetic force input.
Assumptions
- The entered force is due only to a uniform magnetic field.
- Speed and angle are evaluated at the same instant.
- Classical Lorentz-force magnitude is appropriate.
Limitations
- Does not solve the vector direction or separate simultaneous electric force.
- Cannot infer B from zero force when velocity is parallel to the field.
- Does not model relativistic dynamics, spatially varying fields, or uncertainty.
Common mistakes
- Using total force when electric or mechanical forces are also present.
- Entering degrees as radians.
- Using signed charge to make field magnitude negative.
- Calling the result a complete magnetic-field vector.
Practical use cases
Charged-particle physics
Estimate field magnitude from a measured magnetic deflection force.
Coursework verification
Check Lorentz-force magnitude calculations in SI units.
Frequently asked questions
Why is the answer always nonnegative?
The calculator reports field magnitude. Charge sign affects force direction, not the magnitude of B.
Why can’t I use 0°?
When velocity is parallel to the field, sin θ is zero and every field magnitude gives zero magnetic force, so B is not identifiable from this equation.
How do I find the field direction?
Use the vector Lorentz-force relation and right-hand rule, reversing the force direction for a negative charge.
Sources and review
- Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field — OpenStax College Physics 2e. Accessed 2026-07-13.
Reviewed 2026-07-13.