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PHYSICS / CHARGED PARTICLE MOTION

Charged Particle Gyroradius Calculator

Calculate the nonrelativistic circular-path radius from mass, perpendicular speed, charge, and magnetic field.

  • 01 Calculated in this tab
  • 02 Values stay in this browser tab
  • 03 Use boundary

Conversion input

Known value

Filter by unit name, symbol, or code. Your current selections remain available.

Equation inputs

Preparing the calculator...

METHOD / WORKED EXAMPLE

Use only the velocity across the field

Gyroradius measures the circular component of a charged particle's helical path, so only velocity perpendicular to the magnetic field belongs in the numerator.

WORKED DEFAULT

Check the calculation with the default inputs

For a proton moving at 2.0e6 m/s perpendicular to a 1.5 T field, the entered charge and mass produce a gyroradius of about 0.01392 m.

  1. Find perpendicular momentumm x v-perpendicular
  2. Find magnetic scale|q| x B
  3. Divideorbit radius about 0.01392 m

READ THE RESULT

Interpret the output in context

Higher perpendicular momentum widens the orbit, while larger charge magnitude or magnetic field tightens it. Parallel velocity changes helix pitch but not this radius.

ASSUMPTIONS AND LIMITS

Know where the model stops

  • Speed is well below the relativistic regime.
  • The field is uniform over the orbit.
  • The entered velocity is the perpendicular component.

The particle is nonrelativistic in a uniform magnetic field; collisions, electric fields, radiation, and field gradients are omitted.

Use internally consistent units and retain extra precision when carrying the result into another calculation.

OpenStax: charged-particle motion in a magnetic field

COMMON QUESTIONS

Charged Particle Gyroradius Calculator FAQs

What if the particle also moves along the magnetic field?

The parallel velocity component is unchanged by the magnetic force and carries the particle along the field while the perpendicular component circles it, producing a helix. Enter only the perpendicular speed here. Helix pitch additionally requires the parallel speed, orbital period, and consistent field geometry.

Why does the calculator use charge magnitude?

Radius is a positive distance, so its magnitude depends on absolute charge. Charge sign reverses the direction of curvature for a fixed field and velocity, but does not make radius negative. Determine orientation separately using vectors, a stated coordinate system, and the magnetic-force right-hand rule.

When is a relativistic gyroradius required?

When speed is no longer small compared with c, momentum is gamma-mv rather than mv, so the radius must use relativistic perpendicular momentum. This page limits the default workflow to a nonrelativistic range; precision work should evaluate beta and apply the appropriate momentum and field model.

Use boundary

Calculation path

Balance perpendicular magnetic force with centripetal force and solve for circular-path radius. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.

Calculation path

r = mv_perp / (|q|B)