Choose a classical inverse, energy-based relativistic radius, cyclotron frequency or transverse-momentum rigidity calculation. Radius uses the motion perpendicular to a uniform magnetic field.

Classical approximation: total speed must be much smaller than c. Use energy-based mode for relativistic radius.

Uniform magnetic field. Radius uses perpendicular motion; charge sign changes direction, not radius.

Nonzero; the calculation uses its magnitude.

Pitch angle

Blank means 90ยฐ; 0ยฐ and 180ยฐ have no transverse orbit.

Related Calculators

Cyclotron Radius Formula

The following classical formula gives the orbit radius for nonrelativistic motion in a uniform field. For pitch angle ฮธ, vโŠฅ = v sin(ฮธ); charge sign affects rotation direction, not radius.

R = m ร— vperp / (B ร— |q|)

Variables:

  • R is the Cyclotron Radius (m)
  • m is the mass (kg) 
  • vโŠฅ is the speed perpendicular to the magnetic field (m/s)
  • B is the magnetic induction (T) 
  • |q| is the nonzero charge magnitude (C)

Divide mass times perpendicular speed by charge magnitude times field strength. The classical model requires total speed much smaller than c. Relativistically, R = pโŠฅ/(|q|B), where p = โˆš(K(K + 2mcยฒ))/c and K is total kinetic energy.

How to Calculate Cyclotron Radius?

The following steps outline how to calculate the Cyclotron Radius.

  1. First, determine the mass (kg).
  2. Next, determine total speed (m/s) and its angle to the field; a blank pitch angle uses 90ยฐ.
  3. Next, determine the magnetic induction (T). 
  4. Next, determine the charge (C).
  5. Next, use R = m*vโŠฅ/(B*|q|) for the classical estimate.
  6. Finally, calculate the Cyclotron Radius.
  7. After inserting the variables and calculating the result, check your answer with the calculator above. 

Example Problem:

Use the following variables as an example problem to test your knowledge.

mass (kg) = 5

velocity (m/s) = 6

magnetic induction (T) = 8

charge (C) = 1.25

At a 90ยฐ pitch angle, R = (5 ร— 6)/(8 ร— 1.25) = 3 m.