Cyclotron Radius

r = \frac{mv}{qB}

Radius of circular motion of charged particle in magnetic field.

Variables

Radius

Radius of circular path

Allowed values: greater than 0

Mass

Particle mass

Allowed values: 0 or more

Velocity

Particle speed

m/s

Charge

Particle charge

In SI units: A·s

Magnetic field

Field strength

In SI units: kg/(A·s²)

Derivation

From qvB = mv²/r (Lorentz force = centripetal force), r = mv/(qB).

Your notes

0/5000

Check value

Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

m = 2 kg (Mass)
v = 3 m/s (Velocity)
q = 4 C (Charge)
B = 5 T (Magnetic field)

Result: r = 0.3 m

Other electricity & magnetism formulas with the same quantities

Hall Voltage (Magnetism) shares Magnetic field, Charge
Motional EMF (Electromagnetic Induction) shares Magnetic field, Velocity
Magnetic Force on Wire (Magnetism) shares Magnetic field
Magnetic Field (Long Wire) (Magnetism) shares Magnetic field
Magnetic Field (Solenoid) (Magnetism) shares Magnetic field
Energy Density (Magnetic Field) (Magnetism) shares Magnetic field

Where this formula is listed

Electricity & Magnetism formulas, under Magnetism, alongside Biot-Savart Law and Ampere's Law.
In the electricity & magnetism list it comes after Cyclotron Frequency and before Hall Voltage.
Electricity & Magnetism formula sheet, one of 48 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Cyclotron Radius formula?

Cyclotron Radius is written r = mv/(qB). Radius of circular motion of charged particle in magnetic field. It belongs to Electricity & Magnetism, under Magnetism.

What are the units in r = mv/(qB)?

In SI units, r is radius, measured in m; m is mass, measured in kg; v is velocity, measured in m/s; q is charge, measured in A·s; B is magnetic field, measured in kg/(A·s²).

How is the Cyclotron Radius formula derived?

From qvB = mv²/r (Lorentz force = centripetal force), r = mv/(qB). The result is r = mv/(qB).