Waves
Angular Frequency
Angular frequency in radians per second.
Variables
ωrad/s
Angular frequency
Radians per second
Allowed values: greater than 0
fHz
Frequency
Cycles per second
In SI units: 1/s
Allowed values: greater than 0
Ts
Period
Time for one cycle
Allowed values: greater than 0
Derivation
ω = 2π/T = 2πf.
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.
- f = 2 Hz (Frequency)
Result: ω = 12.566371 rad/s
Other waves formulas with the same quantities
- Wave Equation (Wave Properties) shares Frequency
- Group Velocity (Wave Properties) shares Angular frequency
- Phase Velocity (Wave Properties) shares Angular frequency
- SHM Displacement (Simple Harmonic Motion) shares Angular frequency
- SHM Velocity (Simple Harmonic Motion) shares Angular frequency
- SHM Acceleration (Simple Harmonic Motion) shares Angular frequency
Where this formula is listed
- Waves formulas, under Wave Properties, alongside Wave Intensity, Intensity-Amplitude Relation, Inverse Square Law (Intensity), Wave Speed on String and Reflection Coefficient.
- In the waves list it comes after Period and Frequency and before Wave Number.
- Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Angular Frequency formula?
Angular Frequency is written ω = 2πf = 2π/T. Angular frequency in radians per second. It belongs to Waves, under Wave Properties.
What are the units in ω = 2πf = 2π/T?
In SI units, ω is angular frequency, measured in rad/s; f is frequency, measured in 1/s; T is period, measured in s.
How is the Angular Frequency formula derived?
ω = 2π/T = 2πf. The result is ω = 2πf = 2π/T.