Angular Frequency
ω = 2π · f
Quick answer
This calculator solves ω = 2π × f for Angular Frequency. With Frequency 1 kHz, the result is 6283 rad/s. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Angular frequency expresses how fast a sinusoid advances in radians per second, related to the ordinary frequency in hertz by a factor of 2π. It is the form that appears throughout AC analysis—in reactances (ωL, 1/ωC), phase (ωt), and resonance—because the mathematics of sines and complex exponentials is naturally written in radians.
Variables
- ω — Angular frequency (rad/s)
- f — Frequency (Hz)
Practical Notes
Use ω, not f, inside sin/cos and in reactance formulas: XL = ωL, XC = 1/(ωC). One full cycle is 2π radians.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| omega | Angular Frequency | rad/s | rad/s, RPM |
| f | Frequency | Hz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Frequency 1 kHz
- 2. The relation: ω = 2π × f
- 3. Substitute: f = 1 kHz
- 4. Result: Angular Frequency = 6283 rad/s
Worked examples
Minimum range
Given: Frequency 5 Hz
Result: Angular Frequency = 31.42 rad/s
Low range
Given: Frequency 50 Hz
Result: Angular Frequency = 314.2 rad/s
Typical
Given: Frequency 1 kHz
Result: Angular Frequency = 6283 rad/s
High range
Given: Frequency 20 kHz
Result: Angular Frequency = 125700 rad/s
Maximum range
Given: Frequency 0.2 MHz
Result: Angular Frequency = 1.26 × 10⁶ rad/s
Solving for each variable
Solve for Angular Frequency
Frequency 5 Hz → 31.42 rad/s
Solve for Frequency
Angular Frequency 9.549 RPM → 0.1592 Hz
How Angular Frequency changes with Frequency
| Frequency (input) | Angular Frequency (result) |
|---|---|
| 100 Hz | 628.3 rad/s |
| 0.25 kHz | 1571 rad/s |
| 0.5 kHz | 3142 rad/s |
| 0.75 kHz | 4712 rad/s |
| 1 kHz | 6283 rad/s |
| 1.5 kHz | 9425 rad/s |
| 2 kHz | 12570 rad/s |
| 4 kHz | 25130 rad/s |
| 7 kHz | 43980 rad/s |
| 10 kHz | 62830 rad/s |
The same result in other units
| Unit | Value |
|---|---|
| rad/s | 6283 |
| RPM | 60000 |
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<p><a href="https://vbatpower.com/formulas/angular-frequency/">Angular Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Angular Frequency?
Use ω = 2π × f. With Frequency 1 kHz, Angular Frequency works out to 6283 rad/s.
What is the formula for Angular Frequency?
The formula is ω = 2π × f. Angular frequency expresses how fast a sinusoid advances in radians per second, related to the ordinary frequency in hertz by a factor of 2π.
How do you find Frequency when you know the other values?
Rearrange for Frequency: with Angular Frequency 9.549 RPM, Frequency is 0.1592 Hz.
What units does Angular Frequency use?
Angular Frequency is shown in rad/s, RPM. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All AC Circuits formulas →Need more features?
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