📊 Frequency Calculator
Calculate frequency
Leave blank if entering angular frequency
Leave blank if entering period
How to Use This Calculator
Choose Your Input Method
You have two options: Enter the period (T) in seconds - the time for one complete cycle, OR enter the angular frequency (ω) in rad/s - the angular velocity. Leave one blank - you only need to provide either period or angular frequency, not both.
Enter Period (if using period)
If you know the period, input it in seconds. The period is the time for one complete oscillation or cycle. For example, if a pendulum completes one swing in 2 seconds, enter 2. The period must be greater than zero.
Enter Angular Frequency (if using angular frequency)
If you know the angular frequency, input it in radians per second (rad/s). Angular frequency is 2Ï€ times the regular frequency. For example, if angular frequency is 62.83 rad/s, that corresponds to 10 Hz frequency.
Calculate and Review
Click the "Calculate" button to compute the frequency in Hz. The calculator will also display the period and angular frequency, giving you all related parameters. Use these values for your physics calculations or engineering applications.
Formula
f = 1 / T
f = ω / (2π)
ω = 2πf
Where:
• f = Frequency (Hz)
• T = Period (s)
• ω = Angular frequency (rad/s)
• π ≈ 3.14159
Example 1: From Period
A pendulum has a period of 0.5 seconds. Calculate the frequency.
Given:
• Period (T) = 0.5 s
Solution:
f = 1 / T
f = 1 / 0.5
f = 2 Hz
Angular frequency: ω = 2πf = 2π × 2 = 4π ≈ 12.57 rad/s
Example 2: From Angular Frequency
An oscillating system has an angular frequency of 31.42 rad/s. What is the frequency?
Given:
• Angular frequency (ω) = 31.42 rad/s
Solution:
f = ω / (2π)
f = 31.42 / (2Ï€)
f = 31.42 / 6.283
f = 5 Hz
Period: T = 1/f = 1/5 = 0.2 s
Frequently Asked Questions
What is frequency?
Frequency (f) is the number of complete cycles or oscillations that occur per second, measured in hertz (Hz). It's the reciprocal of period: f = 1/T. For example, a frequency of 10 Hz means 10 complete cycles occur every second. Frequency is a fundamental parameter describing periodic motion.
What's the relationship between frequency and period?
Frequency and period are reciprocals of each other: f = 1/T and T = 1/f. Higher frequency means shorter period (faster oscillation), and lower frequency means longer period (slower oscillation). For example, 2 Hz frequency corresponds to 0.5 s period, while 0.5 Hz corresponds to 2 s period.
How do I convert between frequency and angular frequency?
Angular frequency (ω) is related to frequency (f) by: ω = 2πf. To convert frequency to angular frequency, multiply by 2π. To convert angular frequency to frequency, divide by 2π. For example, 10 Hz = 20π rad/s ≈ 62.83 rad/s, and 62.83 rad/s = 10 Hz.
Can frequency be negative?
No, frequency is always positive. It represents the number of cycles per second, which is inherently a positive quantity. However, angular frequency can be negative in some contexts to indicate direction of rotation, but the magnitude (which corresponds to frequency) is always positive.
What if I enter both period and angular frequency?
You should only enter one value - either period OR angular frequency. If you enter both, the calculator will use the first non-empty value. For best results, enter only the value you know and leave the other field blank.
Where is frequency used in real-world applications?
Frequency is used extensively in: AC power systems (60 Hz in North America, 50 Hz in Europe), radio and electromagnetic waves (frequencies determine the wave's properties), musical instruments (pitch is determined by frequency), oscillating systems (pendulums, springs, circuits), signal processing and communications, and analyzing vibrations and resonance in mechanical systems.
About Frequency Calculator
The frequency calculator computes frequency from period using f = 1/T or from angular frequency using f = ω/(2π). Frequency is a fundamental parameter in physics, describing how often periodic events occur.
This calculator is essential for students studying waves and oscillations, engineers working with AC circuits and signals, and anyone analyzing periodic phenomena. It provides conversions between frequency, period, and angular frequency, making it easy to work with different representations of oscillatory motion.