Frequency Calculator
Frequency is how many cycles, oscillations, or waves happen each second, measured in hertz. This calculator finds frequency from a period of time, from a wave speed and wavelength, or from revolutions per minute, and also returns the period and angular frequency for you.
Formula
Worked example
A pendulum with a period of 0.02 s has a frequency of 1 ÷ 0.02 = 50 Hz, an angular frequency of 2π × 50 ≈ 314.16 rad/s. A sound wave at 343 m/s with a 0.5 m wavelength has f = 343 ÷ 0.5 = 686 Hz. An engine at 3000 RPM turns at 3000 ÷ 60 = 50 Hz.
How frequency is calculated
Frequency counts how many complete cycles of a repeating event happen in one second, and its unit is the hertz (Hz), where one hertz is one cycle per second. The most direct way to find it is from the period, the time a single cycle takes, using f = 1 ÷ T. If the period is measured in seconds, the frequency comes out in hertz automatically. For a wave moving through space, frequency relates to how fast the wave travels and how long each wave is, through f = v ÷ λ, where v is the wave speed and λ (lambda) is the wavelength. For anything that spins, revolutions per minute convert to hertz by dividing by 60, since a minute holds 60 seconds. All three routes describe the same underlying quantity from different starting information.
Period, angular frequency and unit scaling
The period T and the frequency f are reciprocals of each other: if you know one, you know the other. A period of 0.5 seconds corresponds to a frequency of 2 Hz, and a frequency of 100 Hz corresponds to a period of 0.01 seconds. Angular frequency ω measures the same oscillation in radians per second and equals 2π times the ordinary frequency, ω = 2πf, because one full cycle sweeps 2π radians. This calculator reports the period and angular frequency alongside the result, and automatically scales large or small values into kilohertz, megahertz, gigahertz, or millihertz so the number stays readable.
Wave speed, wavelength and where frequency matters
Wavelength is the spatial counterpart of the period, the distance over which a wave shape repeats, typically measured from one crest to the next. Because wave speed equals frequency multiplied by wavelength (v = f λ), a faster wave or a shorter wavelength both push the frequency higher, which is why high-pitched sounds and high-energy light have short wavelengths. The wave mode here includes presets for sound in air, water, and steel and for light in a vacuum, or you can enter a custom speed. Frequency appears across physics and engineering: it sets musical pitch in the 20 Hz to 20,000 Hz audible range, drives 50 or 60 Hz mains power, defines radio and Wi-Fi bands in the megahertz and gigahertz range, and fixes the natural frequency of pendulums, springs, and rotating machinery.
Common frequencies and what they mean
| Source | Approximate frequency | Range |
|---|---|---|
| Earth rotation | ~0.0000116 Hz | Very low |
| Mains electricity (Europe) | 50 Hz | Low |
| Lowest audible sound | 20 Hz | Low |
| Middle C (musical note) | ~262 Hz | Audible |
| Highest audible sound | 20,000 Hz | High |
| FM radio broadcast | ~100,000,000 Hz | Very high |
| Wi-Fi (2.4 GHz band) | ~2,400,000,000 Hz | Very high |
Frequency is always measured in hertz (Hz), cycles per second. One kilohertz (kHz) is 1,000 Hz, one megahertz (MHz) is 1,000,000 Hz, and one gigahertz (GHz) is 1,000,000,000 Hz.
Frequently asked questions
What is the formula for frequency?
Frequency is the number of cycles per second. From a period, use f = 1 ÷ T, where T is the time for one cycle in seconds. For a travelling wave, use f = v ÷ λ, where v is the wave speed and λ is the wavelength. For a spinning object, use f = RPM ÷ 60. Every result is in hertz (Hz).
How do I convert RPM to hertz?
Divide the revolutions per minute by 60, because there are 60 seconds in a minute and one hertz is one cycle (revolution) per second. For example, 3,000 RPM ÷ 60 = 50 Hz, and 1,800 RPM ÷ 60 = 30 Hz. To go back the other way, multiply the frequency in hertz by 60.
What is angular frequency and how does it relate to frequency?
Angular frequency ω measures rotation or oscillation in radians per second rather than cycles per second. It equals 2π times the ordinary frequency, ω = 2πf, because each complete cycle covers 2π radians. A 50 Hz signal therefore has an angular frequency of 2π × 50 ≈ 314.16 rad/s. This calculator shows it automatically.
What unit is frequency measured in?
The SI unit of frequency is the hertz (Hz), defined as one cycle per second. Larger frequencies are expressed in kilohertz (1 kHz = 1,000 Hz), megahertz (1 MHz = 1,000,000 Hz), and gigahertz (1 GHz = 1,000,000,000 Hz), which is common for radio and computer clock speeds. The calculator scales the result into the most readable of these units for you.