Frequency Calculator
Frequency Calculator
Results
Common Frequencies
AC Power: 50-60 Hz
AM Radio: 530-1700 kHz
FM Radio: 88-108 MHz
WiFi: 2.4-5 GHz
Light Spectrum
Red Light: ~430 THz
Green Light: ~540 THz
Blue Light: ~670 THz
X-rays: ~10¹⁸ Hz
Key Relationships
- Period-Frequency: T = 1/f and f = 1/T
- Angular Frequency: ω = 2πf (radians/second)
- Angular Period: T = 2π/ω (seconds)
- Wavelength: λ = v/f (where v is wave velocity)
- Angular Wavelength: k = 2π/λ (wavenumber, radians/meter)
Practical Applications
Electronics
For a 555 timer circuit with R = 10kΩ and C = 0.1μF:
f = 1/T = 1/0.000693 = 1443 Hz
Audio Engineering
For middle C note (C4) with frequency 261.63 Hz:
λ = v/f = 343/261.63 = 1.31 meters (wavelength in air)
Radio Communications
For an FM radio station at 98.5 MHz:
λ = v/f = 300,000,000/98,500,000 = 3.05 meters
How Frequency, Period and Wavelength Are Related
Frequency (f) counts how many complete cycles of a repeating wave pass a fixed point each second, measured in hertz (Hz). Period (T) is the time one of those cycles takes. They are reciprocals — nothing more — so a wave that repeats 50 times a second must take 1/50 s = 20 ms per cycle. Every other quantity on this page follows from those two.
Angular frequency (ω) restates the same rate in radians per second rather than cycles per second. One full cycle is 2π radians, so ω=2πf. It appears throughout AC circuit analysis because the reactance of a capacitor (XC=1/ωC) and an inductor (XL=ωL) are written in terms of ω, not f.
Wavelength (λ) is the physical distance the wave travels during one period, so λ=v×T=v/f, where v is the propagation speed in the medium the wave is travelling through. That last qualifier is the part most people get wrong, and it is explained in its own section below.
Formula reference
| Quantity | Formula | SI unit |
|---|---|---|
| Period from frequency | T = 1 / f | second (s) |
| Frequency from period | f = 1 / T | hertz (Hz) |
| Angular frequency | ω = 2πf | radian/second |
| Wavelength | λ = v / f | metre (m) |
| Wavenumber | k = 2π / λ | radian/metre |
| Photon energy | E = h f | joule (J) |
The constants this calculator uses are the exact SI definitions: the speed of light in vacuum c = 299,792,458 m/s, the Planck constant h = 6.62607015×10−34 J·s, and 1 eV = 1.602176634×10−19 J. For sound in air it assumes 343 m/s, the speed at roughly 20 °C.
Why the Medium Changes Wavelength but Never Frequency
When a wave crosses from one medium into another — light entering glass, sound passing from air into water, a signal moving from free space into a coaxial cable — its frequency does not change. Frequency is fixed by whatever is generating the wave, and the far side of a boundary cannot make cycles appear or disappear. What changes is the propagation speed v, and because λ=v/f with f held constant, the wavelength changes in exact proportion to the speed.
This has direct practical consequences. A signal travelling in coax with a velocity factor of 0.66 moves at 66% of the speed of light, so a quarter-wave stub cut for that cable is 34% shorter than the free-space calculation suggests — a classic source of mistuned antennas and filters. The same effect explains why a 1 kHz tone has a 34.3 cm wavelength in air but roughly 1.5 m in water, where sound travels about four times faster.
So when you enter a wave speed in the wavelength tab, you are not choosing a cosmetic preference — you are choosing the medium, and the answer is only as right as that number is.
Worked Examples — Explained in Full
Frequently Asked Questions
What is the formula for frequency?
Frequency is the reciprocal of the period: f = 1/T, where T is the time for one complete cycle in seconds and f is in hertz (Hz). A cycle lasting 20 milliseconds therefore corresponds to 1/0.020 = 50 Hz.
How do I convert a period into a frequency?
Divide 1 by the period expressed in seconds. The only common mistake is forgetting to convert the period first: 5 ms must be entered as 0.005 s, giving 200 Hz, not 1/5 = 0.2 Hz.
What is the difference between frequency and angular frequency?
Frequency f counts complete cycles per second (Hz); angular frequency ω measures the same rate in radians per second, and one cycle equals 2π radians, so ω = 2πf. Angular frequency is used in AC analysis because capacitive and inductive reactance are defined as 1/ωC and ωL.
How do I calculate wavelength from frequency?
Divide the propagation speed in the medium by the frequency: λ = v/f. Use c = 299,792,458 m/s for electromagnetic waves in vacuum or air, and about 343 m/s for sound in air at 20 °C. Using the wrong speed is the single most common source of wrong wavelength answers.
Does a wave change frequency when it enters a different medium?
No. Frequency is set by the source, so it stays the same across a boundary. The propagation speed changes, and since λ = v/f with f fixed, the wavelength changes in exact proportion to the speed. This is why a quarter-wave stub in coaxial cable is shorter than the free-space calculation predicts.
Why is the wavelength of 50 Hz mains power almost 6,000 km?
Because wavelength is c/f, and 50 Hz is an extremely low frequency: 299,792,458/50 ≈ 5,996 km. Since even a national grid is far shorter than one wavelength, voltages and currents are effectively in phase along the line and ordinary circuit theory applies instead of transmission-line theory.
What wave speed should I use for sound?
About 343 m/s for air at roughly 20 °C. The speed of sound in air rises by roughly 0.6 m/s per °C, so it is about 331 m/s at 0 °C. Sound travels far faster in denser media — roughly 1,480 m/s in water and about 5,000 m/s in steel.
How is photon energy related to frequency?
By the Planck relation E = hf, with h = 6.62607015×10−34 J·s. Dividing the result by 1.602176634×10−19 converts joules to electronvolts. Energy is proportional to frequency, so higher-frequency radiation carries more energy per photon — the reason ultraviolet light can break chemical bonds that visible light cannot.
What is a wavenumber and when is it used?
The wavenumber k = 2π/λ expresses spatial frequency in radians per metre, the spatial counterpart of angular frequency in time. It appears in wave equations, transmission-line analysis and spectroscopy, where it compactly describes how much the phase advances per unit distance.
Why are antenna lengths usually a quarter of the wavelength?
A quarter-wave element placed above a ground plane presents a convenient, near-resistive impedance at its feed point and resonates naturally at the design frequency, which makes matching to a standard 50 Ω feed straightforward. That is why a 98.5 MHz FM whip is about 76 cm while a 2.4 GHz Wi-Fi element is only about 3 cm.
Why does switching frequency matter so much in a power converter?
The period T = 1/f sets how long the switch conducts each cycle, which fixes the inductor volt-second product and therefore the ripple current and magnetic size. Raising the frequency shrinks the magnetics but increases switching and gate-drive losses, so the choice is a direct trade between size and efficiency.