Frequency
Calculate wave frequency from wavelength using f = c / λ. Free online frequency calculator for electromagnetic waves, sound waves, and wave physics. Get instant results with charts.
About This Calculator
The Frequency Calculator converts wavelength into frequency using the wave equation f = v / λ. This tool is ideal for students, engineers, physicists, and anyone working with wave phenomena — from electromagnetic radiation and radio signals to sound waves and mechanical vibrations.
The calculator uses the speed of light in a vacuum (299,792,458 m/s) as the wave velocity. By entering the wavelength in meters, the tool computes the corresponding frequency in Hertz (Hz) and kilohertz (kHz). A breakdown chart visualizes how the wavelength relates to the computed frequency.
Formula
The frequency of a wave is calculated using the fundamental wave equation: f = v / λ, where f is the frequency in Hertz, v is the wave velocity in meters per second (default: speed of light), and λ (lambda) is the wavelength in meters. This formula expresses the inverse relationship between frequency and wavelength — shorter wavelengths correspond to higher frequencies.
Frequency and the Electromagnetic Spectrum
The electromagnetic spectrum spans an enormous range of frequencies. Radio waves have the lowest frequencies (kHz to GHz range), followed by microwaves, infrared, visible light (430–750 THz), ultraviolet, X-rays, and finally gamma rays with frequencies exceeding 1019 Hz. Visible light occupies only a tiny fraction of the full spectrum, from about 400 nm (violet) to 700 nm (red).
Relationship Between Frequency and Energy
Frequency is directly proportional to energy through the Planck-Einstein relation: E = h × f, where h is Planck's constant (6.626 × 10−34 J·s). This means higher-frequency waves carry more energy per photon, which explains why gamma rays are ionizing and dangerous while radio waves are harmless.
Frequently Asked Questions
How do I calculate frequency from wavelength?
Enter the wavelength in meters and click Calculate. The calculator uses the formula f = c / λ, where c is the speed of light (299,792,458 m/s) and λ is the wavelength. The result shows frequency in both Hz and kHz.
What is the formula for frequency?
The fundamental frequency formula is f = 1 / T, where T is the period in seconds. When calculating from wavelength and wave velocity, the formula is f = v / λ, where v is wave velocity and λ is wavelength. For electromagnetic waves in a vacuum, v equals the speed of light.
What is the relationship between frequency and wavelength?
Frequency and wavelength are inversely proportional. When wavelength increases, frequency decreases, and vice versa. This relationship is described by the equation f = v / λ. For example, radio waves have long wavelengths and low frequencies, while gamma rays have short wavelengths and extremely high frequencies.
What units is frequency measured in?
Frequency is measured in Hertz (Hz), which represents cycles per second. Common units include kilohertz (kHz, 10³ Hz), megahertz (MHz, 10⁶ Hz), gigahertz (GHz, 10⁹ Hz), and terahertz (THz, 10¹² Hz). The unit is named after Heinrich Hertz, who proved the existence of electromagnetic waves.
How is the frequency of light calculated?
Light frequency is calculated using f = c / λ, where c is the speed of light in a vacuum (299,792,458 m/s). For example, red light with a wavelength of 700 nm has a frequency of approximately 428 THz, while violet light at 400 nm has a frequency of about 749 THz.
What is the relationship between frequency and energy?
Energy is directly proportional to frequency, described by the Planck-Einstein relation E = h × f, where h is Planck's constant (6.626 × 10⁻³⁴ J·s). Higher frequency waves carry more energy. This is why gamma rays (highest frequency) are the most energetic and dangerous electromagnetic waves.
Can this calculator handle different types of waves?
Yes, you can calculate frequency for any type of wave — electromagnetic waves, sound waves, water waves, or any periodic motion. The calculator uses f = v / λ with the speed of light as default, but you can compute frequency for waves in any medium by entering the appropriate wavelength.