Calculate wavelength, velocity, or frequency using λ = v/f or λ = c/f for electromagnetic waves. Free online waves calculator for physics and engineering with multiple unit support.
Calculate wavelength, velocity, or frequency using λ = v/f
Copy the code below to embed this calculator on your website
Wavelength is one of the most fundamental concepts in wave physics, optics, and electromagnetic theory. It describes the distance between consecutive points of the same phase in a wave, such as the distance between two peaks or two troughs. Whether you're studying physics, engineering, working with light, sound, or radio waves, understanding wavelength is essential. Our Wavelength Calculator makes it easy to calculate wavelength, velocity, or frequency using the fundamental formula: λ = v/f (wavelength equals velocity divided by frequency).
Wavelength determines many properties of waves, including color (for light), pitch (for sound), and the ability to interact with objects. It's crucial for understanding everything from visible light and radio waves to sound waves and water waves. Our calculator supports both general waves and electromagnetic waves, automatically using the speed of light for electromagnetic calculations.
Our Wavelength Calculator offers two calculation modes for maximum flexibility. Follow these steps:
The wavelength formula is one of the most important equations in wave physics:
λ = v / f
Where: λ = wavelength, v = velocity, f = frequency
λ = c / f
Where: c = speed of light (299,792,458 m/s)
Wavelength (λ) is the spatial period of a wave - the distance over which the wave's shape repeats. It's measured as the distance between:
Wavelength calculations are used in countless real-world scenarios across various fields:
It's crucial to use consistent units in your calculations. Our calculator supports multiple unit systems and automatically converts between them:
Note: Nanometers (nm) are commonly used for visible light wavelengths (400-700 nm)
Tip: The calculator automatically handles unit conversions, so you can mix different unit systems. For example, you can input wavelength in nanometers, frequency in THz, and get velocity in m/s.
What is the wavelength of red light with a frequency of 4.3 × 10¹⁴ Hz? (Electromagnetic wave)
λ = c / f = 299,792,458 m/s / 4.3 × 10¹⁴ Hz = 6.97 × 10⁻⁷ m = 697 nm
This is indeed in the red light range (620-750 nm)
A radio station broadcasts at a wavelength of 3.41 m. What is its frequency?
f = c / λ = 299,792,458 m/s / 3.41 m = 87.9 MHz
This is in the FM radio band (88-108 MHz)
What is the wavelength of a sound wave with frequency 440 Hz traveling in air at 343 m/s?
λ = v / f = 343 m/s / 440 Hz = 0.779 m = 77.9 cm
This is the wavelength of the musical note A4 (440 Hz)
A wave has a wavelength of 2.5 m and a frequency of 120 Hz. What is its velocity?
v = λ × f = 2.5 m × 120 Hz = 300 m/s
Calculate the frequency of blue light with wavelength 450 nm.
f = c / λ = 299,792,458 m/s / (450 × 10⁻⁹ m) = 6.66 × 10¹⁴ Hz = 666 THz
The electromagnetic spectrum spans a wide range of wavelengths:
All electromagnetic waves travel at the speed of light (c) in vacuum, so wavelength and frequency are inversely related: shorter wavelength = higher frequency = higher energy.
Wavelength changes when waves enter different media, but frequency remains constant:
When a wave enters a medium where it travels slower, the wavelength decreases proportionally, but frequency stays the same. This is why objects appear shifted when viewed through water or glass.
Understanding wavelength has practical applications in daily life:
Wavelength (λ) equals velocity (v) divided by frequency (f): λ = v/f. This means wavelength is inversely proportional to frequency - higher frequency waves have shorter wavelengths. For electromagnetic waves, velocity is the speed of light (c), so λ = c/f. You can rearrange this to solve for velocity (v = λ × f) or frequency (f = v/λ).
For visible light, nanometers (nm) are most common (400-700 nm range). For radio waves, meters are used. For very short wavelengths (X-rays, gamma rays), picometers or smaller units are used. Meters (m) are the SI base unit. The choice depends on the wavelength range - nanometers for light, meters for radio, micrometers for infrared.
For visible light, wavelength directly determines color. Violet light has the shortest wavelengths (around 400-450 nm), while red light has the longest (around 620-750 nm). The visible spectrum spans approximately 400-700 nm. Shorter wavelengths appear blue/violet, longer wavelengths appear red/orange. White light contains all visible wavelengths.
Wavelength (λ) is a distance measurement - the spatial period of a wave. Frequency (f) is a time measurement - how many cycles occur per second. They're inversely related: λ = v/f. Higher frequency means shorter wavelength (for constant velocity). Frequency is measured in Hz, wavelength in meters or nanometers.
Wavelength changes because wave velocity changes in different media, but frequency remains constant. When light enters water, it slows down (velocity decreases), so wavelength decreases proportionally. The relationship λ = v/f means if v decreases and f stays constant, λ must decrease. This is why objects appear shifted when viewed through water or glass.
The speed of light in vacuum (c) is 299,792,458 m/s (approximately 3 × 10⁸ m/s). It's a fundamental constant of nature. According to Einstein's theory of relativity, the speed of light in vacuum is constant for all observers, regardless of their motion. This constancy is why electromagnetic waves always use c in the formula λ = c/f.
For sound waves, use λ = v/f where v is the speed of sound in the medium. Sound speed in air at 20°C is approximately 343 m/s. So for a 440 Hz sound wave in air: λ = 343 m/s / 440 Hz = 0.779 m. Sound speed varies with temperature and medium - faster in water (≈1500 m/s) and solids.
The visible spectrum for humans ranges from approximately 380-400 nm (violet) to 700-750 nm (red). This corresponds to frequencies of about 400-790 THz. Different animals see different ranges - some can see ultraviolet (shorter than 400 nm) or infrared (longer than 700 nm). The peak sensitivity for human vision is around 555 nm (green-yellow).
Understanding wavelength and the relationship λ = v/f is fundamental to wave physics, optics, and electromagnetic theory. Our Wavelength Calculator simplifies these calculations, making it easy to solve problems involving light, sound, radio waves, and other wave phenomena.
Whether you're calculating wavelengths for electromagnetic waves, analyzing sound waves, or working with any wave phenomenon, this calculator provides accurate results with support for multiple unit systems and both general and electromagnetic wave modes. Ready to explore more physics concepts? Check out our other calculators like the Velocity Calculator for motion calculations, or use our Acceleration Calculator for acceleration problems that often complement wave analysis.
Get instant results with our optimized calculation engine
Precise calculations you can trust for any project
Works perfectly on all devices and screen sizes