Wavelength Calculator
Calculate the wavelength of a wave using the formula λ = v/f, where v is the wave speed and f is the frequency. Works for sound waves, light, radio waves, and any periodic wave. See also our Frequency Calculator and Speed of Sound Calculator.
How to Calculate Wavelength
Wavelength is the spatial period of a wave — the distance between consecutive corresponding points (such as two adjacent crests or troughs). It is one of the most fundamental properties of any wave, whether it's a sound wave, light wave, water wave, or seismic wave. Wavelength is typically denoted by the Greek letter lambda (λ) and measured in meters (or appropriate sub-units like nanometers for light).
To calculate wavelength, divide the wave speed by the frequency: λ = v/f. This simple relationship connects three fundamental wave properties. For sound in air at 20°C, use v = 343 m/s. For electromagnetic waves (light, radio, etc.) in vacuum, use v = c = 299,792,458 m/s. For sound in water, use v ≈ 1,480 m/s. The wave speed depends on the medium's properties — temperature, density, and elasticity all play roles.
Wavelength determines how waves interact with objects and environments. Waves diffract (bend around obstacles) most effectively when the obstacle size is comparable to the wavelength. This is why low-frequency sounds (long wavelength) travel around corners easily, while high-frequency sounds (short wavelength) are easily blocked. Similarly, radio waves (meters) pass through walls, while light (nanometers) does not. This principle governs antenna design, acoustic engineering, and optical systems.
For electromagnetic radiation, wavelength determines the type of radiation and its properties. Radio waves have wavelengths from millimeters to kilometers. Visible light spans 390-700 nanometers (violet to red). X-rays have wavelengths of 0.01-10 nm. The energy of a photon is inversely proportional to wavelength: E = hc/λ, where h is Planck's constant. Shorter wavelengths mean higher energy — this is why UV, X-rays, and gamma rays can damage biological tissue while radio waves cannot.
Wavelength Formula
Basic wavelength formula:
λ = v / f
From period:
λ = v × T
Wave number:
k = 2π / λ (spatial frequency)
Photon energy (electromagnetic):
E = hf = hc/λ
h = 6.626×10⁻³⁴ J⋅s (Planck's constant)
De Broglie wavelength (matter):
λ = h / (mv) = h / p
Wavelength in different media:
λ_medium = λ_vacuum / n
n = refractive index of medium
Example Calculation
Calculate the wavelength of concert A (440 Hz) in air at 20°C:
Given: f = 440 Hz, v = 343 m/s (sound in air at 20°C)
λ = v/f = 343/440 = 0.7795 m ≈ 78 cm
Same note in water (v = 1480 m/s):
λ = 1480/440 = 3.364 m (much longer!)
Same frequency as electromagnetic wave:
λ = 3×10⁸/440 = 681,818 m ≈ 682 km (radio wave)
For visible green light (λ = 530 nm):
f = c/λ = 3×10⁸/(530×10⁻⁹) = 5.66×10¹⁴ Hz
Energy: E = hf = 6.626×10⁻³⁴ × 5.66×10¹⁴ = 3.75×10⁻¹⁹ J
Wavelength Reference Table
| Wave Type | Frequency | Speed | Wavelength |
|---|---|---|---|
| AM Radio (1 MHz) | 1,000,000 | 3×10⁸ | 300 m |
| FM Radio (100 MHz) | 100,000,000 | 3×10⁸ | 3 m |
| Microwave (2.4 GHz) | 2.4×10⁹ | 3×10⁸ | 12.5 cm |
| Infrared | 3×10¹³ | 3×10⁸ | 10 µm |
| Red light | 4.3×10¹⁴ | 3×10⁸ | 700 nm |
| Green light | 5.7×10¹⁴ | 3×10⁸ | 530 nm |
| Blue light | 6.7×10¹⁴ | 3×10⁸ | 450 nm |
| Concert A (sound) | 440 | 343 | 0.78 m |
| Middle C (sound) | 261.6 | 343 | 1.31 m |
| Ultrasound (5 MHz) | 5,000,000 | 1540 | 0.31 mm |
Frequently Asked Questions
What is wavelength?
Wavelength is the distance between two consecutive identical points on a wave — typically measured from crest to crest or trough to trough. It represents one complete spatial cycle of the wave. Wavelength is inversely proportional to frequency: higher frequency waves have shorter wavelengths. For electromagnetic waves, wavelength determines the type of radiation (radio, microwave, infrared, visible, UV, X-ray, gamma). For sound, wavelength determines how the wave interacts with rooms and obstacles.
Why does wavelength change in different media?
When a wave enters a different medium, its speed changes but its frequency remains constant (frequency is set by the source). Since λ = v/f, if speed decreases and frequency stays the same, wavelength must decrease. Light entering glass (n ≈ 1.5) slows to 2/3 of its vacuum speed, so its wavelength shrinks to 2/3 as well. Sound entering water speeds up (1480 vs 343 m/s), so its wavelength increases by about 4.3×. This wavelength change is responsible for refraction (bending of waves at interfaces).
What determines the color of light?
The color of visible light is determined by its wavelength (or equivalently, frequency). Red light has the longest visible wavelength (~700 nm) and lowest frequency. Violet has the shortest (~390 nm) and highest frequency. The visible spectrum in order: red (700 nm), orange (620 nm), yellow (580 nm), green (530 nm), blue (470 nm), violet (390 nm). White light contains all visible wavelengths. When light enters a prism, different wavelengths refract by different amounts, separating into a rainbow spectrum.
What is the de Broglie wavelength?
Louis de Broglie proposed in 1924 that all matter has wave-like properties, with wavelength λ = h/p = h/(mv), where h is Planck's constant and p is momentum. For everyday objects, this wavelength is incredibly tiny (a baseball has λ ≈ 10⁻³⁴ m — undetectable). But for electrons, λ can be comparable to atomic spacing, enabling electron microscopy and explaining atomic structure. The de Broglie wavelength is fundamental to quantum mechanics and explains why electrons form standing waves in atoms (quantized energy levels).
How does wavelength affect antenna design?
Antennas are most efficient when their size is comparable to the wavelength they transmit or receive (typically λ/4 or λ/2). FM radio (λ ≈ 3 m) uses antennas about 75 cm long. Cell phones (λ ≈ 15 cm at 2 GHz) have small internal antennas. AM radio (λ ≈ 300 m) requires very tall towers or uses ground-plane effects. WiFi (λ ≈ 12.5 cm) uses compact antennas. Satellite dishes focus short-wavelength signals (cm range) using parabolic reflectors. This wavelength-size relationship is fundamental to all wireless communication design.
What is the relationship between wavelength and energy?
For electromagnetic radiation, photon energy is inversely proportional to wavelength: E = hc/λ = hf. Shorter wavelengths carry more energy per photon. This is why ultraviolet light causes sunburn (high energy photons damage DNA) while radio waves are harmless (low energy). X-rays and gamma rays have enough energy to ionize atoms. In quantum mechanics, this energy-wavelength relationship explains the photoelectric effect, atomic spectra, and why heated objects change color (from red to white as temperature increases).
Wavelength in Science and Technology
Wavelength measurements are fundamental to spectroscopy — the study of how matter interacts with electromagnetic radiation. Each element emits and absorbs light at specific wavelengths, creating unique spectral "fingerprints." This allows astronomers to determine the composition of distant stars, chemists to identify unknown substances, and environmental scientists to monitor atmospheric gases. Spectroscopy is one of the most powerful analytical tools in science.
In telecommunications, wavelength division multiplexing (WDM) sends multiple data streams through a single optical fiber, each on a different wavelength of light. Modern fiber optic systems can carry over 100 wavelengths simultaneously, each carrying 100+ Gbps of data. This technology forms the backbone of the internet, enabling the massive data flows that support streaming, cloud computing, and global communications.