Frequency Wavelength Converter
Convert between frequency and wavelength units including Hz, MHz, GHz, THz, wavelength in meters, nanometers, and particle Compton wavelengths.
Result
100 MHz = 2.99792458 m
Understanding Frequency and Wavelength Units: Hz to Meters to Nanometers
Frequency wavelength converters are essential tools for calculating electromagnetic wave properties, light frequency, and wave characteristics in physics, engineering, telecommunications, and spectroscopy. Whether you're working with hertz (Hz), kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz), petahertz (PHz), exahertz (EHz), wavelength in meters (m), wavelength in nanometers (nm), wavelength in micrometers (µm), Electron Compton wavelength, Proton Compton wavelength, Neutron Compton wavelength, or any of forty frequency and wavelength units, understanding frequency-wavelength conversions is crucial for scientists, engineers, and analysts in physics, engineering, telecommunications, spectroscopy, and electromagnetic wave analysis industries.
Frequency and wavelength measurements quantify electromagnetic wave properties, representing wave characteristics essential for electromagnetic spectrum analysis, light frequency calculations, and wave propagation studies. From low-frequency radio waves at kilohertz to high-frequency gamma rays at exahertz, and from long-wavelength radio waves at kilometers to short-wavelength X-rays at nanometers, this comprehensive converter supports forty frequency and wavelength units with instant, accurate results for all your electromagnetic spectrum, light frequency, and wave calculations across different measurement systems and particle physics applications.
How to Convert Frequency and Wavelength Units: Formulas and Methods
Frequency to Wavelength Conversion
Converting from frequency to wavelength uses the fundamental relationship c = λ × f, where c is the speed of light (299,792,458 m/s), λ is wavelength in meters, and f is frequency in hertz. Rearranging gives λ = c / f. For example, a frequency of 100 MHz equals 100 × 10⁶ Hz, giving wavelength = 299,792,458 / 100,000,000 = 2.998 meters. Converting between frequency units (Hz, kHz, MHz, GHz, THz) and wavelength units (m, cm, mm, µm, nm) helps scientists calculate electromagnetic wave properties and understand the electromagnetic spectrum.
Wavelength to Frequency Conversion
Converting from wavelength to frequency uses f = c / λ, where c is the speed of light (299,792,458 m/s). For example, a wavelength of 500 nm equals 500 × 10⁻⁹ meters, giving frequency = 299,792,458 / 0.0000005 = 599,584,916,000 Hz = 599.585 GHz. Converting wavelength units (m, cm, mm, µm, nm) to frequency units (Hz, kHz, MHz, GHz, THz) helps engineers design communication systems, calculate photon energy, and analyze electromagnetic wave properties in various applications.
SI Prefix Conversions for Frequency
Frequency units use standard SI prefixes: kilohertz (kHz) = 1,000 Hz, megahertz (MHz) = 1,000,000 Hz, gigahertz (GHz) = 1,000,000,000 Hz, terahertz (THz) = 1,000,000,000,000 Hz. For smaller frequencies: millihertz (mHz) = 0.001 Hz, microhertz (µHz) = 0.000001 Hz, nanohertz (nHz) = 0.000000001 Hz. Converting between frequency prefixes helps scientists work with different electromagnetic spectrum ranges, from radio frequencies to gamma rays, and ensures consistent units across different measurement systems.
SI Prefix Conversions for Wavelength
Wavelength units use standard SI prefixes: kilometers (km) = 1,000 m, meters (m) = base unit, centimeters (cm) = 0.01 m, millimeters (mm) = 0.001 m, micrometers (µm) = 0.000001 m, nanometers (nm) = 0.000000001 m. For very large wavelengths: megameters (Mm) = 1,000,000 m, gigameters (Gm) = 1,000,000,000 m. Converting between wavelength prefixes helps engineers work with different electromagnetic wave ranges, from radio waves to gamma rays, and ensures appropriate units for various applications.
Particle Compton Wavelength Conversions
Particle Compton wavelengths are fundamental physical constants: Electron Compton wavelength = 2.426 × 10⁻¹² m, Proton Compton wavelength = 1.321 × 10⁻¹⁵ m, Neutron Compton wavelength = 1.320 × 10⁻¹⁵ m. Converting these to frequency uses f = c / λ, giving frequencies in the exahertz range. For example, Electron Compton wavelength corresponds to approximately 1.236 × 10²⁰ Hz. These conversions are essential in quantum mechanics, particle physics, and high-energy physics applications where particle-wave duality is important.
Electromagnetic Spectrum Applications
The electromagnetic spectrum spans frequencies from below 1 Hz (extremely low frequency) to above 10²⁰ Hz (gamma rays), with corresponding wavelengths from thousands of kilometers to femtometers. Radio waves: 3 kHz - 300 GHz (wavelength 100 km - 1 mm). Microwaves: 300 MHz - 300 GHz (wavelength 1 m - 1 mm). Infrared: 300 GHz - 400 THz (wavelength 1 mm - 750 nm). Visible light: 400-790 THz (wavelength 750-380 nm). Ultraviolet: 750 THz - 30 PHz (wavelength 380-10 nm). X-rays: 30 PHz - 30 EHz (wavelength 10 nm - 10 pm). Gamma rays: above 30 EHz (wavelength below 10 pm). Converting frequency and wavelength units helps scientists and engineers work across the entire electromagnetic spectrum and understand wave properties in different applications.
Frequency Wavelength Conversion Reference Table
| Frequency | Wavelength (m) | Wavelength (nm) | Application |
|---|---|---|---|
| 1 kHz | 299,792 | 2.998e14 | Very low frequency radio |
| 1 MHz | 299.8 | 2.998e11 | AM radio |
| 100 MHz | 3.0 | 3.0e9 | FM radio |
| 1 GHz | 0.30 | 3.0e8 | Microwaves |
| 300 GHz | 0.001 | 1.0e6 | Far infrared |
| 100 THz | 0.000003 | 3,000 | Infrared |
| 400 THz | 0.00000075 | 750 | Red light |
| 500 THz | 0.0000006 | 600 | Green light |
| 700 THz | 0.00000043 | 430 | Blue light |
| 1 PHz | 0.0000003 | 300 | Ultraviolet |
| 1 EHz | 0.0000000003 | 0.3 | X-rays/Gamma rays |
Typical Frequency and Wavelength Values by Application
| Application | Frequency | Wavelength | Description |
|---|---|---|---|
| Power line | 50-60 Hz | 5,000-6,000 km | Electrical power |
| AM radio | 530-1700 kHz | 176-566 m | Broadcast radio |
| FM radio | 88-108 MHz | 2.8-3.4 m | Broadcast radio |
| Wi-Fi | 2.4-5 GHz | 6-12 cm | Wireless networking |
| Visible light | 400-790 THz | 380-750 nm | Human vision |
| X-rays | 30 PHz - 30 EHz | 10 nm - 10 pm | Medical imaging |
| Gamma rays | > 30 EHz | < 10 pm | Nuclear radiation |
| Electron Compton | 1.236e20 Hz | 2.426 pm | Quantum physics |
Industry Applications and Use Cases
Telecommunications and Radio Communications
Telecommunications engineers use frequency-wavelength conversions to design radio systems, calculate antenna sizes, and optimize signal propagation. Typical radio frequencies range from kilohertz to gigahertz, with wavelengths from kilometers to millimeters. Converting between frequency and wavelength units helps engineers design antennas (typically λ/4 or λ/2), calculate propagation characteristics, and ensure appropriate frequency allocation when working with different measurement systems and international communication standards.
Optics and Photonics
Optical engineers calculate frequency-wavelength relationships to design optical systems, analyze light behavior, and optimize optical components. Typical optical frequencies range from terahertz to petahertz, with wavelengths from micrometers to nanometers. Converting between frequency and wavelength units helps engineers design lasers, calculate photon energy (E = hf, where h is Planck's constant), and understand optical phenomena when developing optical communication systems, imaging systems, and photonic devices.
Spectroscopy and Analytical Chemistry
Spectroscopists use frequency-wavelength conversions to analyze molecular structures, identify chemical compounds, and measure spectral properties. Typical spectroscopic frequencies range from megahertz (NMR) to petahertz (UV-Vis), with wavelengths from meters to nanometers. Converting between frequency and wavelength units helps scientists interpret spectra, calculate energy transitions, and compare measurements across different spectroscopic techniques when analyzing materials and compounds.
Quantum Mechanics and Particle Physics
Particle physicists use Compton wavelength conversions to understand particle-wave duality, calculate de Broglie wavelengths, and analyze quantum mechanical systems. Electron, proton, and neutron Compton wavelengths are fundamental constants in quantum mechanics. Converting these to frequencies helps physicists understand particle properties, calculate energy scales, and analyze quantum mechanical interactions when studying atomic and subatomic particles.
Frequently Asked Questions
How do I convert frequency to wavelength?
Use the formula λ = c / f, where c is the speed of light (299,792,458 m/s), λ is wavelength in meters, and f is frequency in hertz. For example, 100 MHz equals 100 × 10⁶ Hz, giving wavelength = 299,792,458 / 100,000,000 = 2.998 meters. Converting frequency units (Hz, kHz, MHz, GHz) to wavelength units (m, cm, mm, nm) helps calculate electromagnetic wave properties.
How do I convert wavelength to frequency?
Use the formula f = c / λ, where c is the speed of light (299,792,458 m/s). For example, 500 nm equals 500 × 10⁻⁹ meters, giving frequency = 299,792,458 / 0.0000005 = 599.585 GHz. Converting wavelength units (m, cm, mm, nm) to frequency units (Hz, kHz, MHz, GHz) helps engineers design communication systems and analyze electromagnetic waves.
What is the relationship between frequency and wavelength?
Frequency and wavelength are inversely related through the speed of light: c = λ × f, where c = 299,792,458 m/s. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. For example, 1 GHz corresponds to 0.3 m wavelength, while 100 THz corresponds to 3 µm wavelength. This relationship is fundamental to understanding the electromagnetic spectrum.
How to convert MHz to nanometers?
First convert MHz to Hz (multiply by 1,000,000), then use λ = c / f to get wavelength in meters, then multiply by 1,000,000,000 to convert to nanometers. For example, 100 MHz = 100,000,000 Hz, wavelength = 299,792,458 / 100,000,000 = 2.998 m = 2,998,000,000 nm. This conversion is useful for optical and photonic applications.
What is Electron Compton wavelength?
Electron Compton wavelength is a fundamental constant equal to 2.426 × 10⁻¹² meters, representing the wavelength of a photon whose energy equals the rest mass energy of an electron. Converting to frequency gives approximately 1.236 × 10²⁰ Hz. This wavelength is important in quantum mechanics and particle physics for understanding particle-wave duality.
How to calculate photon energy from frequency?
Photon energy is calculated using E = hf, where h is Planck's constant (6.626 × 10⁻³⁴ J·s) and f is frequency in hertz. For example, 500 THz gives E = 6.626 × 10⁻³⁴ × 5 × 10¹⁴ = 3.313 × 10⁻¹⁹ J. Converting frequency to wavelength first (using λ = c / f) then calculating energy helps understand the relationship between wave properties and energy in quantum mechanics.
What frequency corresponds to visible light?
Visible light frequencies range from approximately 400 THz (red, 750 nm wavelength) to 790 THz (violet, 380 nm wavelength). Converting these to wavelengths gives 380-750 nm range. This corresponds to the electromagnetic spectrum region visible to the human eye, with red having the lowest frequency (longest wavelength) and violet having the highest frequency (shortest wavelength).
How accurate are frequency-wavelength conversions?
Our converter uses the exact speed of light constant (299,792,458 m/s) with 10-decimal precision. Frequency to wavelength: λ = c / f (exact). Wavelength to frequency: f = c / λ (exact). These conversions ensure precision for scientific and engineering applications in physics, engineering, telecommunications, and spectroscopy. The speed of light in vacuum is an exact constant, making these conversions mathematically precise.
How does frequency affect electromagnetic wave propagation?
Higher frequencies (shorter wavelengths) have different propagation characteristics than lower frequencies (longer wavelengths). Lower frequencies (kHz-MHz) can travel long distances and penetrate obstacles, while higher frequencies (GHz-THz) are more directional and require line-of-sight. Converting frequency to wavelength helps engineers design antennas (typically λ/4 or λ/2), calculate propagation losses, and optimize communication systems for different frequency bands.
What is the electromagnetic spectrum range?
The electromagnetic spectrum spans frequencies from below 1 Hz (extremely low frequency, wavelength thousands of km) to above 10²⁰ Hz (gamma rays, wavelength femtometers). Key ranges include: Radio (3 kHz - 300 GHz, 100 km - 1 mm), Microwaves (300 MHz - 300 GHz, 1 m - 1 mm), Infrared (300 GHz - 400 THz, 1 mm - 750 nm), Visible (400-790 THz, 750-380 nm), Ultraviolet (750 THz - 30 PHz, 380-10 nm), X-rays (30 PHz - 30 EHz, 10 nm - 10 pm), Gamma rays (> 30 EHz, < 10 pm). Converting frequency and wavelength units helps understand the full electromagnetic spectrum.
How to convert between different frequency units?
Frequency units use standard SI prefixes: 1 kHz = 1,000 Hz, 1 MHz = 1,000,000 Hz, 1 GHz = 1,000,000,000 Hz, 1 THz = 1,000,000,000,000 Hz. To convert, multiply by the appropriate factor. For example, 100 MHz = 100 × 1,000,000 = 100,000,000 Hz = 0.1 GHz. Converting between frequency units helps scientists work with different electromagnetic spectrum ranges and ensures consistent units across different measurement systems.
What is de Broglie wavelength?
De Broglie wavelength (λ = h / p, where h is Planck's constant and p is momentum) describes the wave nature of particles. For electrons with kinetic energy, this differs from Compton wavelength. Converting momentum to frequency using f = p² / (2mh) helps understand particle-wave duality in quantum mechanics. Our converter focuses on electromagnetic waves, but the principles apply to particle waves as well.
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