About Wavelength Calculator
What This Calculator Does
Wavelength Calculator is a comprehensive physics tool that performs calculations across six distinct areas of wave physics. Each calculator tab addresses a specific type of wave calculation:
Wave Basics
The fundamental wave calculator uses the core relationship between wavelength, frequency, and wave speed (λ = v/f). You can solve for any of the three variables given the other two. For electromagnetic waves, the calculator defaults to the speed of light, making it easy to convert between frequency and wavelength for radio waves, visible light, X-rays, and other EM radiation. The calculator also classifies your result on the electromagnetic spectrum and displays the corresponding color for visible light wavelengths.
De Broglie Wavelength
This tab calculates the quantum mechanical wavelength of matter using the de Broglie equation (λ = h/mv). You can calculate wavelengths for electrons, protons, neutrons, or any custom particle by specifying its mass. The calculator accepts velocities in meters per second or as a fraction of the speed of light, which is useful for relativistic particles in physics experiments.
Photon Energy ↔ Wavelength
Convert between photon energy and wavelength using the Planck-Einstein relation (E = hc/λ). This bidirectional calculator accepts energy in electron volts (eV), kiloelectron volts (keV), megaelectron volts (MeV), or joules, and wavelength in various units from nanometers to meters. The calculator displays the corresponding frequency and electromagnetic spectrum classification.
Sound Wavelength
Calculate acoustic wavelengths in different media including air, water, and steel. For air, the calculator accounts for temperature effects on the speed of sound using the approximation v = 331.3 + 0.606T (where T is temperature in Celsius). The calculator displays wavelength in multiple units and identifies the nearest musical note for audio frequencies.
Antenna Length
Designed for radio frequency applications, this calculator determines the physical length of quarter-wave, half-wave, and full-wave antennas. It includes a velocity factor adjustment (typically 0.95 for wire antennas, 0.66 for coaxial cable) to account for the slower propagation of electromagnetic waves in physical conductors compared to free space.
Wavenumber Conversion
Convert between wavelength and wavenumber, a quantity commonly used in spectroscopy. The calculator provides both spectroscopic wavenumber (k = 1/λ, typically in cm⁻¹) and angular wavenumber (k = 2π/λ in rad/m), which are used in different physics and chemistry contexts.
The Science Behind It
All calculations in this tool are based on well-established physics equations that have been verified through decades of experimental physics and engineering practice.
Core Formulas
The fundamental wave equation λ = v/f describes all wave phenomena, from ocean waves to gamma rays. For electromagnetic waves traveling through vacuum, the velocity equals the speed of light (c = 299,792,458 m/s exactly, as defined by the International System of Units since 1983).
The de Broglie wavelength equation λ = h/p = h/(mv) was proposed by Louis de Broglie in 1924 and earned him the Nobel Prize in Physics in 1929. This equation describes the wave-particle duality of matter and is fundamental to quantum mechanics.
The Planck-Einstein relation E = hf = hc/λ connects photon energy to frequency and wavelength. This relationship, developed by Max Planck and Albert Einstein in the early 1900s, is the foundation of quantum physics and explains phenomena like the photoelectric effect.
Physical Constants Used
This calculator uses the 2019 SI values for physical constants:
| Constant | Symbol | Value | Source |
|---|---|---|---|
| Speed of light | c | 299,792,458 m/s | Exact (SI definition) |
| Planck constant | h | 6.62607015 × 10⁻³⁴ J·s | Exact (2019 SI) |
| Planck constant (eV) | h | 4.135667696 × 10⁻¹⁵ eV·s | Derived |
| Electron mass | me | 9.1093837 × 10⁻³¹ kg | CODATA 2018 |
| Proton mass | mp | 1.6726219 × 10⁻²⁷ kg | CODATA 2018 |
| Neutron mass | mn | 1.6749275 × 10⁻²⁷ kg | CODATA 2018 |
| hc product | hc | 1240 eV·nm | Derived |
Speed of Sound in Different Media
| Medium | Speed (m/s) | Speed (ft/s) | Temperature |
|---|---|---|---|
| Air | 331.3 + 0.606T | — | Variable (T in °C) |
| Air (0°C) | 331 | 1,087 | 0°C |
| Air (20°C) | 343 | 1,127 | 20°C |
| Water | 1,480 | 4,856 | 20°C |
| Steel | 5,960 | 19,554 | 20°C |
| Glass | 5,640 | 18,504 | 20°C |
| Aluminum | 6,420 | 21,063 | 20°C |
Electromagnetic Spectrum Boundaries
The calculator classifies wavelengths using these standard boundaries:
| Region | Wavelength Range | Frequency Range | Common Applications |
|---|---|---|---|
| Gamma rays | < 10 pm | > 30 EHz | Cancer treatment, sterilization |
| X-rays | 10 pm – 10 nm | 30 PHz – 30 EHz | Medical imaging, crystallography |
| Ultraviolet | 10 nm – 400 nm | 750 THz – 30 PHz | Sterilization, fluorescence |
| Visible light | 400 nm – 700 nm | 430 THz – 750 THz | Human vision, photography |
| Infrared | 700 nm – 1 mm | 300 GHz – 430 THz | Thermal imaging, remote controls |
| Microwaves | 1 mm – 1 m | 300 MHz – 300 GHz | Radar, cooking, WiFi |
| Radio waves | > 1 m | < 300 MHz | Broadcasting, communication |
Formulas at a Glance
Every formula used in this calculator, organized by tab:
| Calculator Tab | Formula | Variables | Use Case |
|---|---|---|---|
| Wave Basics | λ = v / f | λ = wavelength, v = speed, f = frequency | EM waves, general wave calculations |
| De Broglie | λ = h / (m × v) | h = Planck constant, m = mass, v = velocity | Electron/particle wavelengths |
| Energy↔λ | E = hc / λ | E = energy, h = Planck constant, c = speed of light | Photon energy conversions |
| Sound | λ = v_sound / f | v = 331.3 + 0.606T (air) | Acoustic wavelength in media |
| Antenna | L = (c / f) × VF / n | VF = velocity factor, n = fraction (2 or 4) | Antenna element sizing |
| Wavenumber | k = 1 / λ | k in cm⁻¹ (spectroscopic) or rad/m (angular) | Spectroscopy conversions |
Supported Units
The calculator supports a wide range of units across all tabs:
Frequency Units
| Unit | Symbol | In Hertz | Typical Use |
|---|---|---|---|
| Hertz | Hz | 1 | Audio, low-frequency signals |
| Kilohertz | kHz | 10³ | AM radio, audio sampling |
| Megahertz | MHz | 10⁶ | FM radio, amateur radio |
| Gigahertz | GHz | 10⁹ | WiFi, cellular, radar |
| Terahertz | THz | 10¹² | Infrared, visible light |
Wavelength Units
| Unit | Symbol | In Meters | Typical Use |
|---|---|---|---|
| Kilometer | km | 10³ | VLF/ELF radio waves |
| Meter | m | 1 | Radio waves, sound |
| Centimeter | cm | 10⁻² | Microwaves |
| Millimeter | mm | 10⁻³ | Millimeter waves |
| Micrometer | μm | 10⁻⁶ | Infrared radiation |
| Nanometer | nm | 10⁻⁹ | Visible light, UV |
| Angstrom | Å | 10⁻¹⁰ | X-rays, atomic scales |
| Foot | ft | 0.3048 | Antenna dimensions |
| Inch | in | 0.0254 | Antenna dimensions |
Energy Units
| Unit | Symbol | In Joules | Typical Use |
|---|---|---|---|
| Electron volt | eV | 1.602 × 10⁻¹⁹ | Visible/UV photons |
| Kiloelectron volt | keV | 1.602 × 10⁻¹⁶ | X-ray photons |
| Megaelectron volt | MeV | 1.602 × 10⁻¹³ | Gamma rays, nuclear |
| Joule | J | 1 | SI energy unit |
Who This Is For
This calculator serves a wide range of users who need to work with wave physics:
- Physics students studying wave mechanics, quantum physics, or electromagnetism who need to verify homework calculations or explore wave relationships
- Amateur radio operators calculating antenna dimensions for specific frequencies
- Audio engineers and musicians working with sound wavelengths for room acoustics, speaker placement, or instrument design
- Chemistry and spectroscopy students converting between wavelength and wavenumber for spectral analysis
- Teachers and educators demonstrating wave physics concepts
- Engineers working with RF systems, optical systems, or acoustic applications
- Science enthusiasts curious about the relationships between different wave properties
Our Methodology
The calculations performed by this tool follow standard physics methodologies used in educational and professional settings:
Unit conversions use exact conversion factors where defined (such as metric prefixes) and standard approximate values where applicable (such as the speed of sound varying with temperature and medium).
Electromagnetic spectrum classification follows generally accepted boundaries: gamma rays below 10 pm, X-rays from 10 pm to 10 nm, ultraviolet from 10 nm to 400 nm, visible light from 400 nm to 700 nm, infrared from 700 nm to 1 mm, microwaves from 1 mm to 1 m, and radio waves above 1 m. Note that these boundaries are conventions and can vary slightly between sources.
Sound speed in air is calculated using the linear approximation v = 331.3 + 0.606T m/s, which is accurate for typical atmospheric conditions. More precise calculations would account for humidity and pressure, but this approximation is sufficient for most practical applications.
Antenna calculations use the standard velocity factor approach recognized in amateur radio and RF engineering. The physical length of an antenna differs from the theoretical electrical length due to the finite diameter of conductors and end effects.
Limitations and Disclaimer
While this calculator provides accurate results based on established physics equations, please be aware of its limitations:
- Results are theoretical calculations that may not account for all real-world factors in your specific situation
- The de Broglie calculator uses non-relativistic equations; for particles approaching the speed of light, relativistic corrections are needed
- Sound speed calculations assume ideal conditions; actual values depend on humidity, pressure, and material properties
- Antenna calculations provide starting points; actual antenna tuning requires measurement and adjustment
- All electromagnetic spectrum boundaries are approximate and follow common conventions
This calculator is provided for educational and reference purposes only. For professional applications in engineering, research, or safety-critical systems, always verify calculations independently and consult qualified professionals. Do not rely solely on this or any online calculator for decisions that could affect health, safety, or significant financial investments.
How to Use the Calculator
Wave Basics Tab
- Select what you want to solve for: wavelength, frequency, or wave speed
- Check "Speed of light" for electromagnetic waves, or uncheck to enter a custom wave speed
- Enter the known values with appropriate units
- Click "Calculate" to see results including EM spectrum classification and a wave visualization
De Broglie Tab
- Select a particle type (electron, proton, neutron) or choose "Custom" to enter your own mass
- Enter the particle velocity in m/s or as a fraction of the speed of light
- Click "Calculate" to see the de Broglie wavelength and momentum
Energy↔Wavelength Tab
- Choose whether to convert energy to wavelength or wavelength to energy
- Enter the known value with appropriate units
- Click "Calculate" to see the conversion along with frequency and EM classification
Sound Tab
- Enter the sound frequency in Hz
- Select the medium (air, water, steel, or custom)
- For air, enter the temperature; for custom, enter the speed of sound
- Click "Calculate" to see wavelength in multiple units and the nearest musical note
Antenna Tab
- Enter the operating frequency with units (kHz, MHz, or GHz)
- Set the velocity factor (0.95 for wire, 0.66 for coax, 1.0 for free space)
- Select antenna type: quarter-wave, half-wave, or full-wave
- Click "Calculate" to see the physical antenna length in both metric and imperial units
Wavenumber Tab
- Choose conversion direction: wavelength to wavenumber or wavenumber to wavelength
- Enter the known value with appropriate units
- Click "Calculate" to see both spectroscopic (cm⁻¹) and angular (rad/m) wavenumber
Why We Built This
We created Wavelength Calculator to provide a genuinely useful, privacy-respecting tool for anyone working with wave physics. Our guiding principles:
- Completely free: No premium tiers, no feature restrictions, no "upgrade to unlock" prompts
- No signup required: Start calculating immediately without creating an account or providing personal information
- Privacy-focused: All calculations happen entirely in your browser using JavaScript. No data is sent to any server, no calculations are logged, and no personal information is collected
- No tracking: We don't use analytics that track individual users or build profiles
- No ads: The calculator interface is clean and focused on functionality
- Works offline: Once loaded, the calculator functions without an internet connection
We believe useful tools should be accessible to everyone, whether you're a student doing homework, a professional verifying a calculation, or simply curious about wave physics.
Contact
Questions, suggestions, or feedback? Email us at info@wavelengthcalculator.org
For more information about wave physics, explore our educational articles.