Wavelength Calculator

Wavelength Formula

The wavelength formula relates wavelength (λ), frequency (f), and wave speed (v):

For electromagnetic waves (light, radio, X-rays), the wave speed is the speed of light:

This fundamental relationship means higher frequency waves have shorter wavelengths, and vice versa. Understanding this inverse relationship is key to frequency to wavelength conversions.

Electromagnetic Spectrum

The table below shows the complete electromagnetic spectrum with wavelength and frequency ranges. For detailed information about visible light colors and wavelengths, see our dedicated guide.

The photon energy varies across the spectrum—see how photon energy relates to wavelength through the Planck-Einstein relation (E = hc/λ).

How to Use This Calculator

This wavelength calculator provides six specialized tools for different wave physics calculations. Here's how to use each tab effectively:

Wave Basics Tab

The Wave Basics calculator uses the fundamental wave equation λ = v/f to convert between wavelength, frequency, and wave speed.

1. Select what to solve for: Choose wavelength (λ), frequency (f), or wave speed (v) using the radio buttons at the top
2. Set the wave speed: Keep "Speed of light" checked for electromagnetic waves (light, radio, X-rays). Uncheck it to enter a custom speed for other wave types
3. Enter your known value: If solving for wavelength, enter the frequency. If solving for frequency, enter the wavelength. If solving for speed, enter both
4. Select appropriate units: Use the dropdown menus to match your input (Hz, kHz, MHz, GHz, THz for frequency; m, cm, mm, μm, nm, Å for wavelength)
5. Click Calculate: Results show wavelength, frequency, speed, electromagnetic spectrum classification, and a visual wave representation

Tips: For visible light calculations, use THz for frequency or nm for wavelength. The calculator automatically identifies the EM spectrum region and displays the actual color for visible wavelengths (400-700 nm).

De Broglie Tab

Calculate the quantum mechanical wavelength of particles using λ = h/(mv), the de Broglie equation.

1. Select particle type: Choose electron, proton, neutron, or custom. The calculator uses precise particle masses (electron: 9.109×10⁻³¹ kg)
2. Enter velocity: Input the particle speed in m/s, or use "× c" to enter as a fraction of light speed (e.g., 0.01 for 1% of c)
3. For custom particles: Enter the mass in units of 10⁻³¹ kg. An electron is 9.109, a proton is 1672.6
4. Click Calculate: Results show the de Broglie wavelength and particle momentum

Tips: The de Broglie wavelength becomes significant at atomic scales. For electrons in typical experiments (10⁶ m/s), expect wavelengths around 0.7 nm. This calculator uses non-relativistic equations; for particles above 10% of light speed, relativistic corrections may be needed.

Energy↔Wavelength Tab

Convert between photon energy and wavelength using the Planck-Einstein relation E = hc/λ.

1. Select conversion direction: Choose "Wavelength from Energy" if you know the photon energy, or "Energy from Wavelength" if you know the wavelength
2. Enter your known value: For energy, use eV (electron volts), keV, MeV, or J (joules). For wavelength, use nm, μm, Å, or m
3. Click Calculate: Results show the converted value plus frequency and EM spectrum classification

Tips: A useful reference: 1 eV corresponds to 1240 nm (near-infrared). Visible light photons have energies of 1.7-3.1 eV. X-ray photons are typically in the keV range.

Sound Tab

Calculate acoustic wavelengths in different media using λ = v/f with the speed of sound.

1. Enter frequency: Input the sound frequency in Hz. Common references: A4 = 440 Hz, middle C = 262 Hz, human hearing range is 20-20,000 Hz
2. Select medium: Choose air (temperature-dependent), water (1480 m/s), steel (5960 m/s), or enter a custom speed
3. Set temperature: For air, enter the temperature in °C. Sound speed in air is calculated as 331.3 + 0.606×T m/s
4. Click Calculate: Results show wavelength in multiple units (m, cm, ft, in), the speed used, quarter-wavelength, and the nearest musical note

Tips: Quarter-wavelength measurements are important for acoustic treatment and speaker placement. Sound wavelengths are much longer than light—a 440 Hz tone has a 78 cm wavelength in air, while 440 THz light has a wavelength of 680 nm.

Antenna Tab

Calculate antenna dimensions for radio frequency applications using L = λ × VF / n.

1. Enter operating frequency: Input the frequency in kHz, MHz, or GHz. Common amateur bands: 2m (144-148 MHz), 70cm (420-450 MHz)
2. Set velocity factor: Use 1.0 for free space (theoretical), 0.95 for typical wire antennas, 0.66 for coaxial cable
3. Select antenna type: Choose ¼ wave (ground plane, vertical), ½ wave (dipole), or full wave
4. Click Calculate: Results show the physical antenna length in both metric and imperial units

Tips: The velocity factor accounts for slower wave propagation in physical conductors. Start with calculated values and fine-tune with an antenna analyzer. A ¼ wave antenna for 146 MHz (2m band) is approximately 49 cm with VF=0.95.

Wavenumber Tab

Convert between wavelength and wavenumber using k = 1/λ (spectroscopic) or k = 2π/λ (angular).

1. Select conversion direction: Choose wavelength to wavenumber or wavenumber to wavelength
2. Enter your value: Wavelength in nm, μm, m, or cm. Wavenumber in cm⁻¹ or m⁻¹
3. Click Calculate: Results show both spectroscopic wavenumber (cm⁻¹) and angular wavenumber (rad/m), plus the corresponding wavelength

Tips: Spectroscopic wavenumber (cm⁻¹) is standard in infrared spectroscopy and Raman spectroscopy. Visible light spans roughly 14,000-25,000 cm⁻¹. The angular wavenumber (rad/m) appears in wave equations and quantum mechanics.

Common Mistakes to Avoid

• Unit confusion: Always check that your unit selection matches your input. 500 MHz is very different from 500 THz
• Speed of sound vs. light: Sound travels about a million times slower than light. Make sure you're using the correct speed for your wave type
• Temperature effects: Sound speed in air varies significantly with temperature—about 0.6 m/s per degree Celsius
• Velocity factor: Real antennas are shorter than the theoretical length. Always apply the velocity factor for accurate results
• Relativistic particles: The de Broglie calculator uses classical equations. For particles approaching light speed, results become approximate

Real-World Examples

These examples illustrate how different people use the wavelength calculator in practical situations. All calculations use the actual formulas and constants from this calculator.

Example 1: Physics Student Studying Visible Light

Emma, a first-year physics student, needs to calculate the frequency of green light with a wavelength of 550 nm for her optics homework.

Using the Wave Basics tab:

• Selects "Frequency (f)" as the solve target
• Keeps "Speed of light" checked (c = 299,792,458 m/s)
• Enters 550 in the wavelength field and selects "nm"
• Clicks Calculate

Result: The frequency is 545 THz (5.45 × 10¹⁴ Hz). The calculator confirms this is visible light and shows a green color swatch. Emma can verify this makes sense: visible light frequencies range from about 430-750 THz.

Example 2: Ham Radio Operator Building an Antenna

Carlos, a licensed amateur radio operator, wants to build a quarter-wave vertical antenna for the 2-meter band at 146 MHz.

Using the Antenna tab:

• Enters 146 in the frequency field and selects "MHz"
• Sets velocity factor to 0.95 (standard for wire antennas)
• Selects "¼ Wave" antenna type
• Clicks Calculate

Result: The antenna should be 48.8 cm (19.2 inches). The full wavelength is 2.05 m, which is why it's called the "2-meter band." Carlos cuts his antenna wire to 49 cm and fine-tunes with his antenna analyzer.

Example 3: Audio Engineer Treating a Recording Studio

Priya, an audio engineer, needs to calculate bass trap dimensions for frequencies around 80 Hz in her new studio. Room temperature is 22°C.

Using the Sound tab:

• Enters 80 in the frequency field (Hz)
• Selects "Air (temp-dependent)" as the medium
• Enters 22 for temperature
• Clicks Calculate

Result: The wavelength is 4.31 m (14.1 feet). The quarter-wavelength is 1.08 m (3.5 ft). This tells Priya that effective bass trapping for 80 Hz requires absorption panels at least 1 meter deep, or placement in room corners where pressure builds up.

Example 4: Chemistry Student in Spectroscopy Lab

David needs to convert an infrared absorption peak from wavelength (3400 nm) to wavenumber for his IR spectroscopy report.

Using the Wavenumber tab:

• Selects "Wavelength → Wavenumber"
• Enters 3400 in wavelength field and selects "nm"
• Clicks Calculate

Result: The spectroscopic wavenumber is 2941 cm⁻¹. David recognizes this as the O-H stretching region, indicating hydroxyl groups in his sample. IR spectroscopy charts typically use wavenumbers because they're directly proportional to energy.

Example 5: Graduate Student Calculating Electron Wavelength

Dr. Chen's graduate student, Ming, is setting up an electron microscope experiment and needs to know the de Broglie wavelength of electrons accelerated to 0.5% of the speed of light.

Using the De Broglie tab:

• Selects "Electron" as the particle type
• Enters 0.005 in velocity field and selects "× c"
• Clicks Calculate

Result: The de Broglie wavelength is 4.85 × 10⁻¹¹ m (0.485 Å). This is much smaller than visible light wavelengths (400-700 nm), which explains why electron microscopes can resolve much finer details than optical microscopes.

Example 6: High School Teacher Demonstrating Energy-Wavelength Relationship

Mr. Thompson wants to show his AP Physics students why ultraviolet light causes sunburns but visible light doesn't, by comparing their photon energies.

Using the Energy↔Wavelength tab:

• For UV-B light (300 nm): Selects "Energy from Wavelength," enters 300 nm
• For red light (700 nm): Enters 700 nm
• Compares results

Results: UV-B photons have 4.13 eV, while red light photons have only 1.77 eV. This explains the biological effect: UV photons have enough energy to break chemical bonds in DNA and skin cells, while visible light photons don't.

Example 7: RF Engineer Checking WiFi Antenna Design

Fatima is designing a half-wave dipole antenna for a 2.4 GHz WiFi application and needs to calculate the optimal element length.

Using the Antenna tab:

• Enters 2.4 in frequency field and selects "GHz"
• Sets velocity factor to 0.95 for the antenna wire
• Selects "½ Wave Dipole"
• Clicks Calculate

Result: Each dipole element should be 5.9 cm (2.3 inches). The full wavelength at 2.4 GHz is 12.5 cm, so half-wave is 6.25 cm before applying the velocity factor. This matches commercial WiFi antenna dimensions.

Example 8: Underwater Acoustics Researcher

Dr. Patel studies whale communication and needs to know the wavelength of a 52 Hz "loneliest whale" call in seawater.

Using the Sound tab:

• Enters 52 in frequency field (Hz)
• Selects "Water (~1480 m/s)" as the medium
• Clicks Calculate

Result: The wavelength is 28.5 meters (93.5 feet). This explains why low-frequency whale calls travel vast distances through the ocean—wavelengths much larger than typical obstacles pass around them with minimal absorption.

Example 9: Medical Physics Student Studying X-rays

Aisha is studying diagnostic radiology and wants to understand the relationship between X-ray photon energy (typically 20-150 keV) and wavelength.

Using the Energy↔Wavelength tab:

• Selects "Wavelength from Energy"
• Enters 50 in energy field and selects "keV" (typical chest X-ray)
• Clicks Calculate

Result: A 50 keV X-ray photon has a wavelength of 0.0248 nm (24.8 pm). This is about 20,000 times shorter than visible light, which is why X-rays can penetrate soft tissue while visible light cannot.

Example 10: Concert Hall Acoustician

James is analyzing the acoustic properties of a concert hall and needs wavelength data for the standard orchestral tuning pitch (A4 = 440 Hz) at normal room temperature.

Using the Sound tab:

• Enters 440 in frequency field (Hz)
• Selects "Air (temp-dependent)"
• Enters 20 for temperature (°C)
• Clicks Calculate

Result: The wavelength is 78 cm (2.56 feet). The quarter-wavelength is 19.5 cm. James uses this to ensure diffuser panels and seat spacing don't create destructive interference at this critical frequency. The calculator also confirms this is note A4.

When to Use This Calculator

This wavelength calculator is designed for specific situations where you need to convert between wave properties or calculate wave characteristics. Here are the scenarios where it provides the most value:

Education and Learning

• Physics homework and exams: Verify your hand calculations for wave problems, or quickly explore "what if" scenarios to build intuition
• Understanding the electromagnetic spectrum: See how frequency and wavelength relate across radio waves, microwaves, light, and X-rays
• Quantum mechanics concepts: Explore de Broglie wavelengths to understand wave-particle duality
• Lab preparation: Calculate expected values before running experiments in optics or spectroscopy labs

Amateur Radio and RF Engineering

• Antenna design: Calculate the physical length of dipoles, verticals, and other antennas for any frequency band
• Band planning: Convert between frequency and wavelength when discussing or documenting amateur radio bands
• Feedline calculations: Determine wavelength for cutting coax to specific electrical lengths

Audio and Acoustics

• Room acoustics: Calculate wavelengths for bass trapping, diffuser design, and absorber placement
• Speaker placement: Determine quarter-wavelength distances to avoid acoustic cancellation
• Musical instrument design: Relate pipe or string lengths to their resonant frequencies

Spectroscopy and Chemistry

• IR spectroscopy: Convert between wavelength (nm, μm) and wavenumber (cm⁻¹) for spectral analysis
• UV-Vis spectroscopy: Calculate photon energy from wavelength to understand electronic transitions
• Raman spectroscopy: Work with wavenumber shifts and their corresponding wavelengths

Research and Professional Applications

• Electron microscopy: Calculate de Broglie wavelengths for electrons at various accelerating voltages
• X-ray crystallography: Relate X-ray energy to wavelength for diffraction experiments
• Telecommunications: Convert between frequency allocations and wavelength (fiber optics, wireless systems)

Who Benefits Most

• Students: From high school physics through graduate studies in physics, chemistry, engineering, and related fields
• Educators: Teachers demonstrating wave concepts or preparing examples for class
• Amateur radio operators: Hams designing antennas or understanding propagation
• Audio professionals: Sound engineers, acousticians, and studio designers
• Researchers: Scientists needing quick conversions for spectroscopy, microscopy, or wave physics
• Hobbyists: Anyone curious about wave physics, from telescope builders to synthesizer enthusiasts

Quick Reference Tables

These reference tables are based on the constants and formulas used in this calculator. Use them for quick lookups without needing to calculate.

Visible Light Colors and Wavelengths

The visible spectrum spans wavelengths from approximately 380 nm to 780 nm. This table shows the color ranges as defined in the calculator.

Speed of Sound in Different Media

Sound speed varies dramatically depending on the medium. These values are used by the Sound tab calculator.

For air, the calculator uses the formula: v = 331.3 + 0.606 × T (where T is temperature in °C).

Particle Masses for De Broglie Calculations

These are the exact mass values used by the De Broglie tab. The masses are from CODATA 2018 values.

Common Amateur Radio Bands and Antenna Lengths

Quick reference for ¼ wave vertical antenna lengths on popular amateur radio bands (with VF = 0.95).

Full Electromagnetic Spectrum Reference

The electromagnetic spectrum spans over 15 orders of magnitude in wavelength. This table shows each region with its properties and common applications.

Wireless Technology Frequencies

Common wireless standards and their operating frequencies and wavelengths.

Real-World Wavelength Scale Comparisons

Putting wavelengths in perspective by comparing them to familiar objects.

Common Laser Wavelengths

Standard laser types and their emission wavelengths, used in industry, medicine, and research.

Formula Reference

This calculator uses standard physics equations. Here are the formulas with explanations and worked examples.

Wave Equation (Wave Basics Tab)

• λ (lambda) = wavelength in meters (m)
• v = wave speed in meters per second (m/s)
• f = frequency in Hertz (Hz, cycles per second)

Worked example: Calculate the wavelength of a 100 MHz FM radio signal.

λ = c / f = 299,792,458 m/s ÷ 100,000,000 Hz = 2.998 m ≈ 3 meters

De Broglie Equation (De Broglie Tab)

• λ = de Broglie wavelength in meters (m)
• h = Planck's constant = 6.62607015 × 10⁻³⁴ J·s
• m = particle mass in kilograms (kg)
• v = velocity in meters per second (m/s)
• p = momentum = m × v (kg·m/s)

Worked example: Calculate the de Broglie wavelength of an electron traveling at 2 × 10⁶ m/s.

p = m × v = 9.109 × 10⁻³¹ kg × 2 × 10⁶ m/s = 1.822 × 10⁻²⁴ kg·m/s

λ = h / p = 6.626 × 10⁻³⁴ / 1.822 × 10⁻²⁴ = 3.64 × 10⁻¹⁰ m = 0.364 nm

Planck-Einstein Relation (Energy↔Wavelength Tab)

• E = photon energy in joules (J) or electron volts (eV)
• h = Planck's constant = 6.626 × 10⁻³⁴ J·s = 4.136 × 10⁻¹⁵ eV·s
• c = speed of light = 299,792,458 m/s
• λ = wavelength in meters (m)
• f = frequency in Hertz (Hz)

Useful constant: hc = 1240 eV·nm (memorize this for quick calculations!)

Worked example: Calculate the energy of a 620 nm (orange light) photon.

E = hc / λ = 1240 eV·nm / 620 nm = 2.0 eV

Sound Wavelength (Sound Tab)

Speed of sound in air: v = 331.3 + 0.606 × T (T in °C)

Worked example: Calculate the wavelength of a 1000 Hz tone in air at 25°C.

v = 331.3 + 0.606 × 25 = 346.5 m/s

λ = 346.5 / 1000 = 0.347 m = 34.7 cm

Antenna Length (Antenna Tab)

• L = physical antenna length in meters
• λ = free-space wavelength = c / f
• VF = velocity factor (typically 0.95 for wire, 0.66 for coax)
• n = divisor (4 for ¼ wave, 2 for ½ wave, 1 for full wave)

Worked example: Calculate a ½ wave dipole for 14.2 MHz with VF = 0.95.

λ = 299,792,458 / 14,200,000 = 21.11 m

L = (21.11 × 0.95) / 2 = 10.03 m (32.9 ft)

Wavenumber Conversions (Wavenumber Tab)

• k (spectroscopic) = wavenumber in m⁻¹ or cm⁻¹
• k (angular) = angular wavenumber in rad/m
• λ = wavelength

Worked example: Convert 500 nm to wavenumber.

k = 1 / (500 × 10⁻⁹ m) = 2 × 10⁶ m⁻¹ = 20,000 cm⁻¹

k (angular) = 2π × 2 × 10⁶ = 1.26 × 10⁷ rad/m

Understanding Your Results

After calculating, you may wonder: "Is this result reasonable?" Here's how to interpret results from each tab.

Wave Basics Results

What the numbers mean:

• Wavelength: The physical distance between wave peaks. For EM waves, this determines how the wave interacts with matter
• Frequency: How many wave cycles pass a point per second. Higher frequency = more energy (for photons)
• EM Classification: Shows where your wave falls on the electromagnetic spectrum

Sanity checks:

• Radio waves: wavelengths > 1 m, frequencies < 300 MHz
• Visible light: wavelengths 400-700 nm, frequencies 430-750 THz
• X-rays: wavelengths < 10 nm, frequencies > 30 PHz
• If your EM wave has a wavelength in kilometers, it's very low frequency radio (VLF)
• If your wavelength is in picometers, you're in the X-ray/gamma ray range

De Broglie Results

What the numbers mean:

• De Broglie wavelength: The scale at which quantum wave behavior becomes significant
• Momentum: The classical momentum (mass × velocity) of the particle

Typical ranges:

• Electrons at typical lab velocities (10⁶ m/s): λ ≈ 0.7 nm
• Electrons in electron microscopes: λ ≈ 0.01-0.1 nm (much smaller than visible light)
• Thermal neutrons: λ ≈ 0.1-0.2 nm (useful for diffraction studies)
• Macroscopic objects: λ is so small it's unmeasurable (quantum effects invisible)

When results matter: De Broglie wavelengths are significant when comparable to the size of structures being probed (atoms ≈ 0.1-0.3 nm, atomic spacing in crystals ≈ 0.2-0.5 nm).

Energy↔Wavelength Results

What the numbers mean:

• Photon energy: The amount of energy a single photon carries. Higher energy photons can break chemical bonds or ionize atoms
• Wavelength: Inversely related to energy—shorter wavelengths carry more energy

Reference points:

• Chemical bond energies: 1-10 eV (this is why UV and X-rays can damage DNA)
• Visible light: 1.7-3.1 eV (not enough to break most bonds)
• Infrared: < 1.7 eV (causes molecular vibrations, perceived as heat)
• X-rays: 100 eV - 100 keV (ionizing radiation)
• Gamma rays: > 100 keV (highly penetrating, used in cancer treatment)

Sound Results

What the numbers mean:

• Wavelength: The physical size of sound waves—important for acoustic design
• Quarter-wavelength: Key dimension for acoustic treatment. Bass traps need thickness ~¼λ to absorb effectively
• Musical note: Helps identify the pitch corresponding to your frequency

Practical ranges:

• Bass frequencies (20-200 Hz): wavelengths 1.7-17 m (difficult to control in small rooms)
• Midrange (200-2000 Hz): wavelengths 17 cm - 1.7 m
• Treble (2000-20000 Hz): wavelengths 1.7-17 cm (easily absorbed/reflected)
• Ultrasound (>20 kHz): wavelengths < 1.7 cm (used in medical imaging)

Antenna Results

What the numbers mean:

• Physical length: The actual length to cut your antenna element
• Velocity factor adjustment: Real antennas are shorter than the theoretical free-space calculation due to end effects and conductor properties

Practical considerations:

• The calculated length is a starting point; final tuning requires an antenna analyzer
• ¼ wave antennas need a ground plane (radials or car body)
• ½ wave dipoles are balanced; feed point impedance is ~73Ω
• Higher frequencies = shorter antennas (easier to build)
• HF antennas (3-30 MHz) can be physically large; consider space constraints

Wavenumber Results

What the numbers mean:

• Spectroscopic wavenumber (cm⁻¹): Number of wavelengths per centimeter. Standard unit in infrared spectroscopy
• Angular wavenumber (rad/m): Related to spatial frequency; appears in wave equations

Typical ranges in spectroscopy:

• Far-IR / THz: 10-400 cm⁻¹
• Mid-IR (most common for organic chemistry): 400-4000 cm⁻¹
• Near-IR: 4000-14000 cm⁻¹
• Visible: 14000-25000 cm⁻¹
• UV: 25000-50000 cm⁻¹

Comparison: Electromagnetic vs. Sound vs. Matter Waves

This calculator handles three fundamentally different types of waves. Understanding their differences helps you choose the right calculation.

Key insight: The fundamental wave relationship λ = v/f applies to both EM and sound waves, but the "velocity" means very different things. For matter waves, the de Broglie relation λ = h/p is a quantum mechanical result with no classical analogue.

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Frequently Asked Questions