Wavelength Calculator

Calculate wavelength, frequency, or wave speed. Enter any two values to find the third.

Wavelength Formula: λ = v/f Where: • λ = wavelength (meters, m) • v = wave speed (m/s) - Light in vacuum: c = 299,792,458 m/s ≈ 3×10⁸ m/s - Sound in air (20°C): ~343 m/s - Sound in water: ~1,481 m/s • f = frequency (hertz, Hz) Rearrangements: • Frequency: f = v/λ • Wave speed: v = λf Wavelength Units: • 1 m = 100 cm = 10⁹ nm = 10⁶ μm • Visible light: 380-700 nm • Radio waves: cm to km Energy-Wavelength Relation: E = hc/λ (for photons) h = 6.626×10⁻³⁴ J·s (Planck's constant)
Example 1 (Visible light - red): f = 4.3×10¹⁴ Hz, v = 3×10⁸ m/s λ = (3×10⁸)/(4.3×10¹⁴) = 6.98×10⁻⁷ m = 698 nm (red light) Example 2 (FM radio): f = 100 MHz = 100×10⁶ Hz, v = 3×10⁸ m/s λ = (3×10⁸)/(100×10⁶) = 3 m Example 3 (Sound wave): f = 440 Hz (musical A), v = 343 m/s (air) λ = 343/440 ≈ 0.78 m = 78 cm Example 4 (WiFi 2.4 GHz): f = 2.4×10⁹ Hz, v = 3×10⁸ m/s λ = (3×10⁸)/(2.4×10⁹) = 0.125 m = 12.5 cm Example 5 (X-rays): λ = 1 nm = 1×10⁻⁹ m, v = 3×10⁸ m/s f = (3×10⁸)/(1×10⁻⁹) = 3×10¹⁷ Hz Example 6 (Microwave oven): f = 2.45 GHz = 2.45×10⁹ Hz λ = (3×10⁸)/(2.45×10⁹) ≈ 0.122 m = 12.2 cm Example 7 (Blue light): λ = 450 nm = 450×10⁻⁹ m, v = 3×10⁸ m/s f = (3×10⁸)/(450×10⁻⁹) = 6.67×10¹⁴ Hz = 667 THz Photon energy: E = hc/λ = (6.626×10⁻³⁴ × 3×10⁸)/(450×10⁻⁹) ≈ 4.42×10⁻¹⁹ J

What is wavelength?

Wavelength (λ) is the distance between successive peaks (or any corresponding points) of a wave. It's measured in meters, though nanometers (nm) for light and centimeters/meters for radio waves are common. Wavelength determines wave properties like color or pitch.

How do you calculate wavelength from frequency?

Use λ = v/f, where v is wave speed and f is frequency. For electromagnetic waves in vacuum, v = c = 3×10⁸ m/s. For sound in air at 20°C, v ≈ 343 m/s. Higher frequency means shorter wavelength.

What is the electromagnetic spectrum?

EM spectrum ranges from radio waves (km wavelengths) to gamma rays (pm wavelengths): Radio > Microwave > Infrared > Visible (400-700 nm) > Ultraviolet > X-rays > Gamma rays. All travel at light speed c, differing only in wavelength/frequency.

What wavelengths can humans see?

Visible light: ~380-700 nm. Violet/blue: 380-450 nm; green: 495-570 nm; yellow: 570-590 nm; orange: 590-620 nm; red: 620-700 nm. This is a tiny fraction of the EM spectrum.

How does wavelength affect wave properties?

Wavelength determines: color (light), pitch (sound), penetration (short λ = high energy, less penetration; long λ = lower energy, more penetration), diffraction (longer λ bends more around obstacles), and resolution limits in microscopy.

What is the relationship between wavelength and energy?

For photons: E = hc/λ, where h is Planck's constant (6.626×10⁻³⁴ J·s) and c is light speed. Shorter wavelength = higher energy. UV (short λ) is more energetic and damaging than infrared (long λ).

How do you convert between wavelength units?

Common conversions: 1 m = 10⁹ nm = 10¹⁰ Å (angstroms) = 10⁶ μm. For example, 500 nm = 0.0000005 m = 0.5 μm = 5000 Å. Visible light is typically measured in nm, infrared in μm, radio in m or km.

What is the de Broglie wavelength?

All matter has a wavelength λ = h/p = h/(mv), where h is Planck's constant, p is momentum, m is mass, v is velocity. For macroscopic objects it's negligibly small. For electrons it's significant, enabling electron microscopy.

Why does wavelength change in different materials?

Wave speed changes in different media (v = c/n, where n is refractive index), so wavelength changes: λ_medium = λ_vacuum/n. Frequency stays constant. In water (n≈1.33), red light's wavelength decreases from 700 nm to ~526 nm.

What are real-world applications of wavelength?

Spectroscopy (identifying elements by wavelength), fiber optics, radio/WiFi communication (different bands), medical imaging (X-ray wavelengths), astronomy (observing different wavelengths reveals different phenomena), and photosynthesis (chlorophyll absorbs specific wavelengths).

How do you measure wavelength?

Methods include: diffraction gratings (split light by wavelength), interferometry (measures wavelength precisely), spectrometers (measure wavelength distribution), and for long waves like radio, directly measure distance between antenna elements or use frequency counters.

What is the wavelength of common waves?

AM radio: 200-600 m; FM radio: 2.8-3.4 m; WiFi 2.4 GHz: 12.5 cm; microwave oven: 12.2 cm; red light: 700 nm; blue light: 450 nm; X-rays: 0.01-10 nm; gamma rays: <0.01 nm. Sound middle C: 1.3 m in air.