Spectrum Calculator

Convert between wavelength, frequency, and photon energy. Identify the band and visualize the position on the spectrum.

Fundamental relations: λ·ν = c, E = h·ν = h·c/λ (c = speed of light, h = Planck's constant)

Green light (550 nm) Red light (650 nm) Wi-Fi (2.4 GHz) X-ray (0.1 nm) FM radio (100 MHz)
Spectrum Analysis Results
550 nm
Wavelength
545 THz
Frequency
3.61e-19 J
Photon Energy
Band: Visible (Green)

Position on spectrum (log scale). The marker shows your input.

Other units
  • Wavelength: 550 nm, 0.55 µm, 5.5e-7 m
  • Wavenumber: 1.82e6 m⁻¹
  • Energy in eV: 2.25 eV
  • Period: 1.83e-15 s

Understanding the Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, from long‑wavelength radio waves to extremely short‑wavelength gamma rays. Despite their diverse applications, all these waves travel at the speed of light in vacuum (c ≈ 3.00×10⁸ m/s) and differ only in their frequency and wavelength.

Key Relationships:

  • c = λ·ν – wavelength (λ) and frequency (ν) are inversely proportional.
  • E = h·ν = h·c/λ – photon energy increases with frequency.
  • 1 eV = 1.602176634×10⁻¹⁹ J (exact, since 2019 redefinition of SI units).
  • Wavenumber ν̃ = 1/λ (often in cm⁻¹) is used in infrared spectroscopy.

Physical Constants

Constant Symbol Value
Speed of light in vacuum c 2.99792458×10⁸ m/s
Planck constant h 6.62607015×10⁻³⁴ J·s
Planck constant (eV·s) h 4.135667662×10⁻¹⁵ eV·s
hc product (useful) hc 1240 eV·nm (approx.)

Electromagnetic Bands – Detailed View

Each band has unique properties and applications. The ranges are approximate; boundaries can overlap in different contexts.

Band Wavelength range Frequency range Photon energy Typical sources / applications
Gamma rays < 0.01 nm > 30 EHz > 124 keV Radioactive decay, nuclear explosions, astrophysics; cancer radiotherapy
X‑rays 0.01 – 10 nm 30 PHz – 30 EHz 124 eV – 124 keV X‑ray tubes, synchrotrons; medical imaging, crystallography
Ultraviolet (UV) 10 – 400 nm 750 THz – 30 PHz 3.1 – 124 eV Sun, UV lamps; sterilization, fluorescence, vitamin D synthesis
Visible light 400 – 700 nm 430 – 750 THz 1.8 – 3.1 eV Sun, LEDs, lasers; human vision, photography, fiber optics
Infrared (IR) 700 nm – 1 mm 300 GHz – 430 THz 1.24 meV – 1.8 eV Thermal radiation, remote controls, IR spectroscopy, heat cameras
Microwave 1 mm – 1 m 300 MHz – 300 GHz 1.24 µeV – 1.24 meV Microwave ovens, radar, Wi‑Fi, satellite communication
Radio waves 1 m – 100,000 km 3 Hz – 300 MHz < 1.24 µeV AM/FM broadcasts, television, mobile phones, astronomy

Visible Light – The Rainbow

The narrow visible region is what human eyes can detect. Different wavelengths are perceived as colors:

Color Wavelength (nm)
Violet 380 – 450
Blue 450 – 495
Green 495 – 570
Yellow 570 – 590
Orange 590 – 620
Red 620 – 750

Atmospheric Windows

Earth’s atmosphere absorbs some wavelengths but is transparent to others. The optical window (visible and near‑IR) and the radio window (∼1 cm to ∼10 m) allow ground‑based astronomy. Most UV, IR (except some bands), and X‑rays are blocked and must be observed from space.

Applications Across the Spectrum

  • Radio: communication, MRI (radio frequency pulses), radar.
  • Microwave: cooking, wireless networks, Doppler weather radar.
  • Infrared: thermal imaging, fiber‑optic communication, spectroscopy.
  • Visible: illumination, lasers, displays, microscopy.
  • Ultraviolet: sterilization, forensic analysis, UV curing.
  • X‑rays: medical imaging, airport security, material analysis.
  • Gamma rays: cancer treatment (radiosurgery), astrophysical observations.

Frequently Asked Questions

Use ν = c / λ, with c = 2.998×10⁸ m/s. Always convert wavelength to meters first.

Approximately 380 nm (violet) to 750 nm (red).

Rayleigh scattering: shorter wavelengths (blue) are scattered more by air molecules than longer wavelengths (red).

An ideal emitter radiates a continuous spectrum whose peak wavelength is given by Wien’s displacement law: λ_max = b / T (b ≈ 2.9×10⁻³ m·K).

The spectrum spans over 15 orders of magnitude; a log scale compresses it so all bands can be seen together.