Wavelength
λ = c / fLoading page content...
Last updated:
Calculate wavelength, frequency, or wave speed using λ = c/f
Wavelength = Speed ÷ Frequency
Enter values above to see results.
Explore our in-depth guides related to this calculator
Everything you need to know about mortgages — calculate payments, compare rates, understand amortization, and plan your home purchase with expert-reviewed tools.
Expert-reviewed guide to BMI calculation, healthy weight ranges, limitations of BMI, and alternative health metrics. Includes free BMI calculator.
Comprehensive tax planning guide with free calculators. Covers federal tax brackets, deductions, credits, and strategies to minimize your tax burden.
Electromagnetic & Wave Physics
Calculate electromagnetic and acoustic wavelength, frequency, and wave speed for any part of the spectrum.
Formula
λ = c / f
Speed of Light
3 × 10⁸ m/s
Visible Light
380 – 700 nm
Photon Energy
E = hf
Reviewed by: CalculatorApp Physics & Engineering Team
All waves — electromagnetic, acoustic, or mechanical — obey λ = v/f where v is the wave speed, f is the frequency, and λ is the wavelength. For electromagnetic waves in vacuum, v = c = 3 × 10⁸ m/s. This relationship governs antenna design, optics, radio communication, medical imaging, musical acoustics, and every photonic device.
Wavelength
λ = c / fFrequency
f = c / λWave Speed
v = λ × fPhoton Energy
E = h × f (= hc/λ)| Band | Wavelength Range | Frequency Range |
|---|---|---|
| Radio / AM | 10 m – 100 km | 3 kHz – 30 MHz |
| Microwave / WiFi | 1 mm – 30 cm | 1 GHz – 300 GHz |
| Visible Light | 380 – 700 nm | 430 – 790 THz |
| X-ray | 0.01 – 10 nm | 30 PHz – 30 EHz |
1865: James Clerk Maxwell predicts electromagnetic waves propagating at the speed of light.
1887: Heinrich Hertz experimentally confirms EM waves, measures their speed and wavelength.
1900: Max Planck introduces E = hf, founding quantum mechanics and photon energy quantization.
1905: Einstein explains the photoelectric effect using photon energy, confirming E = hf.
1940s-50s: Radar and microwave technology drive precise wavelength-frequency engineering for defense.
Modern era: 5G, LiDAR, OLED, and quantum communication all rely on precise wavelength-frequency control.
Standard values for speed of light and Planck constant.
International Telecommunication Union frequency allocations.
NASA's spectrum overview for science and engineering.
Standards and research in photonics and optical frequency.
Myth: All electromagnetic waves travel at different speeds.
Fact: All EM waves travel at c = 3×10⁸ m/s in vacuum; only their frequency and wavelength differ.
Myth: Wavelength and frequency are the same property.
Fact: They are inversely related: double the frequency halves the wavelength at constant wave speed.
Myth: Visible light is the only part of the EM spectrum that carries energy.
Fact: All EM radiation carries energy proportional to frequency (E = hf); X-rays carry far more than radio waves.
Myth: Sound and light wavelengths follow the same formula.
Fact: They use the same formula (λ = v/f) but with different speeds: sound ~343 m/s vs light 3×10⁸ m/s.
λ = c / f, where c is the wave speed, f is frequency (Hz), and λ is wavelength (m). Wavelength and frequency are inversely proportional at constant wave speed.
In vacuum, c = 299,792,458 m/s (approximately 3 × 10⁸ m/s). Light slows when passing through materials.
The electromagnetic spectrum spans radio (kHz), microwave (GHz), infrared, visible (400-700 nm), UV, X-ray, and gamma ray, all traveling at the speed of light.
Sound travels at ~343 m/s in air at 20°C. At 1000 Hz, λ = 343/1000 = 0.343 m (34.3 cm).
Antenna length is typically a fraction of the operating wavelength (e.g., half-wave dipole = λ/2), determining resonance frequency.
Visible light spans 380 nm (violet) to 700 nm (red). Humans perceive wavelength as color.
E = hf = hc/λ where h = 6.626×10⁻³´ J·s (Planck's constant). Shorter wavelengths carry more energy per photon.
n = c/v, where v is light speed in a medium. It determines how much light slows and bends (Snell's law).
Standing waves form when incident and reflected waves interfere. Wavelength determines the resonant cavity length for lasers, microwave ovens, and musical instruments.
An observed frequency shift caused by relative motion between source and observer; used in radar, sonar, and medical ultrasound.
Spectroscopy identifies materials by their unique absorption/emission wavelengths, used in astronomy, chemistry, and medical diagnostics.
Microwaves: mm to cm (GHz frequencies); optical: nm (×10⁻⁹ m). X-rays and gamma rays: pm to fm range.
Pair wavelength-frequency with Ohm\'s law, voltage divider, and projectile motion calculators for complete physics and electronics coverage.
Open Engineering Suite