Light Speed Calculator

Calculate wavelength, frequency, and photon energy using the wave equation c = fλ and Planck's relation E = hf. Perfect for electromagnetic spectrum and quantum physics problems.

**Wave Equation:** c = f × λ Where: • c = Speed of light = 299,792,458 m/s ≈ 3×10⁸ m/s • f = Frequency (Hz) • λ = Wavelength (m) **Rearrangements:** • λ = c / f • f = c / λ **Photon Energy:** E = h × f = h × c / λ Where: • E = Energy per photon (J or eV) • h = Planck's constant = 6.626×10⁻³⁴ J·s • 1 eV = 1.602×10⁻¹⁹ J **Unit Conversions:** • 1 nm (nanometer) = 10⁻⁹ m • 1 μm (micrometer) = 10⁻⁶ m • 1 THz (terahertz) = 10¹² Hz • 1 GHz (gigahertz) = 10⁹ Hz **Key Principle:** Higher frequency ↔ Shorter wavelength ↔ Higher energy
**Example 1 (Green Light Wavelength):** Frequency = 5.5×10¹⁴ Hz (typical green light) • λ = c / f = 3×10⁸ / 5.5×10¹⁴ • λ = 5.45×10⁻⁷ m = 545 nm • E = hf = 6.626×10⁻³⁴ × 5.5×10¹⁴ = 3.64×10⁻¹⁹ J • E = 2.27 eV **Example 2 (Red Laser Frequency):** Wavelength = 650 nm = 6.5×10⁻⁷ m • f = c / λ = 3×10⁸ / 6.5×10⁻⁷ • f = 4.62×10¹⁴ Hz = 462 THz • E = 1.91 eV (less energy than green) **Example 3 (WiFi Wavelength):** Frequency = 2.4 GHz = 2.4×10⁹ Hz • λ = 3×10⁸ / 2.4×10⁹ = 0.125 m = 12.5 cm • E = 9.93×10⁻⁶ eV (very low energy) **Example 4 (UV Light Energy):** Wavelength = 300 nm = 3×10⁻⁷ m (UV-B) • f = 3×10⁸ / 3×10⁻⁷ = 1×10¹⁵ Hz • E = hc/λ = 6.626×10⁻³⁴ × 3×10⁸ / 3×10⁻⁷ • E = 6.626×10⁻¹⁹ J = 4.13 eV (can damage DNA) **Example 5 (X-ray Energy):** Wavelength = 0.1 nm = 1×10⁻¹⁰ m • f = 3×10¹⁸ Hz • E = 1.99×10⁻¹⁵ J = 12.4 keV (medical X-ray range) **Example 6 (FM Radio):** Frequency = 100 MHz = 1×10⁸ Hz • λ = 3 m (about human height) • E = 4.14×10⁻⁷ eV (non-ionizing)

What is the speed of light?

The speed of light in vacuum (c) is exactly 299,792,458 m/s, or approximately 3×10⁸ m/s. This is a fundamental constant of nature and the maximum speed at which all energy, matter, and information can travel.

What is the relationship c = fλ?

The wave equation c = fλ relates the speed of light (c) to frequency (f) and wavelength (λ). It states that wavelength times frequency equals the speed of light. Higher frequency means shorter wavelength, and vice versa.

How do I calculate photon energy?

Photon energy is calculated using E = hf, where h is Planck's constant (6.626×10⁻³⁴ J·s) and f is frequency. Alternatively, E = hc/λ using wavelength. Higher frequency (shorter wavelength) photons have more energy.

What is the electromagnetic spectrum?

The electromagnetic spectrum ranges from radio waves (longest wavelength, lowest energy) through microwaves, infrared, visible light, ultraviolet, X-rays, to gamma rays (shortest wavelength, highest energy). All travel at speed c in vacuum.

What wavelength range is visible light?

Visible light ranges from approximately 380 nm (violet) to 750 nm (red). This is a tiny fraction of the electromagnetic spectrum. The peak sensitivity of human eyes is around 555 nm (green-yellow).

How does light frequency relate to color?

For visible light, frequency determines color. Red light has the lowest frequency (~430 THz, 700 nm), while violet has the highest (~750 THz, 400 nm). The relationship is inverse: higher frequency = shorter wavelength.

What is Planck's constant?

Planck's constant (h = 6.626×10⁻³⁴ J·s) is a fundamental constant relating photon energy to frequency. It's crucial in quantum mechanics and marks the scale where quantum effects become important.

Does light speed change in different media?

Yes! Light slows down in materials. The speed is v = c/n, where n is the refractive index. In water (n≈1.33), light travels at ~225,000 km/s. In diamond (n≈2.42), it's ~124,000 km/s. Our calculator uses c for vacuum.

What is a photon?

A photon is a quantum (packet) of electromagnetic radiation. It has no mass but carries energy E = hf and momentum p = h/λ. Light exhibits both wave and particle properties (wave-particle duality).

How do I convert between wavelength units?

Common conversions: 1 nm = 10⁻⁹ m, 1 μm = 10⁻⁶ m, 1 Å (angstrom) = 10⁻¹⁰ m. Radio wavelengths use meters, infrared uses micrometers, visible/UV use nanometers, X-rays use angstroms or nanometers.

What are typical photon energies?

Radio waves: ~10⁻⁹ eV, Microwaves: ~10⁻⁶ eV, Infrared: ~0.001 eV, Visible light: 1.6-3.2 eV, UV: 3-100 eV, X-rays: 100-100,000 eV, Gamma rays: >100 keV. 1 eV = 1.602×10⁻¹⁹ J.

Why is c the universal speed limit?

Special relativity shows that as objects approach light speed, their mass effectively increases, requiring infinite energy to reach c. Only massless particles (photons, gluons) can travel at c. This limit applies to information and causality.

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