Photon Energy & Wavelength Calculator

How it works

• E = h·f: Planck’s relation links photon energy to frequency using Planck’s constant h = 6.62607015×10⁻³⁴ J·s.
• λ = c / f: Frequency and wavelength are inverses via the speed of light c = 299,792,458 m/s (vacuum).
• Energy–wavelength: Combine both: E = h·c / λ. Shorter wavelength → higher frequency → higher energy.
• eV: We convert joules to electronvolts using 1 eV = 1.602176634×10⁻¹⁹ J.

Assumes vacuum values (ignores refraction). Educational only.

Homework-friendly examples

• Green laser (532 nm): λ = 532 nm → f ≈ 5.64×10¹⁴ Hz → E ≈ 3.73×10⁻¹⁹ J ≈ 2.33 eV.
• UV light (250 nm): λ = 250 nm → f ≈ 1.20×10¹⁵ Hz → E ≈ 7.95×10⁻¹⁹ J ≈ 4.96 eV.
• Red LED (650 nm): λ = 650 nm → f ≈ 4.61×10¹⁴ Hz → E ≈ 3.05×10⁻¹⁹ J ≈ 1.90 eV.
• Microwave oven (2.45 GHz): f = 2.45×10⁹ Hz → λ ≈ 0.122 m → E ≈ 1.62×10⁻²⁴ J ≈ 1.01×10⁻⁵ eV.
• Violet LED (405 nm): λ = 405 nm → f ≈ 7.41×10¹⁴ Hz → E ≈ 4.91×10⁻¹⁹ J ≈ 3.06 eV.
• Infrared remote (940 nm): λ = 940 nm → f ≈ 3.19×10¹⁴ Hz → E ≈ 2.11×10⁻¹⁹ J ≈ 1.32 eV.
• Wi‑Fi (5 GHz): f = 5×10⁹ Hz → λ ≈ 0.060 m → E ≈ 3.31×10⁻²⁴ J ≈ 2.07×10⁻⁵ eV.
• FM radio (100 MHz): f = 1×10⁸ Hz → λ ≈ 3.00 m → E ≈ 6.63×10⁻²⁶ J ≈ 4.14×10⁻⁷ eV.
• Cosmic microwave background (160 GHz): f = 1.6×10¹¹ Hz → λ ≈ 1.87×10⁻³ m → E ≈ 1.06×10⁻²² J ≈ 6.63×10⁻⁴ eV.
• X-ray (50 keV): E = 50,000 eV → E ≈ 8.01×10⁻¹⁵ J → f ≈ 1.21×10¹⁹ Hz → λ ≈ 2.48×10⁻¹¹ m (0.0248 nm).

Use these as templates: pick the known value, leave the others blank, and hit Calculate. Then compare with your textbook answers.

Why E = h·f and λ = c/f matter (and how to read the outputs)

Photons link three big ideas: energy, frequency, and wavelength. Planck’s relation E = h·f says each photon’s energy is proportional to its frequency with Planck’s constant h = 6.62607015×10⁻³⁴ J·s as the proportionality. Combine that with λ = c/f, where c = 299,792,458 m/s, and you get E = h·c / λ. Shorter wavelength means higher frequency, which means higher energy per photon. That’s why UV light is more energetic than red light, and why X-rays pack enough punch to penetrate tissue.

Energy is often expressed in electronvolts (eV) for convenience. One eV is 1.602×10⁻¹⁹ joules, roughly the energy an electron gains when accelerated through one volt. Visible photons live in the ~1.6–3.3 eV range (750–380 nm). Shifting to nanometers for wavelength avoids long decimals; radio waves and microwaves sit in centimeters to meters, while gamma rays dip below picometers. Frequency spans an even wider range—from a few hertz for very low-frequency radio up to exahertz (10¹⁸ Hz) and beyond for gamma rays. Presenting all three—J/eV, m/nm, Hz/THz—lets you jump between the common units used in labs, textbooks, and homework.

The visible spectrum strip in this tool anchors wavelength to color. Dragging the marker shows where your wavelength sits between roughly 380 nm (violet) and 750 nm (red). Outside that window, the light is still “there” but our eyes can’t see it. Infrared (longer wavelengths) is what you feel as heat from a toaster; ultraviolet (shorter) drives sunburn and some fluorescence. At even shorter wavelengths, X-rays and gamma rays become ionizing, breaking chemical bonds. At much longer wavelengths, microwaves excite water molecules (microwave ovens), and radio waves carry broadcast signals.

This calculator assumes vacuum values and ignores refraction. In glass or water, c drops because the medium’s index of refraction is greater than 1, stretching wavelength (inside the medium) even though frequency stays the same. We also ignore bandwidth, coherence, and photon statistics—those matter for lasers, LEDs, and thermal light sources but are beyond a quick conversion. If you’re troubleshooting homework, double-check that you’re using consistent units (meters vs nanometers, Hz vs THz) before plugging in numbers; most mistakes come from stray powers of ten.

Use the tool to translate between forms: if a problem gives wavelength in nm, you can jump to eV to see if a photon could kick an electron out of a material (photoelectric effect), or to frequency to compare with a spectrometer’s range. If you only have one input, leave the others blank—filling multiple inputs will conflict. Remember that intensity (brightness) depends on how many photons arrive, not just energy per photon. A dim laser pointer and a bright bulb can emit the same color (same photon energy) but differ enormously in photon flux. Knowing the per-photon energy is step one; understanding how many arrive per second is step two.