What Is h in the Wavelength Formula? Planck’s Constant
The calculator for this page is switched off while it is checked. The formula is below, and the worked example in the article shows how to use it by hand.
This calculator works out the energy of a photon from its wavelength using the formula E = hc/λ. You enter the wavelength in nanometres, and you get back the photon energy in electronvolts (eV), which is the standard unit used in spectroscopy and quantum physics. The constant h in that formula is Planck’s constant, one of the most important numbers in physics.
Formula
The wavelength–energy formula is written as:
E = hc / λ
where:
- E = photon energy, in joules (J) or electronvolts (eV)
- h = Planck’s constant, exactly 6.62607015 × 10−34 J·s
- c = speed of light in vacuum, exactly 299,792,458 m/s
- λ = wavelength of the light, in metres (m) — convert from nm by multiplying by 10−9
To get the result in electronvolts, divide the energy in joules by the elementary charge, 1.602176634 × 10−19 C.
Worked Example
Using the default values from the calculator (wavelength = 500 nm):
- Convert wavelength to metres: 500 nm × 10−9 = 5.00 × 10−7 m
- Calculate hc: (6.62607015 × 10−34) × (2.99792458 × 108) = 1.986445857 × 10−25 J·m
- Divide by wavelength: 1.986445857 × 10−25 / 5.00 × 10−7 = 3.972891714 × 10−19 J
- Convert to eV: 3.972891714 × 10−19 / 1.602176634 × 10−19 = 2.479 eV
The calculator shows 2.479 eV, matching the step-by-step result.
What Is Planck’s Constant?
Planck’s constant, symbol h, is a fundamental physical constant that relates the energy of a single photon to its frequency. The relationship is E = hf, where f is the frequency in hertz. When you use wavelength instead of frequency, the formula becomes E = hc/λ because c = fλ.
The constant was introduced by Max Planck in 1900 to explain black-body radiation, and it later became the foundation of quantum mechanics. Its value is now defined exactly as 6.62607015 × 10−34 J·s, meaning it is not measured but fixed by definition in the International System of Units (SI) since 2019.
In the wavelength formula, h is the proportionality factor that converts the spatial property (wavelength) into an energy. A shorter wavelength means a larger energy because the denominator is smaller, and h is the constant that makes the numbers work out correctly.
How to Use the Calculator
Enter the wavelength of light in nanometres (nm). The calculator uses the exact values of h and c, so the only thing you need to supply is the wavelength. The result is the energy of a single photon in eV.
Common wavelengths you might test:
- Visible green light: 550 nm → about 2.25 eV
- Red light: 700 nm → about 1.77 eV
- Blue light: 450 nm → about 2.76 eV
- X-rays: 0.1 nm → about 12,400 eV (12.4 keV)
For quick mental estimates, you can use the approximation E(eV) ≈ 1240 / λ(nm). This works because hc in eV·nm is about 1239.84.
Common Mistakes and Misconceptions
One frequent error is forgetting to convert wavelength to metres before plugging into the formula. If you use nanometres directly, you get an energy that is 109 times too large. The calculator handles this conversion automatically, but when doing manual calculations, always convert first.
Another mistake is confusing h with the reduced Planck constant, ħ (h-bar), which equals h / (2π). The reduced constant appears in angular frequency formulas, but the standard wavelength formula uses h, not ħ.
Some people also think that h is a variable that changes depending on the material or the wavelength. It is not — h is a universal constant, the same everywhere in the universe. What changes with wavelength is the energy, not the constant.
Why the Value of h Matters
Planck’s constant sets the scale of the quantum world. Because h is extremely small (about 10−34 J·s), quantum effects are only noticeable at the atomic or subatomic level. In everyday life, the energy of a single photon is tiny — a 500 nm photon carries only about 4 × 10−19 joules, which is why we don’t feel individual photons hitting our skin.
The constant also appears in the Heisenberg uncertainty principle, the Schrödinger equation, and the definition of the kilogram. Since 2019, the kilogram is defined by fixing the value of h exactly, which shows how fundamental this constant is to modern physics.
Limitations of the Formula
The formula E = hc/λ applies to a single photon in a vacuum. In a medium like glass or water, the speed of light is slower, and the wavelength changes, but the energy of the photon remains the same. If you are working with light in a material, you need to use the vacuum wavelength or adjust for the refractive index carefully.
The formula also assumes the photon is a free particle. For electrons or other massive particles, the de Broglie wavelength is different and uses momentum instead of c. The photon formula does not apply to particles with rest mass.
For very high-energy photons (gamma rays), the formula still holds, but the energy may be better expressed in keV or MeV. The calculator gives results in eV, which is convenient for most optical and X-ray applications.
Frequently Asked Questions
What does h stand for in the wavelength formula?
h stands for Planck’s constant, a fundamental physical constant that relates the energy of a photon to its frequency. In the wavelength formula E = hc/λ, it is the proportionality factor that converts wavelength (a spatial quantity) into energy.
Why is h so small?
Planck’s constant is small because quantum effects are only significant at atomic scales. Its value, 6.626 × 10−34 J·s, reflects the fact that energy quantization is unnoticeable in macroscopic objects. If h were larger, quantum effects would be visible in everyday life.
Can I use the formula with wavelength in nanometres directly?
No, you must convert to metres first. The formula E = hc/λ requires λ in metres because h has units of J·s and c has units of m/s. Using nanometres directly will give an energy that is 109 times too large. The calculator does this conversion for you.
What is the difference between h and ħ?
ħ (h-bar) is the reduced Planck constant, equal to h / (2π). It appears in formulas involving angular frequency, such as E = ħω. The standard wavelength formula uses h, not ħ, because it uses linear frequency (or wavelength) rather than angular frequency.
Is Planck’s constant the same for all types of light?
Yes, h is a universal constant. It does not change with wavelength, frequency, or material. The energy of a photon changes with wavelength, but h remains the same everywhere.
How is Planck’s constant measured?
Historically, it was measured using the photoelectric effect, black-body radiation, and X-ray diffraction. Since 2019, h is defined exactly as 6.62607015 × 10−34 J·s, and the kilogram is defined in terms of it. So it is no longer a measured quantity but a fixed standard.
Related
Formula used
in wl | Wavelength | nm | 500 | 0 out E | Photon energy | eV | (6.62607015e-34 * 2.99792458e8) / (wl * 1e-9) / 1.602176634e-19 | 3
Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work
Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.