What is the h constant in physics? Planck explained

This calculator works out the energy of a photon from its frequency using the Planck constant, h. You enter the frequency in hertz (or the wavelength in meters) and you get back the energy in joules and electronvolts. It also shows the momentum of the photon, which uses the same constant.

Formula

The Planck constant h links the energy of a single photon to its frequency:

E = h × f

• E = energy of the photon, in joules (J)
• h = Planck constant, 6.62607015 × 10⁻³⁴ J·s (exact by definition since 2019)
• f = frequency of the light, in hertz (Hz, which is s⁻¹)

If you know the wavelength instead of the frequency, use the relation c = f × λ, so E = h × c / λ, where c is the speed of light (2.99792458 × 10⁸ m/s) and λ is the wavelength in meters.

Worked Example

Using the default values from the calculator: f = 5.0 × 10¹⁴ Hz (green light, roughly) and λ = 600 nm (orange-red light).

1. Convert wavelength to meters: 600 nm = 600 × 10⁻⁹ m = 6.00 × 10⁻⁷ m.
2. Compute frequency from wavelength: f = c / λ = (2.99792458 × 10⁸) / (6.00 × 10⁻⁷) = 4.9965 × 10¹⁴ Hz. The calculator lets you enter either value; the frequency input takes priority.
3. Energy: E = h × f = (6.62607015 × 10⁻³⁴) × (5.0 × 10¹⁴) = 3.313 × 10⁻¹⁹ J.
4. Convert to electronvolts: 1 eV = 1.602176634 × 10⁻¹⁹ J, so E = 3.313 × 10⁻¹⁹ / 1.602176634 × 10⁻¹⁹ = 2.068 eV.
5. Momentum: p = h / λ = (6.62607015 × 10⁻³⁴) / (6.00 × 10⁻⁷) = 1.104 × 10⁻²⁷ kg·m/s.

The calculator shows E = 3.313 × 10⁻¹⁹ J, eV = 2.068 eV, and p = 1.104 × 10⁻²⁷ kg·m/s.

What the h Constant Actually Is

The Planck constant (symbol h) is a fundamental physical constant that defines the scale of quantum effects. It was introduced by Max Planck in 1900 to explain blackbody radiation, and later used by Einstein in 1905 to describe the photoelectric effect. In the SI system, h is now fixed exactly at 6.62607015 × 10⁻³⁴ joule-seconds, which means it is used to define the kilogram, the ampere, the kelvin, and the mole.

Physically, h is the proportionality constant between the energy of a photon and its frequency, but it also appears in the Heisenberg uncertainty principle, the de Broglie wavelength of matter, and the Schrödinger equation. It sets the fundamental granularity of action (energy × time) in quantum mechanics.

Why the Constant Matters

Without h, quantum mechanics would not have a scale. It tells you how small a quantum of energy is for a given frequency. For example, a radio wave at 1 MHz has photons with energy about 6.6 × 10⁻²⁸ J, while a gamma ray at 10²⁰ Hz has photons with energy about 6.6 × 10⁻¹⁴ J. The constant also appears in the fine-structure constant, a dimensionless number that governs electromagnetic interactions.

When you see h in equations, it often appears as ħ (h-bar), which is h divided by 2π. That version is used in angular frequency and spin calculations. Both are fundamental, but h is the one you use for frequency and wavelength.

Common Mistakes and Misconceptions

• Using nm instead of meters – Always convert wavelength to meters before plugging into E = hc/λ. Forgetting the 10⁻⁹ factor gives an energy that is off by a billion.
• Confusing frequency and wavelength – The calculator takes both, but if you enter both, it uses the frequency. If you only enter wavelength, it computes the frequency from c.
• Mixing up J and eV – Electronvolts are convenient for atomic-scale energies. One eV equals 1.602176634 × 10⁻¹⁹ J exactly.
• Thinking h is a “small number” without units – Its units are J·s, which is action. It is not an energy, it is a conversion factor between energy and frequency.
• Applying classical formulas to photons – Photons have zero rest mass, so you cannot use E = mc² or p = mv. Use E = hf and p = h/λ.

How to Use the Result

The energy value tells you the energy of a single photon. To get the total energy of a beam of light, multiply by the number of photons. The electronvolt value is useful in atomic physics, chemistry, and semiconductor physics, where energy gaps are typically a few eV. The momentum is rarely needed for everyday calculations but is essential in Compton scattering and radiation pressure.

In practice, you might use this to estimate the energy of photons in a laser, the bandgap of a semiconductor, or the energy of a photon in a photoelectric effect experiment. For example, a red laser at 650 nm gives photons of about 1.91 eV, which is enough to trigger some photodiodes but not enough to ionize most atoms.

Limitations of the Formula

E = hf works for all electromagnetic radiation, but it does not account for relativistic effects when the photon has extremely high energy (above about 10¹⁸ Hz) where pair production becomes possible. It also does not include the effect of a medium; in a medium, the wavelength changes but the frequency stays the same, so the energy is unchanged. The formula is exact for single photons in vacuum.

For matter waves (like electrons), you use the de Broglie relation λ = h/p, which is a different application of the same constant. That formula is not included in this calculator because it requires the mass and velocity of a particle.

Frequently Asked Questions

What is the value of h?

The Planck constant is exactly 6.62607015 × 10⁻³⁴ joule-seconds. This value was fixed in the 2019 redefinition of SI units, so it is no longer measured; it defines the kilogram.

Why is h so small?

Because quantum effects only become noticeable at atomic scales. The smallness of h is why everyday objects do not show wave-like behavior. If h were larger, you would see interference patterns from baseballs.

Is h the same as ħ?

No. ħ (h-bar) is h divided by 2π, about 1.054571817 × 10⁻³⁴ J·s. It is used in equations involving angular frequency (radians per second) rather than ordinary frequency.

Can I use this for sound waves?

No. Sound waves are not quantized into photons. The Planck constant applies to electromagnetic radiation and to matter waves, not to mechanical waves in a medium.

Does the energy of a photon depend on intensity?

No. Intensity affects the number of photons, not the energy of each one. A bright red light and a dim red light have the same photon energy; the bright one just has more photons.

Related

• Cell Plating Density: How to Choose & Calculate
• How to Calculate % of Total Sales
• Year Over Year Sales Formula: How to Calculate YoY Growth

in f | Frequency | Hz | 5.0e14 | 0
in l | Wavelength | nm | 600 | 0
out E | Energy | J | h * f | 4
out eV | Energy | eV | h * f / 1.602176634e-19 | 3
out p | Momentum | kg·m/s | h / (l * 1e-9) | 30