Are the Units for h Fundamental? Planck Constant Explained

This article answers whether the units of Planck’s constant (h) are fundamental units of measurement. The direct answer is no: the units for h (joule-seconds, or kg·m²/s) are derived units, not fundamental units. They are built from the seven base units of the International System of Units (SI): the kilogram, meter, and second.

Formula

The relationship that defines h is the Planck-Einstein relation:

E = h × ν

• E = energy of a photon (joules, J)
• h = Planck constant (joule-seconds, J·s)
• ν = frequency of the radiation (hertz, Hz = 1/s)

Rearranged, h = E / ν, so the units are J / (1/s) = J·s. In SI base units, 1 J = 1 kg·m²/s², so 1 J·s = 1 kg·m²/s.

Worked Example

Using the default values in the calculator above: a photon with frequency 5.0 × 10¹� Hz (green light).

1. E = h × ν = 6.62607015 × 10�³� J·s × 5.0 × 10¹� s�¹
2. E = 3.313 × 10�¹� J
3. Convert to electronvolts: 3.313 × 10�¹� J ÷ 1.602 × 10�¹� J/eV ≈ 2.07 eV

So the photon carries about 2.07 eV of energy, matching the calculator output.

What Are Fundamental Units?

Fundamental (base) units are the seven independent units defined by the SI: meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity). Every other unit is derived from these. For example, the newton (force) is kg·m/s², and the joule (energy) is kg·m²/s². The units of h, kg·m²/s, are therefore a combination of three base units—not a new fundamental unit.

Why Does h Have Such Odd Units?

The units of h come directly from the physical quantity it represents: action (energy × time) and angular momentum. In quantum mechanics, h is the proportionality constant between a photon’s energy and its frequency. Since frequency has units of 1/time, multiplying by h must yield energy, forcing h to carry units of energy × time. This is not arbitrary—it reflects the deep relationship between energy and time in quantum systems.

Common Misconception: h as a Fundamental Unit

Some confuse h with a fundamental constant, which it is—but a fundamental constant is different from a fundamental unit. A fundamental constant has a fixed value that defines our measurement system (like the speed of light c), but its units are still derived. In fact, the 2019 redefinition of the SI fixed h’s value exactly at 6.62607015 × 10�³� J·s, making it a defining constant. However, that does not make its units fundamental; it only means the kilogram is now defined using h, the meter, and the second.

How to Read the Result

When you use the calculator above, you get the photon energy in joules and electronvolts. The first output (h) is just a constant—it doesn’t change with input. The second output (E_ev) is what you actually need for most physics or chemistry problems. Electronvolts are the standard unit for photon energies in spectroscopy and semiconductor physics. For example, visible light ranges from about 1.65 eV (red) to 3.10 eV (violet).

Common Mistakes and Limits

• Unit mix-ups: Always use frequency in hertz (1/s), not angular frequency (rad/s). If you have angular frequency ω, use E = ħω, where ħ = h/(2π).
• Rounding: The calculator rounds to 2 decimals for eV, which is fine for most purposes. For precision work, keep more digits.
• Limits: This formula applies to single photons. For macroscopic objects, the energy is not quantized in this simple way—you’d need the full quantum formalism.

Frequently Asked Questions

Is h the same as ħ?

No. h is the Planck constant, and ħ (h-bar) is the reduced Planck constant, defined as h/(2π). ħ appears naturally in equations involving angular momentum and angular frequency. Both have units of action, but ħ is about 1.0545718 × 10�³� J·s.

Why was h redefined in 2019?

The SI redefinition fixed h’s exact value to define the kilogram. Previously, the kilogram was defined by a physical artifact (the international prototype). By fixing h, scientists could define mass in terms of the meter, second, and h, which are all based on fundamental constants and atomic properties.

Can h be expressed in other units?

Yes, but they are all equivalent. Common alternatives include eV·s (electronvolt-seconds) and erg·s (erg-seconds). In atomic units, h is set to 1. The SI units (J·s) are the standard for most scientific work.

Does h change with the medium or environment?

No. h is a universal constant—it is the same everywhere in the universe and does not depend on temperature, pressure, or the medium. This is why it can serve as a defining constant for the SI.

What does h have to do with the uncertainty principle?

Heisenberg’s uncertainty principle states Δx·Δp ≥ ħ/2. The units of h (action) are exactly what you need to multiply position (m) and momentum (kg·m/s) to get a unitless product. So h sets the scale at which quantum effects become significant.

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in v | Frequency | Hz (1/s) | 5.0e14 | 0
in E | Photon energy | J | v * h | 2
out h | Planck constant | J·s | 6.62607015e-34 | 2
out E_ev | Energy in eV | eV | E / 1.602176634e-19 | 2