Pm to Watts Conversion: Formula & Calculator
- Wavelength
- 500 pm
- You entered
This calculator converts picometers (pm) to watts (W) — but only in the specific context where you’re working with photon energy and wavelength. You enter a wavelength in picometers, and the calculator returns the energy of a single photon in watts (joules per second), using the Planck–Einstein relation. The result is the power carried by one photon per second; for real beams, multiply by the number of photons per second.
Formula
The conversion uses the Planck–Einstein relation for a photon:
E = h × c / λ
- E = energy of one photon (joules, J)
- h = Planck constant = 6.62607015 × 10−34 J·s
- c = speed of light in vacuum = 2.99792458 × 108 m/s
- λ = wavelength in meters (m)
Since 1 picometer = 10−12 meters, you first convert pm to meters: λ(m) = λ(pm) × 10−12. The energy in joules is numerically equal to the power in watts when you consider one photon per second (1 J/s = 1 W).
Worked Example
Using the default value of 500 pm (which is in the X-ray/gamma-ray range):
- Convert wavelength to meters: 500 pm = 500 × 10−12 m = 5.00 × 10−10 m
- Multiply h × c: (6.62607015 × 10−34) × (2.99792458 × 108) = 1.98644586 × 10−25 J·m
- Divide by wavelength: 1.98644586 × 10−25 / 5.00 × 10−10 = 3.97289172 × 10−16 J
- Since 1 J/s = 1 W, the photon energy is 3.9729 × 10−16 W (per photon per second).
The calculator shows 0.0000000000000004 W (rounded to 4 decimal places in scientific notation display, but internally it uses the full value).
Why Convert pm to Watts at All?
Picometers are an extremely small unit of length, used for atomic-scale distances and very short wavelengths. Watts measure power, which is energy per unit time. The connection arises in quantum physics when you need to know the energy carried by electromagnetic radiation of a given wavelength. This is common in:
- X-ray and gamma-ray spectroscopy
- Synchrotron and free-electron laser experiments
- Astrophysics (e.g., gamma-ray bursts)
- Radiation safety calculations (photon energies)
The result is always a tiny number because a single photon carries very little energy. To get a practical power value (like milliwatts), you multiply by the photon flux (photons per second).
How to Use the Result
The calculator gives you the energy of one photon in watts (joules per second). To find the total power of a beam, multiply by the number of photons emitted per second. For example, if your source emits 1018 photons per second at 500 pm, the total power is:
3.9729 × 10−16 W/photon × 1018 photons/s = 3.9729 × 102 W = 397.29 W
That’s a very powerful X-ray beam. Conversely, if you know the beam power and wavelength, you can find the photon flux by dividing power by photon energy.
Common Mistakes and Misconceptions
A frequent error is forgetting to convert picometers to meters. The formula requires meters, so always multiply pm by 10−12. Another mistake is confusing energy (joules) with power (watts). The calculator outputs watts because it assumes one photon per second. If you want energy per photon in electronvolts (eV), divide the energy in joules by 1.602176634 × 10−19.
Also note that this conversion is only valid for photons (electromagnetic radiation). It does not apply to particles with mass, like electrons or protons, which require a different formula (E = pc for relativistic particles, or E = mc² for rest energy).
Limits of the Formula
The Planck–Einstein relation is exact for single photons in vacuum. However, in real materials, the speed of light is slower (c/n, where n is the refractive index), but for most practical purposes, vacuum values are used. The formula also assumes the photon has no rest mass (which is true) and that you’re dealing with a monochromatic (single-wavelength) beam.
For extremely short wavelengths (below ~10 pm), the photon energy becomes so high that it can produce electron-positron pairs when interacting with matter, but the energy calculation itself remains valid.
Frequently Asked Questions
What is 1 pm in watts?
1 picometer corresponds to a photon energy of about 1.986 × 10−13 J, which is 1.986 × 10−13 W per photon per second. That’s roughly 1.24 MeV (million electronvolts).
Can I convert pm to watts for any wavelength?
Yes, the formula works for any wavelength, but the result is meaningful only for electromagnetic radiation. For radio waves (millimeters to kilometers), the photon energy is extremely small; for gamma rays (picometers), it’s much larger.
Why is the result so small?
Because a single photon carries a tiny amount of energy. For example, a green photon (500 nm) has about 2.5 eV, which is 4 × 10−19 J. In picometers, you’re dealing with even shorter wavelengths, so the energy is higher, but still minuscule on a macroscopic scale.
How do I convert photon energy to electronvolts?
Divide the energy in joules by 1.602176634 × 10−19. For 500 pm, that gives 3.9729 × 10−16 / 1.602 × 10−19 ≈ 2.48 keV.
Does this calculator work for sound waves?
No. Sound waves are mechanical, not photons. Their energy depends on amplitude and medium properties, not on a simple wavelength-to-energy formula.
What is the difference between pm and nm?
1 nanometer (nm) = 1000 picometers (pm). So 500 pm = 0.5 nm. The conversion factor is 103.
Related
Formula used
in pm | Wavelength | pm | 500 | 0 out watts | Photon energy | W | (6.62607015e-34 * 2.99792458e8) / (pm * 1e-12) | 4
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.