Calculate the number of photons emitted per second from power in watts and wavelength (N = Pλ/hc), or convert photons per second back to watts.
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Watts To Photons Per Second Formula
The following formula gives the target photon flux for monochromatic source radiant power P and vacuum wavelength λ. The transmitted fraction η is 1 at 100%; electrical input watts require a separate optical-power conversion.
Variables:
- PS is the number of photons per second
- P is source radiant power in watts; η is the fraction reaching the target (0 < η ≤ 1)
- λ is the wavelength of the light (meters)
- h is Planck’s constant (6.62607015 × 10-34 J·s); c is the speed of light in vacuum (299792458 m/s)
Multiply source radiant power in watts by the transmitted fraction and vacuum wavelength in meters, then divide by h × c. Use P = N h c/(η λ) to reverse-solve source radiant power, or λ = N h c/(P η) for the implied monochromatic wavelength.
| Power (W) | Wavelength (nm) | Photons per second |
|---|---|---|
| 0.001 | 405 | 2.04e15 |
| 0.1 | 405 | 2.04e17 |
| 0.001 | 450 | 2.27e15 |
| 0.1 | 450 | 2.27e17 |
| 0.001 | 488 | 2.46e15 |
| 0.1 | 488 | 2.46e17 |
| 0.001 | 514 | 2.59e15 |
| 0.1 | 514 | 2.59e17 |
| 0.001 | 532 | 2.68e15 |
| 0.1 | 532 | 2.68e17 |
| 0.001 | 561 | 2.82e15 |
| 0.1 | 561 | 2.82e17 |
| 0.001 | 594 | 2.99e15 |
| 0.1 | 594 | 2.99e17 |
| 0.001 | 633 | 3.19e15 |
| 0.1 | 633 | 3.19e17 |
| 0.001 | 650 | 3.27e15 |
| 0.1 | 650 | 3.27e17 |
| 0.001 | 680 | 3.42e15 |
| 0.1 | 680 | 3.42e17 |
| * N = (P × λ) / (h × c). Uses h = 6.62607015e-34 J·s and c = 299792458 m/s. Rounded to 3 significant figures. Note: λ is shown in nanometers. | ||
What is Watts To Photons Per Second?
Watts to photons per second relates monochromatic radiant power to photon count rate using the wavelength. Broad-spectrum sources require spectral information; a single implied wavelength represents energy equivalence, not a unique spectrum. The watt is a unit of power that measures the rate of energy conversion or transfer, while photons per second measures the number of photons emitted by a light source in one second. This conversion is particularly useful in fields such as quantum physics and photonics, where the behavior and properties of photons are studied.
How to Calculate Watts To Photons Per Second?
The following steps outline how to calculate the Watts To Photons Per Second using the given formula:
- First, determine the source radiant power P in watts and the fraction η reaching the target.
- Next, determine the wavelength of the light in meters (λ).
- Next, use PS = P × η × λ ÷ (h × c).
- Finally, calculate the Watts To Photons Per Second (PS).
- Select the solve mode, enter the required values and optional target transmission, then select Calculate. Power, wavelength and flux unit changes convert the entered quantity.
Example Problem:
Use the following variables as an example problem to test your knowledge:
Source radiant power P = 50 W; target transmission η = 1 (100%).
Wavelength of the light (λ) = 5 x 10-7 meters
Planck’s constant h = 6.62607015 × 10-34 J·s and c = 299792458 m/s. The target flux is approximately 1.25853 × 1020 photons/s.
