Nanometers are a unit of length to measure very small magnitudes such as wavelengths. Joules, abbreviated as J, is a unit of energy in the metric system. The conversion between nanometers and joules is important in physics because many scientists need to calculate the energy of electromagnetic radiation from the wavelength. To do so, apply the following formula derived from Planck's equation: Energy = Planck Constant x Speed of light / wavelength.
Retrieve the Planck constant value: 6.626 069 57 x10^-34 J s.
Get the speed of light constant: 299,792,458 m/s.
Multiply the Planck constant by the speed of light: 6.62606957 x10^-34 J s x 299,792,458 m/s = 1,98645 x10^-25 J m.
Divide the wavelength in nanometers by 10^-9 to calculate the value in meters. For example, the wavelength of 500 nm corresponds to 500/10^-9 = 5x10^-7 meters (m).
Divide the product of the constants by the wavelength in meters to calculate the energy in Joules. In this example, the energy is 1,98645 x10^-25 J m / 5x10^-7 m = 3.973 x10-19 J.