Enter the temperature in Kelvin and the wavelength in nanometers into the calculator to determine the missing variable.
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Nm to Temperature Formula
The following formula is used to calculate the temperature for a given wavelength.
T = \frac{b}{\lambda}Variables:
- T is the temperature in Kelvin
- b is Wien’s displacement constant (approximately 2.898 x 106 nm·K)
- λ is the wavelength in nanometers
To calculate the temperature, divide Wien’s displacement constant by the wavelength.
| Wavelength (nm) | Temperature (K) | Temperature (°C) | Temperature (°F) |
|---|---|---|---|
| 100 | 28980.0 | 28706.9 | 51704.3 |
| 200 | 14490.0 | 14216.9 | 25622.3 |
| 300 | 9660.0 | 9386.9 | 16928.3 |
| 380 | 7626.3 | 7353.2 | 13267.7 |
| 400 | 7245.0 | 6971.9 | 12581.3 |
| 450 | 6440.0 | 6166.9 | 11132.3 |
| 500 | 5796.0 | 5522.9 | 9973.1 |
| 550 | 5269.1 | 4995.9 | 9024.7 |
| 600 | 4830.0 | 4556.9 | 8234.3 |
| 650 | 4458.5 | 4185.3 | 7565.6 |
| 700 | 4140.0 | 3866.9 | 6992.3 |
| 800 | 3622.5 | 3349.4 | 6060.8 |
| 900 | 3220.0 | 2946.9 | 5336.3 |
| 1000 | 2898.0 | 2624.9 | 4756.7 |
| 1500 | 1932.0 | 1658.9 | 3017.9 |
| 2000 | 1449.0 | 1175.9 | 2148.5 |
| 3000 | 966.0 | 692.9 | 1279.1 |
| 4000 | 724.5 | 451.4 | 844.4 |
| 5000 | 579.6 | 306.5 | 583.6 |
| 10000 | 289.8 | 16.7 | 62.0 |
| Using Wien’s displacement law: T(K) ≈ 2.898×10^6 nm·K ÷ λ(nm). Values rounded to 1 decimal place. | |||
What is the Relationship Between Wavelength and Temperature?
The relationship between wavelength and temperature is described by Wien’s displacement law. This law states that the wavelength at which the emission of a black body spectrum is maximized is inversely proportional to the temperature of the black body. In simpler terms, as the temperature of an object increases, the peak wavelength of its emitted radiation shifts to shorter wavelengths. This principle is fundamental in fields such as astrophysics and thermal imaging, where it helps in determining the temperature of stars and other celestial bodies based on their emitted light.
How to Calculate Temperature from Wavelength?
The following steps outline how to calculate the temperature from the wavelength.
- First, determine the wavelength (λ) in nanometers.
- Next, use Wien’s displacement constant (b), which is approximately 2.898 x 106 nm·K.
- Calculate the temperature (T) using the formula T = b / λ.
- Finally, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Wavelength (λ) = 500 nm
Wien’s displacement constant (b) = 2.898 x 106 nm·K