`\lambda_{max} = (2.8977729\times 10^{-3} m K)/ 5800 `

499.61601724138

The Wavelength of a Black Body calculator compute the wavelength of the strongest emissions from a black body based on its temperature.

INSTRUCTIONS: Choose units and enter the following:

• (T) Temperature of the Black Body

Wavelength (λ): The calculator returns the wavelength (λ) in nanometers.  However, this can be automatically converted to other length units (e.g. angstroms) via the pull-down menu. 

General Information

A black body at a fixed temperature emits most strongly at a particular wavelength that depends only on the temperature. This formula describes that relationship. Formally, Wien's displacement law states that the spectral radiance of black body radiation per unit wavelength, peaks at the wavelength λ_max.  Therefore the formula for the temperature of a black body is::

   ` T = b /( λ_max) `

where 

• T is the black body absolute temperature in kelvins.
• λ_max is the maximum wavelength of the black body
• b is a constant of proportionality called Wien's Displacement constant , equal to 2.8977729(17)×10−3 m⋅K[1], or more conveniently to obtain wavelength in micrometers, b ≈ 2900 μm·K. 

---

Astronomy Calculators

The Astronomy Calculator Suite includes functions that are useful for studying astronomy and include the following:

• Kepler's 3^rd Law formula                             T² = (4π • R³)/(G • M)
  • (M) - mass of the system. 
  • (T) - period of the orbit.
  • (R) - separation distance between the two objects.
  • (G) - universal gravity constant
• Small Angle Formula        Small Angle Formula    α = S / D
  • (α) - angle
  • (D) - distance to astronomical object
  • (S) - size or diameter of astronomical object
• Flux and Magnitude formulas
  • Change in Magnitude from Flux Ratio
  • Flux Ratio from Magnitudes
• Telescope formulas
  • Resolving Power of a Telescope
  • Magnification of a Telescope
• Mass formulas
  • Mass from Luminosity
  • Mass from Acceleration and Radius
  • Mass from Speed and Separation
  • Mass of extra-solar planet from mass of star, radius of star orbit and radius of exoplanet orbit
  • Mass of extra-solar planet from mass and velocity of star and velocity of planet
  • Black Hole Mass Calculator
  • Black Hole Event Horizon Calculator
• Relative Size Formulas
  • Relative Size from Relative Temperature and Luminosity
  • Relative Temperature from Relative Size and Luminosity
  • Relative Luminosity from Relative Temperature and Size
• Wavelength Formulas
  • Velocity from shift in Wavelength and Unshifted Wavelength
  • Wavelength Shift from Wavelength and Speed
  • Blackbody Wavelength from Temperature
  • Blackbody Temperature from Peak Wavelength
  • Photon Energy from Wavelength
  • Photon Wavelength from Energy
• Other Formulas
  • Distance from absolute and apparent magnitude
  • Radius from Speed and Period
  • Speed of Circular Motion
  • Hubble Time
  • Galaxy Recession Velocity
  • Luminosity from Mass
  • Hubble's Law
  • Exoplanet Calculator 
  • Orbital Radial Acceleration
  • Distance to Barycenter
  • Sakuma-Hattori Equation
  • Astronomical Distance Calculator provides the distance from the Earth to numerous astronomical bodies (e.g. Sun, Moon, planets, stars, Milky Way's Center and Edge, Andromeda Galaxy)
  • Astronomical Distance Travel Time Calculator computes the time to travel to distant parts of space at different velocities.
  • 3D Vector Calculator
  • Drake Equation Calculator
  • Seager Equation Calculator
  • Friedman Equation Calculator
  • Lagrange Points L1 and L2
  • Schwarzschild Radius
  • Hill Sphere Radius
  • Escape Velocity