Plancks Equation

The Planck's Equation calculator computes the energy of a photons based on their frequency (f) and Planck's Constant.

INSTRUCTIONS: Choose units and enter the following:

• (f) Frequency

Energy (E):  The calculator returns the energy in Joules.  However this can be automatically converted into other energy units via the pull-down menu.

The Math / Science

Planck's theory asserted that energy was transferred in units known as quanta in the ratio employed in Plank's Equation.  With this, one can calculate the energy of photons given their frequency. Plank's Equation is:

                  `E = h * f`

where:

• E is energy in Joules
• h is Planck's Constant
• f is the frequency

Note the following relations are also true:

`f = c/λ`

`f = E/h`

`E = (h⋅c) /λ` 

`λ = (h⋅c)/E`

`E = h * f`

where:

• E = energy of light
• f = frequency
• h = Planck's Constant
• c = Speed of Light in a vacuum 

The formula in this calculators is derived from the above relationships.

Light Frequency Range

The frequency of light (photons) ranges from approximately 1 kHz for plasma in space to 2.4 x 10²³ Hz for gamma rays.

Energy Calculators

• Kinetic Energy:                                    `KE= 1/2 *m * v^2`
• Kinetic Energy (change of velocity):    `KE = 1/2*m*(V_1-V_2)^2`
• Relativistic Kinetic Energy:                    `E_K = (m*c^2)/sqrt(1 - v^2"/"c^2") - m*c^2`
• Potential Energy:                                  `U(y) = m*g*y`
• Potential Energy of Gravity (two bodies):   `U(G) = - (G*m1*m2)/r`
• Nuclear Binding Energy:                       `E = m*c^2`
• Quantum Energy (Planck's Equation):   `E = h*f`
• Energy of a Particle in a Box:                `E_n=(n^2h^2)/(8mL^2)`
• Molecular Kinetic Energy:                      `KE = 3/2 * k_B *T`
• Electrostatic Potential Energy:               `E_(el) = k_e * (Q_1*Q_2)/d`
• Photon Energy from Wavelength:          `E = (h*c)/lambda`
• Heat Energy to Change Material Temperature:  `Q = C * m *DeltaT`