# How Much Does Light Weigh?

Light is made of photons. And photons are massless particles, which means they have no invariant/resting mass. Therefore, light has no mass and no weight. End of story, right?

### The Force of Light

Did you know that light exerts pressure on objects? This force can even increase an objects weight, albeit to a small degree. For instance, Vsauce explains how much a landmass might weigh covered in sunlight (for the city of Chicago, sunlight only adds 300 lbs).

Although insignificant on a small scale, scientists must account for this force – called radiation pressure or solar radiation pressure – in planing space missions.

Solar radiation pressure plays a role in the formation of galaxies, stars and clusters, and solar/planetary systems. Additionally, solar radiation shapes the tails of comets.

### A Common Misconception

Light carries energy and momentum. We know that energy, momentum and mass are related. Can we assume that light also has mass? $E = mc^{2}$

This misconception stems from Einstein’s mass-energy equivalence formula. Einstein proposed that an object with energy has an equivalent amount of mass. Einstein’s formula only applies to objects with invariant/resting mass. Since photons have no resting mass, we have to use a different formula: $E = pc$

where p is the momentum of the particle. Therefore, we can observe momentum and energy for massless particles.

tl;dr Light does not have weight or mass. Light can push an object or increase its weight, to a minimal degree.

### We Weigh Less in the Dark, technically

Do we actually weigh more in sunlight? Functionally, no. But, we can still estimate an upper bound.

First, solar radiation pressure is applied to objects in the direction of sunlight. For this problem, let us pretend that we are shaped like rectangular solar panels.

Second, we learned from Vsauce that light exerts a force of pressure on the surface of Earth of about 1e-9 lbs per square inch. Considering the average human has a surface area of 1.9 meters squared, we can calculate the following: $\frac{1.0*10^{-9} lbs}{in^{2}} * \frac{1550 in^{2}}{m^{2}}\ * 1.9m^{2}$ $= 3.0 * 10^{-6}lbs$

So the next time you weigh yourself, turn off the lights. You might not notice a difference, but you just shaved a couple millionths of a pound.