# How is the speed of light calculated?

How is the speed of light calculated? My knowledge of physics is limited to how much I studied till high school. One way that comes to my mind is: if we throw light from one point to another (of known distance) and measure the time taken, we could know the speed of light. but do we have such a precise time measuring tool?

• Light speed, as all speeds, is calculated by dividing a length by the time needed to travel that length. – Georg Feb 15 '11 at 10:52
• @Georg: basically no speed is calculated like that. There are zillions of physical laws involving speed and one can use whichever one of them is most suitable. – Marek Feb 16 '11 at 16:58
• @Marek, No speed is calculated by that ratio? But, to explain what my comment was aimed for: it should start "learnerforever" to think about the difference of "calculating" and "measurement". Not distinguishing that is a common beginner mistake. – Georg Feb 16 '11 at 17:10
• @Geord: I interpreted the word "calculated" as measured. Because otherwise the question doesn't really make any sense to me... – Marek Feb 16 '11 at 17:13

From Wikipedia:
Presently, the speed of light in a vacuum is defined to be exactly 299,792,458 m/s (approximately 186,282 miles per second). The fixed value of the speed of light in SI units results from the fact that the metre is now defined in terms of the speed of light.

Different physicists have attempted to measure the speed of light throughout history. Galileo attempted to measure the speed of light in the seventeenth century. An early experiment to measure the speed of light was conducted by Ole Rømer, a Danish physicist, in 1676. Using a telescope, Ole observed the motions of Jupiter and one of its moons, Io. Noting discrepancies in the apparent period of Io's orbit, Rømer calculated that light takes about 22 minutes to traverse the diameter of Earth's orbit. Unfortunately, its size was not known at that time. If Ole had known the diameter of the Earth's orbit, he would have calculated a speed of 227,000,000 m/s.

Another, more accurate, measurement of the speed of light was performed in Europe by Hippolyte Fizeau in 1849. Fizeau directed a beam of light at a mirror several kilometers away. A rotating cog wheel was placed in the path of the light beam as it traveled from the source, to the mirror and then returned to its origin. Fizeau found that at a certain rate of rotation, the beam would pass through one gap in the wheel on the way out and the next gap on the way back. Knowing the distance to the mirror, the number of teeth on the wheel, and the rate of rotation, Fizeau was able to calculate the speed of light as 313,000,000 m/s.

Léon Foucault used an experiment which used rotating mirrors to obtain a value of 298,000,000 m/s in 1862. Albert A. Michelson conducted experiments on the speed of light from 1877 until his death in 1931. He refined Foucault's methods in 1926 using improved rotating mirrors to measure the time it took light to make a round trip from Mt. Wilson to Mt. San Antonio in California. The precise measurements yielded a speed of 299,796,000 m/s.

• Good answer, +1. Just to add: the modern precise measurements of both distance and time are always based on "atomic clocks", the wavelength or periodicity of the electromagnetic radiation emitted by various atoms. They're how the meter and the second were defined before the speed of light was fixed by the SI definition you mentioned. Those atomic-clock measurements therefore yield the very same relative accuracy of distances $x$ and times $t$ if $x\approx ct$. – Luboš Motl Feb 15 '11 at 10:24
• Atomic clocks use low-frequency microwaves. The early ones used masers; newer ones, to be more accurate, cool down the matter by lasers and then they probe the resonant states by cavities, in atomic fountains. The distances are measured by similar radiation and interferometry - usually shorter wavelengths are being used to achieve the highest accuracy (for short enough distances). – Luboš Motl Feb 15 '11 at 10:26
• Wow - the next question should be How was the distance between the two mountains so accurately calculated! – DefenestrationDay Apr 9 '12 at 11:49
• How did Rømer overestimate the diameter of Earth's orbit (in light-minutes) by so much? – Anton Sherwood Sep 26 '19 at 16:19

The title of your question is about calculating the speed of light ($c$), but the body asks about measuring $c$. Others have answered you on the measurement issue, but I'd like to include a bit about the calculation of $c$ from principles.

Light, as an electromagnetic phenomenon, is described by Maxwell's equations:

$$\begin{eqnarray} \nabla \cdot E &=& \frac{\rho}{\epsilon_0}\\ \nabla \cdot B &=& 0\\ \nabla \times E &=& -\frac{\partial B}{\partial t}\\ \nabla \times B &=& \mu_0 J + \mu_0 \epsilon_0 \frac{\partial E}{\partial t} \end{eqnarray}$$

where $\rho$ is the charge density, $J$ is the current density, $E$ and $B$ are the electric and magnetic fields, respectively, $\mu_0$ is the magnetic permeability of free space, and $\epsilon_0$ is the electrical permittivity of free space. In the absence of any charges, one solution to these equations is a traveling plane wave with velocity

$$c= \frac{1}{\sqrt{\mu_0 \epsilon_0}}$$

Of course, this leaves the problem of measuring $\mu_0$ and $\epsilon_0$, but is a great demonstration of the fact that light is truly an electromagnetic phenomenon. As an added bonus, $\mu_0$ and $\epsilon_0$ can be measured in a variety of ways, without requiring very high time resolution.