The speed of an electromagnetic wave in a vacuum is a fundamental constant of nature, known as the speed of light. It's denoted by the letter c and has a value of approximately:

c = 299,792,458 meters per second (m/s)

Here's how we know this value:

1. Maxwell's Equations: James Clerk Maxwell's equations of electromagnetism predict the existence of electromagnetic waves and relate their speed to the permittivity (ε₀) and permeability (μ₀) of free space:

c = 1 / √(ε₀μ₀)

2. Experimental Verification: Various experiments have been conducted to measure the speed of light, starting with Ole Rømer's observations of Jupiter's moons in the 17th century. Modern measurements use techniques like interferometry and atomic clocks, achieving incredible precision.

3. Definition of the Meter: In 1983, the International Bureau of Weights and Measures (BIPM) redefined the meter based on the speed of light. The meter is now defined as the distance traveled by light in vacuum in 1/299,792,458 of a second. This makes the speed of light a fixed constant, by definition.

Therefore, the speed of light in a vacuum is a well-established and fundamental constant, a cornerstone of physics and our understanding of the universe.