When you calculate results that are aiming for known values, the percent error formula is useful tool for determining the precision of your calculations. The formula is given by:

The experimental value is your calculated value, and the actual value is the known value (sometimes called the accepted or theoretical value). A percentage very close to zero means you are very close to your targeted value, which is good. It is always necessary to understand the cause of the error, such as whether it is due to the imprecision of your equipment, your own estimations, or a mistake in your experiment.

Example Question

The 17th century Danish astronomer, Ole Rømer, observed that the length of the eclipses of Jupiter by its satellites would appear to fluctuate depending on the direction Earth was traveling relative to Jupiter at the time of the eclipse. If Earth was traveling toward Jupiter, the eclipes of Jupiter by, say, Io, would last for a shorter amount of time, while if Earth was traveling away from Jupiter, the eclipses would appear to be longer. In 1676, he determined that this phenomenon was due to the fact that the speed of light was finite, and subsequently estimated its velocity to be approximately 220,000 km/s. The current accepted value of the speed of light is almost 299,800 km/s. What was the percent error of Rømer's estimate?

Solution

Experimental value = 220,000 km/s = 2.2 x 10⁸ m/s

Actual value = 299,800 km/s = 2.998 x 10⁸ m/s

So Rømer was quite a bit off by our standards today, but considering he came up with this estimate at a time when a majority of respected astronomers, like Cassini, still believed that the speed of light was infinite, his conclusion was an outstanding contribution to the field of Astronomy.