If a measurement has 5% error, can we say it has 95% accuracy? Most often when, in a numerical problem, it is demanded that we calculate the accuracy of the final result, we write the final result in terms of the error.
So I want to know if, in a measurement, there is 10% error, can we convey the same information by saying that the measurement has 90% accuracy?
 A: You need to define what "error" means; typically it is an estimate of the standard deviation based on a series of measurements.  If you take a series of measurements, you can estimate the standard deviation of the population.  You can also estimate the mean and the standard deviation of the mean.  When you report your result you should report $\mu \pm \sigma_{\mu}$ where $\mu$ is the estimate of the mean from your measurements and $\sigma_{\mu}$ is your estimate of the standard deviation of the mean, not the standard deviation of the population which you can also estimate. See my answer to Uncertainty in ripetitive measurements this exchange for details.  If you told me "my result is x with 10% error", without more information I would assume that based on your measurements, x is the mean and 0.1x is the standard deviation of the mean.
You can also establish a confidence interval based on the measurements, and some call that the accuracy.  See discussions of confidence interval online or in a statistics text such as Probability and Statistics for the Engineering, Computing, and Physical Sciences by Dougherty.
A: *

*Prefer “uncertainty” over “error.” When you say “error” you imply that Someone Out There has determined the Right Answer.  This isn’t how it works outside of an introductory lab class.


*When you say “I’ve measured $x$ with 5% uncertainty,” you are saying something very specific: your result $x=100$ means that another high-quality measurement of $x$ would probably also give a result in the interval $95 < x < 105$.


*If you start saying things like “95% accurate,” you are going to confuse people who are listening for a confidence interval, which is another way to analyze uncertainties.  Physicists tend to like “one-sigma” confidence intervals, which in your case would mean, roughly,

a repeat of my experiment would have a 68% chance of getting (again) a value in the interval $95 < x < 105$

In other fields, especially the social sciences, people like to report “two-sigma” confidence intervals, which would mean something like

a repeat of my experiment would have a 95% chance of getting (again) a value in the interval $90 < x < 110$

Beware that this description of the confidence interval is specifically listed in the linked encyclopedia article as a misunderstanding (mea culpa).  For Gaussian-distributed measurements which all have the same uncertainty, the probability that "your" measurement lies within "my" one-sigma confidence interval is just slightly better than fifty-fifty.  The definition of the confidence interval is based on the "true value" of the measured parameter. However, whether that "true value" exists is both a philosophical and a practical question. The world is different from our models of it.


*As a commenter says: sometimes you do a measurement and end up with 200% uncertainty, in which case your experiment has not (yet) determined whether your quantity is positive or negative.
So, to your title question: no, don’t do that.  If your measurement has 5% uncertainty, communicate this by saying “my measurement has 5% uncertainty.”
