Percent Error Calculator

The Percent Error Formula

Percent error measures how far a measured or experimental value strays from a known, accepted, or theoretical value, expressed as a percentage of that accepted value. The standard formula is: percent error = |experimental value − theoretical value| ÷ |theoretical value| × 100. Using the absolute value in the numerator (the standard scientific convention) means the result is always reported as a positive percentage, since the focus is usually on the size of the discrepancy rather than its direction. Note that the theoretical value always goes in the denominator, not the experimental value — dividing by the wrong number is the most common mistake when calculating this by hand.

Signed Error: Knowing Which Way You Missed

Sometimes it matters whether your measurement overshot or undershot the accepted value, not just by how much. Switching to "Signed" above skips the absolute value step, so a positive result means your experimental value was higher than the theoretical value, and a negative result means it was lower. This is useful in lab settings where systematic bias (a scale that always reads slightly high, for example) is itself a meaningful finding.

Percent Error vs. Percentage Change

Percent error is easy to confuse with a plain percentage difference between two numbers. The formula looks similar, but percent error specifically implies one value is the "true" or accepted reference point and the other is a measurement being judged against it. If you're just comparing two arbitrary numbers with no accepted reference, the percentage calculator is the more appropriate tool. If your raw data itself needs summarizing first — for example averaging several trial measurements before checking their error — the average calculator can help.