The formula and why it's always positive
Percent error = |Experimental − Theoretical| ÷ |Theoretical| × 100. The absolute value around the difference is deliberate: percent error is conventionally reported as a non-negative magnitude, since its purpose is to answer "how far off was this measurement, as a percentage" rather than "which direction did it miss in." The signed difference (experimental minus theoretical) is still useful contextual information — it tells you whether the measurement overshot or undershot — but the percent-error figure itself strips that sign away.
A worked example
A student measures the acceleration due to gravity as 9.7 m/s² in a lab experiment, where the accepted theoretical value is 9.8 m/s². The signed error amount is −0.1 m/s² (the measurement came in slightly low). The percent error is |−0.1| ÷ |9.8| × 100 ≈ 1.02% — a small, and for most undergraduate lab setups, quite reasonable amount of experimental error.
What counts as "theoretical" isn't always a textbook constant
In a physics lab, the theoretical value is often a well-known physical constant (like standard gravity, 9.8 m/s²). But percent error is used more broadly than physics labs — any situation with a known correct or accepted value and a separately obtained measurement or estimate can use the same formula: a forecast versus the actual outcome, a rough estimate versus a precise calculation, or a prototype's measured specification versus its designed specification.
Percent error vs percentage change — a common mix-up
Percent error and percentage change use structurally similar formulas — both divide a difference by one of the two values — but they answer different questions. Percentage change describes a value's own movement over time (old value to new value); percent error describes how far a single measurement deviates from a separately known correct value. The two aren't interchangeable even though a value could technically be plugged into either formula — using percent error's language ("experimental" and "theoretical") only makes sense when there's a genuinely correct reference value to measure against, not just an earlier point in a time series.
Interpreting the size of a percent error
What counts as an "acceptable" percent error depends entirely on context — a chemistry titration might target under 1% error, while a rough back-of-envelope engineering estimate might consider 10-15% error perfectly fine for its purpose. There's no universal threshold; percent error is a way to quantify deviation, not a pass/fail test on its own, so the acceptable range should come from the standards of whatever field or experiment you're working in.