Percent Error Calculator
Calculate the percent error between an experimental value and a theoretical value.
The Formula
Positive result = overestimate
Negative result = underestimate
= |9.8 − 9.81| / |9.81| × 100
= 0.01 / 9.81 × 100
= 0.102% error
What Is Percent Error?
Percent error measures how far an experimental or measured value is from the accepted theoretical (true) value, expressed as a percentage. It is one of the most fundamental tools in experimental science for evaluating the accuracy of a measurement or result. A low percent error means your measurement is close to the true value. A high percent error indicates significant deviation, which could mean systematic measurement error, imprecise equipment, flawed procedure, or that the theoretical model does not accurately describe the real-world situation.
The Percent Error Formula
Percent Error = (|Experimental Value - Theoretical Value| / |Theoretical Value|) × 100%. The absolute value in the numerator ensures the result is always positive — we typically care about the magnitude of the error, not its direction. The absolute value in the denominator handles cases where the theoretical value is negative. If direction matters for your application (overestimate vs. underestimate), you can use the signed version without absolute values.
What Is Acceptable Percent Error?
It depends heavily on the field, context, and precision requirements. In a high school chemistry lab, 5% or less is generally considered a good result given the equipment limitations. In analytical chemistry or pharmaceutical manufacturing, tolerances of 1–2% or less may be required. In physics experiments with simple equipment, 10% might be acceptable. In engineering and manufacturing, specifications often require less than 1%. And in surveys and polling, 5–10% sampling error is typical. Always interpret percent error relative to the precision required by your application.
Frequently Asked Questions
What is the difference between percent error and percent difference?
Percent error compares a measurement to a known theoretical value. Percent difference compares two experimental values to each other when neither is a "true" value.
Can percent error be negative?
The standard formula uses absolute value, giving a positive result. Some applications do track the sign (positive = overestimate, negative = underestimate).