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Percent Error

Percent error is a way to describe how far off a measured or estimated value is from the true (accepted) value, written as a percentage. A smaller percent error means your result was closer to the correct value.

Percent error quantifies the relative difference between an experimental (or estimated) value and a known accepted value. It is calculated by dividing the absolute difference between the two values by the accepted value, then multiplying by 100. The result is always non-negative because of the absolute value in the numerator.

Key Formula

Percent Error=∣Experimental Value−Accepted Value∣∣Accepted Value∣×100\text{Percent Error} = \frac{|\text{Experimental Value} - \text{Accepted Value}|}{|\text{Accepted Value}|} \times 100
Where:
  • ExperimentalValueExperimental Value = the value you measured, calculated, or estimated
  • AcceptedValueAccepted Value = the true or known correct value

Worked Example

Problem: In a lab experiment, you measure the density of aluminum as 2.85 g/cm³. The accepted density of aluminum is 2.70 g/cm³. What is your percent error?
Step 1: Find the difference between the experimental value and the accepted value.
2.85−2.70=0.152.85 - 2.70 = 0.15
Step 2: Take the absolute value of that difference. Since 0.15 is already positive, it stays 0.15.
∣0.15∣=0.15|0.15| = 0.15
Step 3: Divide by the absolute value of the accepted value.
0.152.70=0.0556\frac{0.15}{2.70} = 0.0556
Step 4: Multiply by 100 to convert to a percentage.
0.0556×100=5.56%0.0556 \times 100 = 5.56\%
Answer: The percent error is approximately 5.56%.

Why It Matters

Percent error shows up constantly in science labs. When you measure the boiling point of water or the acceleration due to gravity, your teacher wants to know how close you got to the real value — and percent error is the standard way to report that. It also helps you compare results across experiments that use different units or scales, since everything is converted to a single percentage.

Common Mistakes

Mistake: Dividing by the experimental value instead of the accepted value.
Correction: The denominator must be the accepted (true) value. Dividing by your experimental value gives a different — and incorrect — result.
Mistake: Forgetting the absolute value and reporting a negative percent error.
Correction: Percent error uses absolute value, so the answer is always zero or positive. A negative sign would suggest direction (over vs. under), but the standard formula drops the sign.

Related Terms

  • Accuracy — Percent error directly measures accuracy
  • Precision — Consistency of measurements, distinct from accuracy