Percent Error Calculator

About the Percent Error Calculator

A percent error calculator quantifies the accuracy of an experimental measurement by comparing it to a known theoretical or accepted value — expressing the discrepancy as a percentage of the true value. Percent error is one of the most fundamental calculations in experimental science, used in chemistry labs, physics experiments, engineering measurements, and quality control to communicate how close a measurement or result is to the accepted standard. A 5% percent error means the measured value differs from the theoretical by 5% of the theoretical value. In most high school and university lab courses, reporting percent error is a required part of every lab report as a standard of scientific practice. Our calculator computes percent error using the standard formula: |experimental − theoretical| / |theoretical| × 100%, and also shows the signed error (positive means measured high, negative means measured low) and the relative error as a decimal fraction. Whether you are measuring the density of aluminum (theoretical 2.70 g/cm³), the acceleration due to gravity (theoretical 9.81 m/s²), or verifying a chemical yield, this calculator provides immediate quantification of your measurement accuracy.

How It Works

% Error = |Experimental − Theoretical| / |Theoretical| × 100. The absolute value ensures a non-negative result regardless of direction. Absolute error = Experimental − Theoretical (signed). Relative error = Absolute error / |Theoretical| (dimensionless fraction). Example 1: measuring density of copper. Experimental: 8.75 g/cm³. Theoretical: 8.96 g/cm³. % Error = |8.75 − 8.96| / 8.96 × 100 = 0.21 / 8.96 × 100 = 2.34%. Absolute error = −0.21 g/cm³ (measured low). Example 2: chemistry titration. Experimental molarity: 0.105 M. Theoretical: 0.100 M. % Error = |0.105 − 0.100| / 0.100 × 100 = 5.0%. Measured 5% high. Example 3: measuring g (acceleration due to gravity) with pendulum. Measured: 9.65 m/s². Theoretical: 9.81 m/s². % Error = |9.65 − 9.81| / 9.81 × 100 = 1.63%.

Tips & Best Practices

• ✓Use the theoretical value in the denominator — always. Percent error is a measure of how far the experimental result is from the truth, not how far the true value is from the measurement. This asymmetry matters when errors are large.
• ✓Systematic versus random error: if your percent error is consistently in the same direction across multiple trials (always measuring low, for example), you likely have systematic error (instrument calibration, consistent procedural error). Random error produces inconsistent positive and negative errors around the true value.
• ✓Precision versus accuracy: a measurement can be precise (low spread between repeated measurements) but inaccurate (consistently wrong due to systematic error). Percent error measures accuracy. Standard deviation measures precision. Good science requires both.
• ✓Percent difference versus percent error: percent difference compares two experimental measurements without a known true value: |A−B| / ((A+B)/2) × 100. Use percent error when there is an accepted theoretical value; use percent difference when comparing two uncertain experimental values.

Who Uses This Calculator

Students completing lab reports for chemistry, physics, and biology courses. Scientists and researchers quantifying measurement uncertainty in experiments. Quality control engineers comparing measured values against specification tolerances. Calibration technicians verifying instrument accuracy against reference standards.