Percent Error Calculator — Experimental vs Theoretical
Enter an experimental measurement and the theoretical (accepted) value to calculate percent error. Shows the signed percent error, absolute percent error, and the raw numerical difference. Toggle absolute mode to ignore the sign.
Enter experimental and theoretical values to calculate.
How it works
What is percent error?
Percent error measures how far an experimental (measured) value deviates from a theoretical (accepted or true) value, expressed as a percentage of the theoretical value. The formula is: Percent Error = ((Experimental − Theoretical) / |Theoretical|) × 100%. A positive result means the experimental value is higher than theoretical; a negative result means it is lower.
Absolute percent error ignores the sign — it only measures the magnitude of the discrepancy regardless of direction. Scientists use signed error when the direction matters (systematic bias, such as a scale that always reads high), and absolute error when only accuracy matters (as in evaluating a measurement technique).
Sources of experimental error
Systematic errors shift all measurements in the same direction — a poorly calibrated instrument, consistent technique errors, or environmental factors like temperature affecting a chemical reaction. These produce a non-zero signed percent error. Random errors scatter measurements around the true value — they average out over many trials and are reduced by repeating the experiment. Precision refers to consistency; accuracy refers to closeness to the true value.
Acceptable percent error depends heavily on the field and measurement type. In chemistry labs, errors under 5% are generally acceptable for standard procedures; under 1% for analytical chemistry. In engineering, tolerances as tight as 0.001% are required for precision parts. In physics demonstrations, 5–10% errors are common given equipment limitations. Always state your accepted error threshold before taking measurements.
Percent error vs. percent difference vs. relative error
Percent error compares one value to a known reference (theoretical). Percent difference compares two measured values when neither is the accepted standard: Percent Difference = |A − B| / ((A + B) / 2) × 100%. Use percent difference when comparing two experimental results without a known true value.
Relative error is the ratio of the absolute error to the true value (without multiplying by 100): Relative Error = |Experimental − Theoretical| / |Theoretical|. It is dimensionless and expresses error as a fraction rather than a percentage. Multiplying relative error by 100 gives the absolute percent error. These terms are used interchangeably in some contexts, so check your textbook or field's conventions.
Frequently asked questions
›What is the percent error formula?
Percent Error = ((Experimental Value − Theoretical Value) / |Theoretical Value|) × 100%. The absolute value in the denominator ensures that a negative theoretical value doesn't flip the sign of the result unexpectedly. For absolute percent error, also take the absolute value of the numerator.
›What does a negative percent error mean?
A negative percent error means your experimental value is lower than the theoretical value. For example, if you measured the density of water as 0.95 g/mL instead of the accepted 1.00 g/mL: error = (0.95 − 1.00) / 1.00 × 100% = −5%. Your measurement underestimates the true value by 5%.
›What percent error is acceptable in a chemistry lab?
It depends on the experiment and level of precision required. For a first-year chemistry lab, under 5% is commonly considered acceptable. For quantitative analytical chemistry (titrimetry, gravimetric analysis), under 1% or even 0.5% is expected. For physical constants measured with specialized equipment, errors under 0.01% are possible.
›Can the theoretical value be zero?
No — the formula requires dividing by the theoretical value, so division by zero is undefined. If the theoretical value is zero, the concept of percent error does not apply. In such cases, use absolute error (the raw difference) instead.
›What is the difference between precision and accuracy?
Accuracy measures how close a measurement is to the true value — a small percent error means high accuracy. Precision measures how consistent repeated measurements are with each other, regardless of whether they are close to the true value. You can be precise but inaccurate (systematic error) or accurate but imprecise (random scatter). Ideally, measurements should be both.
›Why do we use the absolute value in the denominator?
The absolute value |Theoretical| in the denominator handles cases where the theoretical value is negative. Without it, a negative theoretical value would flip the sign of the error in a potentially confusing way. For example, if theoretical = −10 and experimental = −9, the error should be positive (experimental is 10% higher than theoretical), which the absolute value ensures.
›What is percent error used for in real life?
Scientists use it to evaluate experimental technique quality. Engineers use it to check if manufactured parts fall within specification. Quality control uses it to audit production consistency. Students use it to assess lab results. Analysts use it to compare model predictions to actual data — for example, checking if an economic forecast came within 3% of the actual GDP growth.
›How is percent error different from percent change?
Percent change compares two values over time: Percent Change = (New − Old) / |Old| × 100%. Percent error compares a measurement to a reference truth. The formulas are nearly identical but serve different purposes: percent change tracks change (stock price moved +12%); percent error evaluates accuracy (measurement was off by 3.5%).
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