Percent Error Calculator

A percent error calculator measures how far off an experimental or estimated value is from the true (theoretical) value, expressed as a percentage. The formula is straightforward: Percent Error = |Experimental - Theoretical| / |Theoretical| x 100%. It tells you the accuracy of your measurement or estimate relative to the accepted value.

Percent error is a cornerstone of scientific analysis. Every measurement has some degree of error, and quantifying that error is just as important as reporting the measurement itself. This calculator handles the absolute value computation, preventing sign confusion, and instantly tells you whether your result is within an acceptable margin.

• Chemistry labs - Comparing experimental yields, boiling points, and concentrations to known values
• Physics experiments - Evaluating the accuracy of measured constants like gravity (9.81 m/s^2) or the speed of sound
• Quality control - Determining if manufactured parts fall within acceptable tolerance ranges
• Forecasting - Measuring how far off a prediction was from the actual outcome
• Data analysis - Assessing model accuracy by comparing predicted vs. observed values
• Student lab reports - Properly reporting and analyzing experimental error is required in every science course

• Absolute vs. relative error - An error of 5 grams is huge when measuring 10 grams (50% error) but negligible when measuring 5000 grams (0.1% error). Context matters enormously
• Which value is "theoretical" can be unclear - In some contexts, the theoretical value is a textbook constant. In others, it is an average, a target, or a previous measurement
• Signed vs. unsigned error - The standard formula uses absolute values, but sometimes knowing the direction (positive = overestimate, negative = underestimate) is valuable
• Zero theoretical value breaks the formula - If the theoretical value is 0, dividing by it is undefined. Alternative metrics like absolute error must be used instead

The formula is: Percent Error = |Experimental Value - Theoretical Value| / |Theoretical Value| x 100%. The absolute value bars ensure the result is always positive, regardless of whether you overestimated or underestimated. A lower percent error means a more accurate measurement.

Absolute error is simply |Experimental - Theoretical|, the raw difference in the same units as the measurement. Relative error is the absolute error divided by the theoretical value (without the x 100). Percent error is the relative error expressed as a percentage. Each gives you a different perspective on the same concept.

Example

A student measures the density of aluminum as 2.85 g/cm^3. The accepted value is 2.70 g/cm^3. Absolute error: |2.85 - 2.70| = 0.15 g/cm^3. Percent error: 0.15 / 2.70 x 100% = 5.56%. This is a reasonable result for a student lab, though professional measurements would expect under 1%.

• Measured 9.65 m/s^2 for gravity (theoretical 9.81) - Percent error: 1.63%, a very good experimental result
• Estimated a crowd at 800 people (actual count 1000) - Percent error: 20%, indicating significant underestimation
• Lab yield of 4.2 grams (theoretical yield 5.0 grams) - Percent error: 16%, common in chemistry experiments
• Predicted sales of $120K (actual $115K) - Percent error: 4.35%, a solid forecast
• Measured boiling point of 99.1 C (theoretical 100 C) - Percent error: 0.9%, excellent precision

• Instant accuracy assessment - Know immediately how far off your measurement is from the accepted value
• Compare across different scales - Percent error normalizes the comparison so you can compare the accuracy of measuring mass, length, temperature, or any other quantity
• Get absolute and relative error too - See all three error metrics side by side for complete analysis
• Avoid sign errors - The absolute value calculation is handled automatically so you never accidentally report a negative percent error
• Improve your experimental technique - Track percent error across multiple trials to see if your accuracy is improving

What is an acceptable percent error?

It depends on the context. In a student chemistry lab, under 5% is generally considered good and under 10% is acceptable. In professional manufacturing, tolerances might require less than 0.1% error. In social science surveys, 3-5% margin of error is standard. There is no universal threshold.

What is the difference between percent error and percent difference?

Percent error compares a measurement to a known correct value and tells you accuracy. Percent difference compares two measurements to each other (neither is assumed correct) using their average as the denominator: |A - B| / ((A + B) / 2) x 100%. Use percent error when you have a true value; use percent difference when you are comparing two equivalent measurements.

Can percent error be greater than 100%?

Yes. If your experimental value is more than double the theoretical value (or less than zero in the signed version), the percent error exceeds 100%. For example, estimating a population at 300 when the actual count is 100 gives a 200% error. There is no upper limit.

What if the theoretical value is zero?

The percent error formula requires dividing by the theoretical value, so a theoretical value of zero makes it undefined (division by zero). In this case, use absolute error instead, or use an alternative metric like mean absolute error. Some fields use a modified formula that uses the average of both values in the denominator.

Should I report signed or unsigned percent error?

The standard convention is unsigned (absolute value), which tells you the magnitude of the error. However, signed error is useful when the direction matters. A positive signed error means your result was too high; a negative signed error means it was too low. Lab reports typically use unsigned unless specifically asked for the direction.

How does percent error relate to significant figures?

Your percent error should be reported with the same number of significant figures as your least precise measurement. If your experimental value has 3 sig figs and the theoretical value has 4, report your percent error with 3 sig figs. A percent error of 5.5555% from a 3-sig-fig measurement should be reported as 5.56%.