Percent Error Calculator
Calculate the percent error between a measured value and the accepted true value, or work backwards: enter the percent error and one value to recover the missing one. Switch between signed and unsigned modes, see the absolute error and relative error alongside the percent error, and get a step-by-step breakdown of every calculation.
Formula
Worked example
Measured g = 9.8 m/s2, true g = 9.81 m/s2: |9.8 - 9.81| / |9.81| x 100 = 0.01 / 9.81 x 100 = 0.1019% error. Relative error = 0.001019.
How to calculate percent error
Percent error tells you how far a measured value is from the accepted true value, expressed as a percentage of that true value. Subtract the theoretical value from the experimental value, take the absolute value of that difference, divide by the absolute value of the theoretical value, and multiply by 100. Because the difference is taken in absolute value, percent error is reported as a positive number regardless of whether your measurement came out high or low. A smaller percent error means your measurement agrees more closely with the accepted value. The relative error is the same calculation without the final multiplication by 100, giving a dimensionless ratio rather than a percentage.
Why you divide by the theoretical value
A common mistake is dividing by the experimental value instead of the theoretical one. The theoretical value is your standard of truth: the accepted, expected, or exact figure. Dividing by the measured value would change your reference every time you take a new reading, making results impossible to compare across experiments. Keep the true value in the denominator and your percent errors will be consistent and meaningful. When the true value itself is zero, percent error is undefined and only the absolute error can be reported.
Reverse-solve mode: find the experimental or theoretical value
Sometimes you know the percent error and one of the two values, and you need to find the other. If you know the theoretical value T and the percent error P, the experimental value is E = T x (1 + P/100) when the measurement was high, or E = T x (1 - P/100) when the measurement was low. If instead you know the experimental value E and the percent error P, the theoretical value is T = E / (1 + P/100) for a high measurement or T = E / (1 - P/100) for a low one. Select "Solve for: Experimental value" or "Solve for: Theoretical value" in the mode dropdown to use these forms directly.
Signed vs. unsigned percent error
By default this calculator always reports a positive percent error using the absolute value of the difference. This is the standard convention in most scientific lab reports and textbooks. If you need to know the direction of your error (whether you measured too high or too low), toggle on "Report signed error." A positive result then means your measurement was above the true value; a negative result means it was below. The magnitude is the same either way, only the sign changes.
Interpreting percent error by field
| Percent error | Interpretation | Typical context |
|---|---|---|
| Under 1% | Excellent agreement | Precise physics / chemistry instruments |
| 1% to 5% | Good agreement | Most lab experiments, engineering tolerances |
| 5% to 10% | Fair agreement | Field measurements, rough estimates |
| 10% to 20% | High error | Review method or instrument |
| Over 20% | Very high error | Significant systematic error, check setup |
Acceptable error ranges vary widely by discipline and instrument precision. These are general benchmarks.
Frequently asked questions
Can percent error be negative?
In the standard absolute-value formula, no: percent error is always a positive number. However, if you turn on the "Report signed error" option in this calculator, a negative result means your measurement came out below the true value, while a positive result means it came out above. The signed form is used in some advanced contexts but the unsigned form is far more common in introductory and applied science.
What is the difference between percent error and percent difference?
Percent error compares a measured value to a known true value and divides by that true value. Percent difference compares two measurements when neither is the accepted truth and divides by their average. Use percent error when one value is the accepted standard and percent difference when both values are experimental and equally uncertain.
What is a good percent error?
It depends on the field and the precision of your instruments. In many lab settings, under 5% is considered good and under 1% excellent. Errors above 10% usually signal a problem with the method, the equipment, or the calculation. Highly sensitive physics and chemistry instruments may require errors under 0.1% to be acceptable.
What is relative error and how does it differ from percent error?
Relative error is the ratio of the absolute error to the theoretical value: |experimental - theoretical| / |theoretical|. Percent error is simply relative error multiplied by 100. A relative error of 0.05 is the same as a 5% percent error. Relative error is a dimensionless ratio useful for direct comparison across different scales and units.
How do I find the experimental value if I know the percent error?
Use the formula E = T x (1 + P/100) when the experimental value is above the theoretical, or E = T x (1 - P/100) when it is below. Switch the calculator to "Solve for: Experimental value," enter the theoretical value and the known percent error, and choose the direction of the measurement to get the result automatically.
How do I find the theoretical value if I know the percent error?
Use the formula T = E / (1 + P/100) when the experimental value is above the theoretical, or T = E / (1 - P/100) when it is below. Switch the calculator to "Solve for: Theoretical value," enter the experimental value and the known percent error, and choose the direction to get the result automatically.