Percent Error Calculator

Calculate the percent error between an experimental (measured) value and a theoretical (accepted) value using the percent error formula: |(Experimental - Theoretical) / Theoretical| × 100%

What is Percent Error?

Percent error measures how far off an experimental or measured value is from the true or accepted value, expressed as a percentage.

Percent Error Formula:

Percent Error = (|Experimental Value − Theoretical Value| ÷ |Theoretical Value|) × 100%

where: - Experimental Value = the value you measured or observed - Theoretical Value = the accepted, true, or expected value - | | = absolute value (makes the result positive)

How to Calculate Percent Error

1. Subtract the theoretical value from the experimental value
2. Take the absolute value of the difference (remove any negative sign)
3. Divide by the absolute value of the theoretical value
4. Multiply by 100 to convert to a percentage

Example

You measured the boiling point of water as 99.1°C, but the accepted value is 100°C:

• |99.1 − 100| = 0.9
• 0.9 ÷ 100 = 0.009
• 0.009 × 100 = 0.9% percent error

Percent Error vs. Percent Change vs. Percent Difference

These three formulas are often confused:

• Percent Error — compares a measured value to a known correct value. Uses the theoretical value as the denominator.
• Percent Change — measures how much a value has increased or decreased over time. Uses the original value as the denominator.
• Percent Difference — compares two values when neither is considered the "correct" one. Uses the average of both values as the denominator.

Use percent error when you have a known standard to compare against.

What is an Acceptable Percent Error?

Acceptable percent error varies by field:

• Chemistry: under 5% for most lab experiments
• Physics: under 5–10% for student-level experiments
• Engineering: often under 1%, depending on tolerances
• Manufacturing: may require less than 0.1% for precision parts
• Biology: varies widely, but under 10% is a common benchmark

The key is context — higher-stakes applications require lower error.

Sources of Error

Common reasons for percent error in experiments:

• Measurement limitations — instruments have finite precision
• Human error — misreading scales, inconsistent technique
• Environmental factors — temperature, humidity, vibration
• Systematic errors — consistently biased equipment or methods
• Random errors — unpredictable fluctuations in measurements

Real-World Applications

• Chemistry labs — comparing experimental yields to theoretical yields
• Physics experiments — verifying known constants (gravity, speed of light)
• Quality control — checking if manufactured parts meet specifications
• Pharmacology — ensuring drug concentrations match target doses
• Environmental science — comparing field measurements to models
• Cooking and baking — recipe scaling accuracy

Common Questions

What is the percent error formula?

The percent error formula is: Percent Error = (|Experimental Value − Theoretical Value| ÷ |Theoretical Value|) × 100%. It gives you a single percentage that shows how accurate your measurement was.

Can percent error be negative?

The standard percent error formula uses absolute value, so the result is always positive (or zero). However, some teachers and textbooks use a signed version — without the absolute value — to indicate whether the experimental value was above (+) or below (−) the expected value.

What is a good percent error?

It depends on the field and experiment. In a high school chemistry lab, under 5% is considered good. In precision manufacturing, even 1% may be too high. The acceptable range depends on the application's tolerance requirements.

Can percent error be over 100%?

Yes. If your experimental value is more than double (or less than half) the theoretical value, percent error will exceed 100%. For example, measuring 25 when the expected value is 10 gives a percent error of 150%.