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Percent Error Calculator

Percent error compares a measured (experimental) value to a reference (true or accepted) value. Enter both numbers to see absolute error, relative error as a decimal, and percent error—standard steps on many science and maths mark schemes without substituting for method taught by your teacher.

The value you obtained from an experiment or estimate.

Known, literature, or target value you are comparing against.

How it works

Percent error compares a measured (experimental) value to a reference (true or accepted) value. Enter both numbers to see absolute error, relative error as a decimal, and percent error—standard steps on many science and maths mark schemes without substituting for method taught by your teacher.


The Formula

Absolute error = |measured − reference|

Relative error = absolute error ÷ |reference|

Percent error = relative error × 100%

Worked Example

  1. Lab-style check

    If you measure 24.8 g but the accepted value is 25.0 g, absolute error is |24.8 − 25.0| = 0.2 g. Relative error is 0.2 ÷ 25.0 = 0.008, so percent error is 0.8%.


Tips, Assumptions & Limitations

  • Use the accepted or true value as reference, not the other way round.
  • If the reference is exactly zero, percent error is undefined—you cannot divide by zero.
  • Percent error is always non-negative because we use the absolute difference.
FAQ

Compute absolute error as the absolute difference between your measured value and the reference value, divide by the absolute value of the reference, then multiply by 100 to express it as a percentage.

Percent error divides by the reference, so a reference of zero is not allowed here. Use a different summary, such as absolute error only, or follow your course’s guidance for that special case.

Yes if you have a clear reference and a measured figure—examples include a budget target in $ or £ versus what you spent, or a target mark versus the mark you earned. This tool does not estimate taxes or official grades; it only applies the formula you enter.

They are related but not identical. Percent error usually compares a measurement to an accepted true value, while percent difference often compares two measurements to each other. Use the definition your scheme specifies.

Companion article

Percent Error Calculator: Absolute and Percentage Error for Labs and Homework

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How this calculator works

Percent error is one of the most common ways teachers ask you to reflect on how close a measured value is to an accepted one. It shows up in science practical write-ups, applied maths tasks, and skills-based questions where you must compare a reading to a handbook or specification value.

Explanation

Start from two numbers: the value you actually measured (sometimes called experimental) and the reference value you treat as true or accepted. Absolute error is the size of the gap between them without caring about direction. Turning that into percent error means expressing that gap as a fraction of the reference, then scaling to a percentage. That is why the reference cannot be zero—there is no sensible relative comparison when the denominator would vanish. Both US customary and metric questions use the same arithmetic once the numbers are in consistent units.

Formula

Absolute error = |measured − reference|. Relative error = absolute error ÷ |reference|. Percent error = relative error × 100%.

Worked example

A student times 10 oscillations and gets 21.4 s while the teacher’s demonstration value is 20.0 s for the same setup. Absolute error is 1.4 s; dividing by 20.0 gives relative error 0.07, so percent error is 7%. For a non-science illustration, if a budget reference is £200 and spending was £212, the same steps yield 6% percent error versus that target—still just the formula, not financial advice.

How to use this tool

Type your measured value into the first box and the accepted reference into the second. The page returns absolute error, relative error as a decimal, and percent error as a percentage, plus a short line stating whether the measurement sat above or below the reference. If you leave non-numeric text or put zero in the reference field, you will see a plain-language error instead of a misleading percentage.

Frequently asked questions

Why can percent error never be negative here?
This calculator uses the absolute difference in the numerator, which matches the usual school definition focused on magnitude of error, not direction. If your teacher wants signed error, compare your course notes.
Do the units need to match before I type them in?
Yes. The formula only makes sense when both numbers describe the same quantity in the same units, whether grams, seconds, dollars for a simple comparison, or metres.
Is this the same as instrument uncertainty?
Not exactly. Percent error summarizes deviation from one reference number; uncertainty may combine calibration limits, repeated readings, and resolution. Treat this page as a formula aid for the definition above.

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