Percent Error Calculator

Compare a measured or experimental value against the true, accepted, or theoretical value. The calculator reports the absolute error, the relative error, and the percent error — with the signed version so you can also see the direction of the miss.

Before You Calculate

  • The measured (experimental) value is what you observed; the accepted (true, theoretical) value is the reference you compare against.
  • Percent error is conventionally reported as a positive number; the signed version below tells you whether you over- or under-estimated.
  • Both values must be in the same units — comparing grams to kilograms will inflate the error a thousandfold.

The Three Error Measures

Absolute error = |measured − accepted|

Relative error = |measured − accepted| / |accepted|

Percent error = relative error × 100%

The absolute error keeps the units of the measurement and answers “how far off, in raw terms?” The relative and percent errors strip the units away by dividing by the accepted value, which is what makes measurements of different scales comparable: being 0.17 m/s² off on gravity (1.7%) is far better than being 0.17 seconds off on a 2-second stopwatch reading (8.5%).

Percent error is a measurement quality metric — it compares an observation to a known truth. That distinguishes it from percent change (new vs old value over time) and percent difference (two equally valid values compared to their average), which use different denominators for different questions.

Worked Example: Measuring Gravity

A physics class times a pendulum and computes g = 9.98 m/s². The accepted value is 9.81 m/s².

  1. Absolute error: |9.98 − 9.81| = 0.17 m/s².
  2. Relative error: 0.17 / 9.81 ≈ 0.017329.
  3. Percent error: 0.017329 × 100 ≈ 1.7329%.
  4. Direction: the signed error is +1.7329%, an overestimate — often a hint of systematic timing bias rather than random noise.

Whether 1.73% is good depends on the context: for a stopwatch-and-string pendulum lab it is a solid result; for a metrology laboratory calibrating instruments it would be enormous. Percent error has no universal “passing” threshold — the instrument, method, and purpose set the bar.

Systematic vs Random Error

A single percent error blends two different failure modes. Random error scatters measurements symmetrically around the truth and shrinks when you average repeated measurements — its size is summarized by the standard deviation of the readings. Systematic error (bias) pushes every reading the same direction — a miscalibrated scale, a consistently slow reaction time — and no amount of averaging removes it. Repeating the measurement and watching whether the signed error keeps the same sign is the quickest diagnostic for bias.

Frequently Asked Questions

What is the formula for percent error?

Percent error = |measured - accepted| / |accepted| x 100%. Take the difference between your measurement and the accepted value, divide by the accepted value, and express the result as a percentage. In the gravity example, |9.98 - 9.81| / 9.81 x 100 = 1.73%.

Can percent error be negative?

By the standard convention, no - the absolute value makes it positive, since it measures the size of the miss. Some courses do use a signed version where a negative result means the measurement came in below the accepted value. This calculator reports both, so you can follow whichever convention your course or field expects.

What is the difference between percent error and percent difference?

Percent error compares a measurement against a known correct value, dividing by that accepted value. Percent difference compares two equally trustworthy values - say, two students' independent measurements - dividing by their average because neither one is 'the truth'. Using percent error between two measurements silently treats one of them as correct.

What counts as a good percent error?

It depends entirely on the method and the field. Introductory physics labs often consider under 5% good and under 10% acceptable, while analytical chemistry may demand under 1% and surveying under 0.01%. Compare your percent error against the precision your instruments can plausibly deliver rather than against a universal cutoff.

Why is percent error undefined when the accepted value is zero?

The formula divides by the accepted value, and dividing by zero is undefined - conceptually, there is no scale against which to express the miss as a percentage. When the true value is zero (for example, a null measurement), report the absolute error in original units, or use percent difference against a meaningful reference scale instead.

Does a small percent error mean my experiment was accurate?

It means this particular result landed close to the accepted value, which is evidence of accuracy but not proof. A lucky cancellation of two opposing systematic errors can produce a deceptively small percent error once. Repeating the measurement tells you more: consistent small signed errors indicate genuine accuracy, while scattered ones indicate luck riding on low precision.