Percent Error Calculator

This percent error calculator (sometimes called a percentage error calculator or experimental error calculator) compares a measured value against a known accepted value and returns the percent error, absolute error, and relative error in one pass. It runs in your browser, so you can keep retyping values while you work through a lab report or problem set.

1. Enter the experimental (measured) value. This is the number your instrument, your calculation, or your procedure produced. If you timed a pendulum and computed g = 9.78 m/s², 9.78 is the experimental value.
2. Enter the theoretical (accepted) value. This is the reference number from a textbook, a certified standard, or a well-established measurement. For gravitational acceleration at sea level it is 9.80665 m/s². For the density of water at 4 degrees C it is 1.000 g/cm³.
3. Read the results. The big number is the percent error, rounded to four decimals. Below it the calculator shows the absolute error (the raw difference) and the relative error (the fraction form). A worked step-by-step line at the bottom shows exactly how the percent error was produced from your two inputs.

By default this calculator uses the absolute-value form, so the result is always positive. That is the convention used in most chemistry, physics, and engineering lab reports, where the question is "how far off was I?" rather than "in which direction did I miss?" If you need a signed percent error (positive means you overestimated, negative means you underestimated), just drop the absolute value bars from the numerator, or check the Formula section below for the signed version.

The percent error formula is short, but it has a few variations that matter depending on what you are measuring and which discipline you are in. The calculator above uses the standard absolute-value form. The variants below cover the cases the standard form leaves out.

1. Standard Percent Error Formula (absolute value)

%Error = |Experimental − Theoretical| ÷ |Theoretical| × 100

Where:
  Experimental = the value you measured or computed
  Theoretical  = the accepted, true, or reference value

This is what most textbooks mean when they say "how to calculate percent error." The absolute value bars guarantee a positive result, so you can compare trials without caring about direction.

2. Signed Percent Error (used in some sciences and engineering)

%Error = (Experimental − Theoretical) ÷ Theoretical × 100

Positive result → you overestimated (measurement too high)
Negative result → you underestimated (measurement too low)

Signed percent error is common in analytical chemistry spike recoveries, in gauge R&R studies, and anywhere a bias direction matters. If a scale reads 102 g for a 100 g standard, the signed error is +2%. A reading of 98 g gives −2%. Both have an unsigned error of 2%, which is why the unsigned form hides systematic bias.

3. Percent Difference vs Percent Error

Percent error compares a measurement to a known truth. Percent difference compares two measurements when neither is considered "correct." The denominators are different:

%Error      = |Experimental − Theoretical| ÷ |Theoretical| × 100
%Difference = |Value1 − Value2| ÷ ((Value1 + Value2) ÷ 2) × 100

Use percent difference when you run a measurement twice on two instruments and want to know how close the two readings are to each other. Use percent error when one of the two numbers is an accepted standard. Mixing them up is one of the most common grading mistakes on chemistry lab reports.

4. Absolute Error and Relative Error

Absolute Error = |Experimental − Theoretical|
Relative Error = Absolute Error ÷ |Theoretical|
Percent Error  = Relative Error × 100

Absolute error carries units (grams, seconds, meters). Relative error is unitless. Percent error is just relative error written as a percentage. This relative error calculator chain is why the widget above displays all three at once.

Worked Example 1: Gravitational Acceleration

Experimental g = 9.81 m/s²
Accepted g     = 9.80665 m/s²

Absolute Error = |9.81 − 9.80665| = 0.00335 m/s²
Relative Error = 0.00335 ÷ 9.80665 = 0.0003416
Percent Error  = 0.0003416 × 100 ≈ 0.034%

A timed-pendulum experiment that lands within 0.034% of the accepted value is an excellent result for an introductory physics lab.

Worked Example 2: Density of Aluminum

Experimental density = 2.65 g/cm³
Accepted density     = 2.70 g/cm³

Absolute Error = |2.65 − 2.70| = 0.05 g/cm³
Relative Error = 0.05 ÷ 2.70   = 0.01852
Percent Error  = 0.01852 × 100 ≈ 1.85%

A 1.85% percent error is well within the 5% tolerance most introductory chemistry courses accept for a density determination using a graduated cylinder and a balance.

Quick Reference: Common Lab Scenarios

Use this table to sanity-check a percent error before you commit it to a lab report. All numbers are computed with the standard formula in section 1.

*When the accepted value is zero, percent error is undefined because the denominator is zero. Use absolute error instead, or compare against a non-zero reference point (for example, use Kelvin instead of Celsius for the ice row).

A small percent error looks like a win, but it is only useful if you know what counts as "small" in your field, where your error came from, and what the number cannot tell you. This section covers the judgment calls that every lab report and every quality-control spec sheet relies on.

Acceptable Percent Error by Discipline

There is no universal cutoff. A 3% result that earns full credit in a high-school physics lab would get a process flagged in a GMP pharmaceutical plant. Rough industry and classroom ranges:

If a lab rubric does not state a cutoff, the safe rule is: under 5% is usually acceptable, under 10% needs a short explanation of likely sources, over 10% needs a serious error analysis and probably a repeat measurement.

Systematic vs Random Sources of Error

Every lab report asks you to identify sources of error. There are only two kinds, and they behave differently:

• Systematic error pushes every measurement in the same direction. Causes include a miscalibrated balance, a thermometer reading 0.5 °C high, parallax when reading a meniscus from the wrong angle, an uncorrected zero offset on a digital scale, or a room temperature that changes the density of your reagent. Repeating the measurement does not help. You have to fix the source or apply a correction.
• Random error scatters measurements around the true value. Causes include reading precision limits (you can only read a buret to ±0.02 mL), small vibrations, air currents, and human reaction time on a stopwatch. Averaging many trials reduces random error by roughly 1/√n.

Percent error combines both. If your percent error is large and consistent across trials, suspect a systematic problem. If it is large on one trial and small on the next, suspect random error and take more measurements.

Why a Low Percent Error Is Not Proof of Correctness

Two measurements with the same percent error can reflect very different experiments. A student who writes down "9.80 m/s²" without actually timing the pendulum has a percent error of 0.07%, which is better than any real student could achieve. A careful measurement that happens to land on the accepted value by coincidence has the same number but much more uncertainty behind it. Good lab practice reports the percent error alongside the standard deviation of repeated trials, the instrument precision, and the propagated uncertainty. A single-trial result with low percent error is weaker evidence than a multi-trial mean with small standard deviation, even if the second one has a slightly higher percent error.

Percent Error vs Accuracy vs Precision

Three words that get used interchangeably in casual speech but have strict meanings in measurement:

A rifle that groups five shots into a tight cluster three inches off the bullseye is precise but not accurate. A rifle that scatters five shots around the bullseye is accurate on average but not precise. Percent error answers the accuracy question only. Precision needs standard deviation of repeated trials. A rigorous lab result reports both, plus the uncertainty from instrument specs.