Percent Error Calculator

A percent error calculator compares a measured value with the accepted value: percent error = |experimental − theoretical| ÷ |theoretical| × 100. If you measure gravity as 9.65 m/s² and the accepted value is 9.81 m/s², the error is 0.16, and 0.16 ÷ 9.81 × 100 ≈ 1.63%. Use the tabs for signed error, several trials, percent difference or a missing value.

How to use the percent error calculator

1. Pick a tab: Percent error for one measurement, Multiple trials for a set of repeated measurements, % difference to compare two measurements, or Find a value to work backwards from a percent error.
2. Type the experimental (measured) value and the theoretical (accepted) value. Commas and negative numbers are fine.
3. Choose Absolute or Signed, and set the rounding to decimals or significant figures.
4. Read the answer, then open Show steps for the working and use Copy result for your lab notebook.

Percent error formula

Percent error = |E − T| ÷ |T| × 100, where:

• E is the experimental value: what you measured or estimated.
• T is the theoretical value: the accepted, true, expected or textbook value.
• The bars |…| mean absolute value, so the answer is never negative.

The formula is built from two smaller pieces. The absolute error is the size of the miss, |E − T|. NIST defines the error of a measurement as the result of the measurement minus the value being measured. The relative error divides that miss by the accepted value, |E − T| ÷ |T|, which turns it into a fraction of the true size. Multiplying the relative error by 100 gives the percent error.

Dividing by the accepted value is what makes percent error useful. Missing by 0.16 is small when you measure 9.81 m/s², but large when the true value is 0.5.

How to calculate percent error step by step

1. Subtract: E − T = 9.65 − 9.81 = −0.16.
2. Take the absolute value: |−0.16| = 0.16.
3. Divide by the accepted value: 0.16 ÷ 9.81 ≈ 0.01631.
4. Multiply by 100: 0.01631 × 100 ≈ 1.63%.

Signed percent error: positive or negative

Leave out the absolute value in the top part and you get the signed percent error, (E − T) ÷ |T| × 100. With the convention used here, a positive answer means the measurement came out too high and a negative answer means it came out too low. Gravity measured as 9.65 m/s² gives −1.63%.

The sign is useful when you repeat an experiment: if every trial is negative, something is pushing all your results low, such as friction or a timing delay. Be careful, though, because books disagree on the order of subtraction. NIST’s Dataplot software defines percent error as 100 × (accepted − measured) ÷ accepted, which gives the opposite sign. State your convention in a lab report.

Worked percent error examples for lab reports

Example 1: Density of aluminum

A student finds the density of an aluminum block to be 2.85 g/cm³. The accepted value is 2.70 g/cm³. The error is 2.85 − 2.70 = 0.15, so the percent error is 0.15 ÷ 2.70 × 100 ≈ 5.56%. The signed error is +5.56%: the measured density is too high, which often means the volume was measured too small.

Example 2: Boiling point of water

Water at sea level boils at 100 °C, and a thermometer reads 99.1 °C. The percent error is |99.1 − 100| ÷ 100 × 100 = 0.9%. Temperature has a catch: in kelvins the same reading is 372.25 K against 373.15 K, and the percent error drops to 0.9 ÷ 373.15 × 100 ≈ 0.24%. Percent error on a Celsius or Fahrenheit scale depends on where that scale puts zero, so use kelvins when your course asks for it.

Example 3: Speed of sound

The speed of sound in air at 20 °C is about 343 m/s. A resonance-tube experiment gives 329 m/s. The absolute error is 14 m/s, the relative error is 14 ÷ 343 ≈ 0.0408, and the percent error is about 4.08%.

Average percent error for multiple trials

Most labs repeat a measurement. Suppose five trials of the aluminum density give 2.65, 2.74, 2.68, 2.77 and 2.71 g/cm³. There are two different questions you can ask:

• Average percent error. Find the percent error of each trial (1.85%, 1.48%, 0.74%, 2.59% and 0.37%), add them and divide by 5: 7.04 ÷ 5 ≈ 1.41%. This tells you how far a typical single trial was from the accepted value.
• Percent error of the mean. Average the measurements first: 13.55 ÷ 5 = 2.71. Then |2.71 − 2.70| ÷ 2.70 × 100 ≈ 0.37%. This tells you how accurate your final answer is.

The second number is never bigger than the first, because high and low trials cancel when you average them. That is the difference between accuracy (closeness to the accepted value) and precision (closeness of the trials to each other). The Multiple trials tab gives both, plus the standard deviation of the trials; the standard deviation calculator shows that part in more detail.

Percent error vs. percent difference

Use percent error when one value is known to be right. Use percent difference when you compare two measurements and neither one is the accepted value, such as two lab groups’ results:

Percent difference = |A − B| ÷ ((A + B) ÷ 2) × 100.

For 48.2 and 50.6, the gap is 2.4 and the average is 49.4, so the percent difference is 2.4 ÷ 49.4 × 100 ≈ 4.86%. Swapping the two numbers gives the same answer. The percentage calculator has a percentage difference tab for everyday numbers, and the percent change calculator covers changes from an old value to a new one.

Percent error and significant figures

Your percent error cannot be more precise than your data. The subtraction rule keeps the fewest decimal places: 9.65 − 9.81 = −0.16 has two decimal places and two significant figures. The division rule then keeps the fewest significant figures: 0.16 (two) divided by 9.81 (three) gives an answer to two significant figures, so report 1.6%, not 1.6310%. The calculator works this out from the numbers you type. For practice with the rules, try the significant figures calculator.

Percent error quick reference

Common percent error mistakes

• Dividing by the measured value. Always divide by the accepted value. For 2.85 vs 2.70, 0.15 ÷ 2.85 ≈ 5.26% is wrong; 0.15 ÷ 2.70 ≈ 5.56% is right.
• Forgetting to multiply by 100. 0.0163 is the relative error; the percent error is 1.63%.
• Averaging signed errors and calling it the average percent error. Positive and negative errors cancel, so the result looks better than your trials were.
• Using percent error when the accepted value is 0. It is undefined, because you cannot divide by zero. Report the absolute error instead.
• Reporting too many digits. Round to the significant figures your data supports.

Writing percent error in a lab report

Give the formula, one line of working and the rounded result, then interpret it: “The measured value of g was 9.65 m/s², a percent error of 1.6% below the accepted 9.81 m/s². All trials were low, which suggests a systematic error such as a reaction-time delay in starting the timer.” Name a likely cause for the size and the sign of the error rather than writing “human error.”

Sources

Definitions checked November 2026:

• NIST Technical Note 1297, Appendix D: error and accuracy of measurement
• NIST Dataplot reference: PERCERR (percent error) and its sign convention
• North Carolina State University physics lab manual: percent error and percent difference
• Clemson University physics lab tutorial: % error and % difference

Percent error practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What is an acceptable percent error?

There is no single cutoff. It depends on the equipment and the experiment, so your instructor or lab manual sets the target. A percent error larger than the uncertainty of your instruments is a sign of a mistake or a systematic error worth explaining.

Can percent error be negative?

The standard formula uses an absolute value, so percent error is zero or positive. Signed percent error can be negative: with (E − T) ÷ |T| × 100, a negative answer means the measured value was below the accepted value.

Can percent error be more than 100%?

Yes. If the measured value is more than twice the accepted value, the error is larger than the accepted value itself. Measuring 30 when 10 is expected gives |30 − 10| ÷ 10 × 100 = 200%.

How do I find the average percent error of several trials?

Find the percent error of each trial, add them, and divide by the number of trials. For trials with errors of 1.85%, 1.48%, 0.74%, 2.59% and 0.37%, the average is about 1.41%.

What if the theoretical value is zero?

Percent error is undefined, because the formula divides by the theoretical value. Report the absolute error |E − T| instead, or, for temperatures, switch to kelvins so the accepted value is not zero.

Related calculators

• Percentage calculator
• Significant figures calculator
• Percent change calculator
• Standard deviation calculator
• Rounding calculator
• Scientific notation converter