Percent Error Calculator
Enter your measured value and the accepted (true) value, and this percent error calculator shows how far off your result is as a percentage, the way most lab reports ask for it. It also gives the absolute and relative error and tells you whether you came in high or low. A second mode finds the percent difference between two trials when there's no accepted value to compare against.
Updated
Results
- Signed errorPositive: measured above the true value
- Absolute error (in your unit)|measured − true|
- Relative error (decimal)Absolute error ÷ |true value|
- Measured value is
- Difference (in your unit)|value 1 − value 2|
- Average (in your unit)(|value 1| + |value 2|) ÷ 2
- Formula with your numbers
Results are estimates. See the methodology below.
How to use the calculator
- Choose Percent error when you compare a measurement with a known or accepted value: a textbook constant, a labeled standard or a theoretical prediction. Choose Percent difference when you have two measurements and neither one is the reference.
- In percent error mode, enter the measured value and the true (accepted) value. Both must be in the same unit; the unit itself cancels out.
- Tick Show signed error to keep the sign: positive means your measurement was above the accepted value, negative means below.
- In percent difference mode, enter the two values in any order. The result is the same either way.
The formula line shows your numbers plugged in, ready for a lab report.
Formulas used
Percent error
percent error = |measured − true| ÷ |true| × 100
The top of the fraction is the absolute error, the gap between the two numbers in the original unit. Dividing by the true value gives the relative error as a plain decimal, and multiplying by 100 turns it into a percentage. The signed version removes the absolute value on top: (measured − true) ÷ |true| × 100. This calculator uses measured minus true, the same order as the relative error definition on Wolfram MathWorld. Some lab manuals reverse it, so check which sign your instructor expects.
Percent difference
percent difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100
The gap is divided by the average of the two values, so neither one is treated as the right answer. Absolute values in the average keep the result symmetric and defined when a value is negative. For two values with the same sign it can't go above 200%, which is what you get when one of them is 0 (0 vs. 5 gives exactly 200%).
Percent error is undefined when the true value is 0, and percent difference when both values are 0; the calculator shows an error instead.
Worked examples
1. Measuring g with a pendulum
Your pendulum data give 9.6 m/s², and the accepted value for the lab is 9.81 m/s². The formula line reads |9.6 − 9.81| ÷ |9.81| × 100 = 2.140672783%, shown as 2.140673%, about 2.14%. The absolute error is 0.21 m/s², the relative error 0.021407, and the signed error −2.140673%: your value is low.
2. Density of an aluminum block
You measure 2.85 g/cm³ against a reference value of 2.70 g/cm³. The percent error is 5.555556%, about 5.56%, and the signed error is positive: your result is high.
3. Two stopwatch trials
Two lab partners time the same cart run at 4.52 s and 4.38 s. There's no accepted value, so use percent difference: the difference is 0.14 s, the average 4.45 s and the percent difference 3.146067%, about 3.15%.
Why the reference matters
| Comparison | Result |
|---|---|
| Measured 12, true value 10 | Percent error 20% |
| Measured 10, true value 12 | Percent error 16.666667% |
| 10 and 12, no reference | Percent difference 18.181818% |
The same gap of 2 gives three different answers depending on what you divide by, so pick the mode that matches your situation.
Reading your result
There's no universal cutoff for a good percent error. What's acceptable depends on the instrument, the method and the field: a few percent can be fine for a ruler-and-stopwatch experiment and far too much for a calibrated balance. Your lab handout or instructor sets what's expected.
The sign often tells you more than the size. If repeated trials all come out high, or all low, look for a systematic cause such as a miscalibrated scale or friction. Signs that jump around point more to random error.
Percent error is not percent change: to see how much a value grew or shrank from an old figure to a new one, use the percentage change calculator.
Frequently asked questions
What is the formula for percent error?
Subtract the true value from the measured value, take the absolute value, divide by the absolute value of the true value and multiply by 100: |measured − true| ÷ |true| × 100. A measured 96.2 against a true 100 gives 3.8%.
Can percent error be negative?
The standard percent error uses an absolute value, so it's never negative. The signed error keeps the direction: with measured 96.2 and true 100 it's −3.8%, meaning the measurement fell short. Tick the signed option if your report asks for it.
What's the difference between percent error and percent difference?
Percent error compares a measurement with a value you accept as correct and divides by that value. Percent difference compares two values of equal standing, such as two trials or two instruments, and divides by their average.
How does it work with negative values?
The formula still works because both the gap and the true value go through an absolute value. A measured −2.3 against a true −2.5 gives |−2.3 − (−2.5)| ÷ |−2.5| × 100 = 8%, and the signed error is a positive 8%: the measurement is above the true value on the number line.
Why can't the true value be zero?
Percent error divides by the true value, and dividing by zero has no answer. If the accepted value is 0, report the absolute error (the plain difference in your unit) instead.
Sources
Results are computed in floating-point arithmetic and rounded for display. Follow the formula and sign convention your course or lab protocol requires.