Percent Error Calculator
This percent error calculator uses your experimental and theoretical values to calculate percent error, along with absolute and relative error. It also gives step by step solutions for each input.
Enter your values
Compare an experimental result with an accepted value.
Step-by-step solution
See the formula, substitution, and final calculation.
A percent error calculator shows how much an experimental value (measured value) differs from a theoretical value (actual value), expressed as a percentage.
If your kitchen scale shows a different weight from the amount printed on a food package, percentage error expresses that difference as a percentage of the stated weight. A jelly bean bag labeled 10 oz that weighs 10.3 oz misses by only 3%.
That gap is what the number quantifies: how far the measured value lands from the known value. In science labs and quality control, a lower percent error points toward greater accuracy, though human error and instrument limits never vanish.
What Is Percent Error Definition?
Percent error is how far a measurement landed from the accepted value, written as a percentage of that known value.
Getting 0% is the best possible result, yet in real lab reports it often points to rounding rather than perfect skill.
In physics and chemistry, the observed value almost never equals the true value. Device limits and plain human error open a gap, and the difference between them is the absolute error. Relative error then compares that deviation to the baseline (true value).
Anyone who has weighed a bag of candy on a lab scale has felt that gap. A small percentage error says the method worked, while a large percentage error calls for re-evaluating, not just blaming one mistake.
Percent Error Formula
The denominator decides what percent error means: the gap is judged against the accepted value (theoretical value), even when the experimental value is larger. To find percent error, the standard formula is
% error = (|experimental value – Theoretical value| ÷ |Theoretical Value|) × 100
Another name for this formula is the percent error equation.
Both quantities must use the same units for this comparison between the reading and its accepted or theoretical value to work.
A reading of 48 against the accepted value of 50 gives a gap of two; dividing by 50 gives a decimal fraction of 0.04, which becomes 4% when you multiply by 100.
The absolute value makes the answer non-negative, whether the reading falls above or below the true value, so the percentage alone cannot show direction. When the reference is zero, the formula is undefined because it requires division by zero.
How to Calculate Percent Error (Steps)
Percent error builds on absolute error and relative error. These connections explain how the formula turns a measurement gap into a percentage. To calculate percent error, follow this step-by-step procedure:
- Start with the accepted value (theoretical value): Identify the accepted reference value and the measured value. Keep both in matching units before doing any arithmetic.
- Subtract the accepted number from the experimental number. Take the absolute value of this gap to find the size of the measurement error. This gives us the absolute error.
- Divide that gap by the theoretical value (accepted value). A common mistake is dividing by the measured value, which changes the comparison. This gives us relative error. A zero theoretical value makes this calculation undefined.
- Convert the ratio into percent error by multiplying it by 100. For example, a reading of 34 compared with a reference value of 30 produces an error of (4 ÷ 30) × 100 ≈ 13.3333333%.
You can also take the absolute value at the end after performing all calculations instead of taking it at the start.
How to Use the Percent Error Calculator?
Use our percent error calculator to check how closely your experimental value matches an expected value. How to use this calculator is explained step by step here:
- Take your measurement and enter it in Experimental value. Enter the true value in Theoretical value.
- Use matching units in both fields; the reference cannot be 0.
- Enter numbers using international or Indian comma grouping, or scientific notation, then select Calculate to quickly check your estimation.
- Review the percentage, absolute error, relative error, and calculation steps: subtract, divide, and multiply by 100.
- Select Copy result to copy the reported percentage. Pick Reset to clear entries.
Rounded results show up to nine significant digits in our percent error calculator. A smaller % error suggests better agreement.
Percent Error Examples
A machined shaft measuring 25.08 mm against 25.00 mm has a 0.32% error. It passes a 0.5% tolerance, showing why a small result still needs a stated limit.
A negative case reveals direction: pendulum gravity measured at 9.72 m/s² against 9.80 m/s² gives ≈0.816% error. Its signed error is -0.816%, meaning the measurement is below the accepted value. Check timing precision, air resistance, and string stretch before blaming the theoretical value.
For the boiling point of water, 101.5 °C against 100.0 °C gives 1.5%; 99.1 °C gives 0.9%. Both miss the true value, although on opposite sides.
A jelly bean serving size of 30 against 20. Subtract 20 from 30, then divide the difference by the labeled serving size of 20 and multiply by 100. It gives a percent error of 50%.
For speed of sound in air at 20 °C, 329 m/s against 343 m/s differs by 14 m/s, giving 4.08163265%. Finally, generic values of 56.891 against 62.327 give 8.722%; the same calculation works without a laboratory setting.
Even 9.80 m/s² against 9.81 m/s² produces ≈0.102% error. This sub-1% difference can look strong, yet the decision still depends on the required tolerance and consistent testing conditions.
Absolute Error and Relative Error
Our percent error calculator also shows Absolute and Relative error values along with percent error.
Absolute error (or experimental error) gives the absolute difference between a measured and a known standard value. To find absolute error, the formula is
Absolute Error = |Experimental Value-Theoretical value|
Relative error divides this gap by the standard value. This makes gaps easier to assess across different standard sizes.
Relative Error = Absolute Error / Theoretical Error
For a measured density of 0.92 g/mL against an accepted density value of 1.00 g/mL, the absolute error is 0.08 g/mL. The relative error is 0.08 ÷ 1.00 = 0.08, which becomes 8% when multiplied by 100.
A zero reference makes relative error undefined because it would divide by zero. In that case, report the raw difference with its units.
The revision uses 45 distinct database entries, removing 69 entries across all headings, including repeats.
Negative / Signed Percent Error and the Absolute Value
Signed or Negative percent error occurs when we don’t take into account the absolute value.
Negative % error describes signed direction, not automatically poor accuracy. For a positive accepted value, a negative result means the observed value undershot the theoretical value; a positive result means it overshot.
In physics labs, weighing 50 N against the theoretical value of 60 N produces -16.6666667% using signed error, but 16.6666667% using percentage error with absolute value. These percentages share a magnitude: underestimation and overestimation describe direction, while absolute error shows the size of deviation.
Use this formula for absolute percentage error:
% error = |(E – T) / T| × 100
Here, E is the experimental or measured value, and T is the true or theoretical value or certified reference. The numerator captures separation; the denominator supplies the baseline.
Check subtraction order when comparing displayed results. With a negative accepted value, dividing by |accepted| preserves the above-or-below interpretation; a zero reference makes this ratio undefined.
Percent Error vs. Percent Difference
Percent error compares a lab measurement with a trusted reference accepted or theoretical value. Its denominator is the absolute accepted value, so swapped values can change the result; percent difference stays unchanged.
Two lab readings can disagree without either being a known real value. To compare two values with equal status, choose percent difference. It measures their gap against the average of both values. To calculate percentage difference, we use the following formula
Percentage Difference = (|M1 – M2|/(M1 + M2) / 2) * 100
For quick examples, readings of 48 and 50 give 4% error if 50 is accepted, but about 4.08% difference.
Percent Error FAQs
1) What is the experimental value in percent error
The experimental value is the result you obtain from a measurement or experiment. In a % error calculation, you compare this result with the theoretical or accepted value to determine how far they differ.
2) What if the accepted value is 0?
When the accepted value is 0, % error is undefined because its formula divides by zero. Even if both values are zero, the result remains undefined. Report the absolute error to show the difference in magnitude.
3) Can percent error be negative?
No. Standard percent error is zero or positive because its formula uses absolute values. A negative result occurs with signed error when you omit the absolute value, where underestimation means the measured value falls below a positive true value.
4) Can percent error be over 100%?
Yes. A reading of 25 against an actual value of 10 gives 150% error: |25 − 10| ÷ 10 × 100. % error has no upper limit; greater overestimation can push it higher.
5) Why does the percent error formula use absolute value?
The absolute value shows the positive magnitude of a nonzero error, whether a measurement overshot or undershot the true value. Equal deviations produce equal percent errors. Signed %error preserves direction when that detail matters.
6) Does percent error measure accuracy or precision?
Percent error measures accuracy by comparing a measured result with an accepted value. A smaller % error indicates closer agreement. Precision describes how closely repeated measurements agree with one another.