Percent Error Calculator
Calculate percent error between an observed and true value. Shows absolute error, relative error, and a quality rating. Supports signed (negative) error for directional analysis.
You might also need
How It Works
Take the absolute difference between observed and true values. Divide by the absolute value of the true value. Multiply by 100. The result tells you the error as a percentage of the expected value.
|Observed − True| / |True| × 100%|9.8 − 10| / |10| × 100 = 2%The absolute error is the magnitude of the difference between your measurement and the true value. It has the same units as the measurement — grams, meters, seconds, etc.
Absolute Error = |Observed − True||56.891 − 62.327| = 5.436Relative error normalizes the absolute error by the true value, making it dimensionless. A 5g error on a 10g sample is far more significant than a 5g error on a 10kg sample.
Relative Error = |Observed − True| / |True|5.436 / 62.327 = 0.08722 = 8.722%If you disable absolute value, a negative error means you measured less than expected. A positive error means you measured more. This directional information can reveal systematic bias in a measurement method.
(Observed − True) / |True| × 100%(7 − 9) / 9 × 100 = −22.22%Excellent: < 1% — the measurement is very close to accepted value. Good: 1–5% — acceptable for most lab work. Acceptable: 5–10% — common in introductory labs. High Error: > 10% — experiment likely needs revision.
Rating based on |% error| threshold2% → Good | 8% → Acceptable | 15% → High ErrorYou measure the density of aluminum as 2.64 g/cm³. The accepted value is 2.70 g/cm³. Percent error = |2.64 − 2.70| / 2.70 × 100 = 2.22%. This falls in the "Good" range — a solid experimental result.
|2.64 − 2.70| / 2.70 × 1000.06 / 2.70 × 100 = 2.22%Quick Reference
Common lab scenarios — verify instantly above.
Physics
Obs 9.8, True 9.81
0.102%
Chemistry
Obs 48, True 50
4%
Biology
Obs 98, True 100
2%
Excellent
Obs 9.99, True 10
0.1%
Acceptable
Obs 92, True 100
8%
High Error
Obs 85, True 100
15%
Negative
Obs 7, True 9 (signed)
−22.22%
Density Lab
Obs 2.64, True 2.70
2.22%
Tips & Shortcuts
Always use the accepted true value in the denominator — not the observed (measured) value. This is the most common mistake in lab reports.
A percent error of 0% is ideal but rare. Focus on whether your error is within the acceptable range for your specific experiment.
If your percent error is consistently in one direction (always + or always −), you likely have a systematic error in your measurement method.
For very small true values (close to zero), percent error can be enormous even with small absolute errors. Context matters.
When comparing experiments, relative error is more meaningful than absolute error — 5 grams off on a 10-gram sample is catastrophic; on 10 kg, it is negligible.
The quality thresholds (< 1%, < 5%, < 10%) vary by field. Physics experiments often require tighter tolerances than biology experiments.
Common Mistakes
Dividing by the observed value instead of the true value
Always divide by the true (accepted, known) value. The true value is your reference point.
Forgetting the absolute value signs
Without |...| you can get negative results that misrepresent direction as error magnitude. Use |Observed − True| unless you specifically need signed error.
Reporting percent error without context or units
Always state what you were measuring: "2% error in density measurement" not just "2% error".
Using percent error when the true value is unknown
If the true value is unknown, percent error is meaningless. Use standard deviation or range instead.
Thinking a lower percent error always means a better experiment
A very low percent error could result from luck or error cancellation. Look at multiple trials.
Confusing percent error with percent difference
Percent error compares to a known true value. Percent difference compares two measurements with no established "truth".
Frequently Asked Questions
Percent error measures how far a measured value deviates from the accepted true value, expressed as a percentage of the true value.
Under 1% is excellent. Under 5% is generally good. Under 10% is acceptable in many high school and university labs depending on the experiment.
With the standard formula using absolute value, no. But if you allow signed error (disable absolute value), a negative result means your observed value was smaller than the true value.
Percent Error = (|Observed − True| / |True|) × 100%. The absolute value ensures the result represents magnitude regardless of direction.
Absolute error is the raw difference: |Observed − True|. Relative error divides by the true value: |Observed − True| / |True|. Percent error is relative error × 100.
The true value is the reference point. Dividing by it gives you the error as a fraction of what the value should be, making it comparable across different scales.
Percent error compares an experimental value to a known true value: |experimental − theoretical| / |theoretical| × 100. It requires a correct reference. Percent difference compares two experimental values when neither is "correct": |V₁ − V₂| / ((V₁+V₂)/2) × 100. Use percent error in lab experiments with a known standard; use percent difference when comparing two equivalent measurements.
Related Calculators
Percentage Change Calculator
Calculate increase or decrease between two values.
Percent Off Calculator
Find the sale price after a percentage discount.
Average Calculator
Mean, median, mode, and range of any data set.
Molecular Weight Calculator
Calculate the molecular weight of any chemical formula.
Student Loan Calculator
Monthly payment and payoff timeline for student debt.
Basic Calculator
Fast arithmetic: add, subtract, multiply, divide.