How to Calculate Percentage Error
Percentage error measures how far an estimated or measured value is from the true (accepted) value, expressed as a percentage. It is used in science, engineering, and quality control to judge how accurate a result is.
The percentage error formula
- Subtract the true value from the measured value.
- Take the absolute value (ignore any minus sign).
- Divide by the true value.
- Multiply by 100 to express as a percentage.
The absolute value means percentage error is always reported as a positive number. A separate note of whether the measurement was too high or too low tells you the direction.
Example: You measure a piece of wood as 52 cm, but the true
length is 50 cm.
Difference = |52 − 50| = 2 cm
Divided by true: 2 ÷ 50 = 0.04
Result = 0.04 × 100 = 4%
Worked examples
| Scenario | Measured value | True value | Percentage error |
|---|---|---|---|
| Lab thermometer | 99°C | 100°C | 1% |
| Scale weight | 510 g | 500 g | 2% |
| Distance estimate | 9.5 km | 10 km | 5% |
| Speed gun reading | 63 mph | 60 mph | 5% |
| Chemical yield | 18.9 g | 20 g | 5.5% |
Percentage error vs percentage difference
These two terms are often confused:
- Percentage error compares a measured value to a known true value. There is a definitive "correct" answer.
- Percentage difference compares two values where neither is treated as the reference. It uses the average of the two as the denominator.
Use percentage error when you know the accepted value (a textbook result, a certified measurement). Use percentage difference when comparing two equally uncertain values.
Percentage error vs percentage change
Percentage change measures how a value evolves over time — for example, a price rising from $40 to $46. Percentage error measures accuracy against a fixed benchmark. The formulas look similar, but the intent is different.
Common mistakes
Forgetting the absolute value
If your measurement is lower than the true value, the subtraction gives a negative number. Always take the absolute value before dividing. Percentage error is a magnitude, not a direction.
Dividing by the measured value instead of the true value
Always divide by the true (accepted) value, not the measured value. Dividing by the wrong number gives a different result and is not percentage error by the standard definition.
Confusing a small error with a good result
A 5% error may be acceptable in a rough field measurement but completely unacceptable in a pharmaceutical assay. Whether an error is "good" depends on the context and the required tolerance.
When percentage error cannot be used
The formula requires a non-zero true value. If the true value is zero, dividing by it is undefined. In that case, use absolute error (the raw difference) instead.
FAQ
What is the formula for percentage error?
(|Measured − True| ÷ True) × 100. The result is always a positive number.
Can percentage error be greater than 100%?
Yes. If your measurement is more than double the true value, the error exceeds 100%. There is no upper limit.
What is an acceptable percentage error?
It depends on the field. In many school labs, under 5% is considered acceptable. In manufacturing or medicine, tolerances can be much tighter — often under 1%.
What is the percentage error if I measure 95 and the true value is 100?
(|95 − 100| ÷ 100) × 100 = (5 ÷ 100) × 100 = 5%.
Use the Percentage Change Calculator to quickly find the difference between two values.