If your measured value differs from a true or accepted value, percent error quantifies the size of that difference in plain percentages. Use this Percent Error Calculator to plug in your numbers and get an accuracy score you can compare across experiments, products, or models.
What Is Percent Error?
Percent error measures how far a measured (experimental) value is from an accepted (true) value. It reports the difference as a percent, which makes results easier to compare.
Because it uses the absolute difference, percent error is usually reported as a positive number. Some classes also use a signed version (showing whether you’re above or below), but the standard “percent error” is magnitude-focused.
Percent Error Formula (Core Concept)
Percent error uses this relationship:
Percent Error (%) = (|Measured − Accepted| ÷ Accepted) × 100
- Measured: your observed value from an experiment, survey, or calculation.
- Accepted: the reference value you treat as correct (textbook value, lab standard, or verified benchmark).
- |Measured − Accepted|: the absolute difference (always non-negative).
If the measured value equals the accepted value, percent error is 0%. Larger differences produce larger percent error.
Variables and Common Unit Rules
Percent error is unitless because the difference is divided by the accepted value. Still, you must use consistent units for both inputs.
- If accepted is in meters, measured must also be in meters.
- If you switch units (like cm to m), convert first or use a calculator that supports unit conversion.
- If accepted is 0, percent error is undefined (division by zero).
How to Use the Percent Error Calculator
Follow these steps to compute percent error quickly and correctly:
- Enter your Measured value.
- Enter the Accepted value.
- Choose consistent units (if the calculator offers unit options).
- Click Calculate to get percent error.
- Use the result to judge how close your measurement is to the reference.
When you interpret the output, remember that percent error depends on the accepted value. The same absolute difference can lead to different percent errors if the accepted value changes.
Interpreting Percent Error (What the Number Means)
Percent error tells you the relative size of the mistake. While “good” depends on the field and method, these rules of thumb are common:
- 0%–1%: very close; often indicates strong accuracy.
- 1%–5%: reasonable; may be acceptable depending on measurement uncertainty.
- 5%–10%: noticeable deviation; check method, rounding, or assumptions.
- >10%: large mismatch; likely a problem with setup, calculation, or reference value.
Percent error is not the same as percent uncertainty, and it doesn’t automatically tell you why the difference happened. It only quantifies the gap between your value and the accepted value.
Practical Examples
Example 1: Lab Measurement Accuracy
You measure the length of a wire as 9.8 cm, but the accepted length is 10.0 cm. The calculator computes percent error as:
Percent Error = (|9.8 − 10.0| ÷ 10.0) × 100 = 2%
This means your measurement is off by about 2% relative to the accepted value.
Example 2: Forecasting or Modeling Check
A model predicts a demand of 120 units, but the accepted/actual value is 100 units. Percent error becomes:
Percent Error = (|120 − 100| ÷ 100) × 100 = 20%
A 20% percent error signals that the prediction deviated strongly from the reference, so you may need to recalibrate the model or revisit assumptions.
Common Mistakes to Avoid
- Using inconsistent units (e.g., meters vs. centimeters) without converting.
- Putting zero as the accepted value (percent error becomes undefined).
- Mixing rounding too early: keep extra digits until the final step.
- Confusing percent error with percent difference: percent difference often uses a different denominator (like the average).
Frequently Asked Questions
How do you calculate percent error step by step?
Subtract the accepted value from the measured value, then take the absolute value. Divide that absolute difference by the accepted value. Multiply the result by 100 to convert it into a percent. Use the same units for both values to avoid unit mistakes.
Why do we use the absolute value in percent error?
Absolute value removes the negative sign so the percent error represents magnitude only. That way, an overestimate and an underestimate of the same size give the same percent error. Some courses also ask for a signed percent error to show direction.
What does a percent error of 0% mean?
A percent error of 0% means the measured value exactly matches the accepted value. In practice, this can happen when values are rounded to the same number or when you directly measure a known reference. It indicates no difference, not necessarily perfect precision.
Can percent error be negative?
Standard percent error is usually reported as a positive number because the formula uses absolute value. If you remove the absolute value, the result can be negative, which indicates whether the measured value is below the accepted value. Follow your class or lab instructions.
What if the accepted value is zero?
If the accepted value is zero, percent error cannot be computed because it requires dividing by the accepted value. In that case, you need a different metric, like absolute error or percent change with a nonzero baseline. Always check your denominator before calculating.
Next Steps: Use Percent Error with Uncertainty
Percent error measures accuracy against a reference. To evaluate overall measurement quality, pair it with uncertainty (how spread out your measurements are). A small percent error with large uncertainty suggests inconsistency; a larger percent error with small uncertainty suggests a consistent bias.
If you want a deeper check, compare percent error across repeated trials, track how it changes with improved technique, and document your assumptions about the accepted value.
