Percent Error Calculator

Percent Error equals the absolute value of measured minus actual, divided by the absolute value of actual, times 100 percent

Percent Error =

1.3%

Absolute Error

1.3

Relative Error

0.013

Show Your Work

Measured = 101.3
Actual = 100
Percent Error = |Measured − Actual| / |Actual| × 100%
Percent Error = |101.3 − 100| / |100| × 100%
Percent Error = 1.3 / 100 × 100%
Percent Error = 1.3%
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Percent Error Formula

The standard percent error formula quantifies how far an experimental measurement deviates from a known or accepted value. The absolute value ensures the result is always positive, reflecting the magnitude of deviation regardless of direction.

Percent Error = |Measured − Actual| / |Actual| × 100%

How It Works

Percent error quantifies how far an experimental measurement deviates from a known or accepted value, expressed as a percentage. The formula takes the absolute difference between the measured and actual values, divides it by the absolute value of the actual value, and multiplies by 100. Three related values are calculated: the absolute error (the raw difference), the relative error (absolute error divided by actual), and the percent error (relative error times 100). A lower percent error indicates a measurement that closely matches the accepted value.

Example Problem

You conduct a lab experiment and record the boiling point of water as 101.3 degrees Celsius. The accepted boiling point at standard pressure is 100.0 degrees Celsius.

  1. Identify the measured value from your experiment: 101.3°C.
  2. Identify the actual (accepted) value from a reference: 100.0°C.
  3. Write the formula: Percent Error = |Measured − Actual| / |Actual| × 100%.
  4. Substitute: Percent Error = |101.3 − 100.0| / |100.0| × 100%.
  5. Simplify the numerator and divide: 1.3 / 100.0 = 0.013.
  6. Multiply by 100 to convert to a percentage: Percent Error = 1.3%.

A 1.3% error is generally acceptable for a classroom experiment, suggesting your thermometer and technique produced a reliable measurement.

Key Concepts

Percent error compares a measured value to a known standard, while percent difference compares two measured values using their average as the denominator. Use percent error when you have an accepted reference value. The formula is undefined when the actual value is zero because it requires division by the actual value. In such cases, consider using absolute error alone or a different metric like mean absolute error.

Applications

  • Science labs — comparing experimental results to known constants like the density of water, speed of sound, or gravitational acceleration
  • Manufacturing and quality control — verifying that produced parts match design specifications within acceptable tolerances
  • Financial forecasting — measuring how far predicted revenue or cost figures landed from actual outcomes
  • Survey and polling accuracy — evaluating how close pre-election polls were to final vote counts
  • Calibration checks — testing whether instruments like scales, thermometers, or voltmeters read within rated accuracy

Common Mistakes

  • Using percent error when there is no accepted reference value (use percent difference instead)
  • Forgetting the absolute value, which can produce misleading negative results
  • Attempting to calculate percent error when the actual value is zero (the result is undefined)
  • Confusing percent error with percent difference or percent change, which use different denominators

Frequently Asked Questions

How do you find percent error from measured and actual values?

Subtract the actual value from the measured value, take the absolute value of the result, divide by the absolute value of the actual, and multiply by 100. For example, if you measured 105 when the accepted value is 100, the percent error is |105 − 100| / |100| × 100% = 5%.

What equation does the percent error calculator use?

The formula is Percent Error = |Measured − Actual| / |Actual| × 100%. The absolute value bars ensure the result is non-negative, and the division by the actual value normalizes the error as a fraction of the reference quantity.

Can percent error be negative?

By the standard formula, no. The absolute value in the numerator ensures the result is always zero or positive. Some instructors use a signed version (without absolute value) to show whether the measurement was above or below the actual value, but the unsigned version is the most widely accepted definition.

What happens if the actual value is zero?

The formula requires dividing by the actual value, so when the actual value is exactly zero the result is undefined (division by zero). In such cases, consider using absolute error alone or a different error metric like mean absolute error.

What is a good percent error?

There is no universal threshold. In a college chemistry lab, anything under 5% is typically considered acceptable. In precision manufacturing, tolerances may demand errors below 0.1%. The acceptable range depends entirely on the context and how sensitive the application is to measurement accuracy.

What is the difference between percent error and percent difference?

Percent error compares a measured value to a known standard (actual/theoretical value). Percent difference compares two measured values to each other using their average as the denominator. Use percent error when you have an accepted reference value; use percent difference when comparing two independent measurements.

Can percent error exceed 100%?

Yes. If the measured value deviates from the actual value by more than the actual value itself, percent error will exceed 100%. For example, measuring 250 when the actual value is 100 gives a percent error of 150%.

Worked Examples

Chemistry Lab

How accurate was your density measurement for aluminum?

A student measures the density of an aluminum sample as 2.63 g/cm³. The accepted density of pure aluminum at room temperature is 2.70 g/cm³. How close is the measurement?

  • Measured = 2.63 g/cm³, Actual = 2.70 g/cm³
  • Absolute Error = |2.63 − 2.70| = 0.07 g/cm³
  • Percent Error = 0.07 / 2.70 × 100%
  • Percent Error ≈ 2.59%

Under 5% is typical for student chemistry labs and suggests reliable balance and displacement technique.

Manufacturing QC

Is this machined part within tolerance?

A CNC mill cuts a shaft to a measured diameter of 24.97 mm. The engineering drawing specifies a nominal diameter of 25.00 mm with a ±0.2% tolerance. Does this part pass?

  • Measured = 24.97 mm, Actual (spec) = 25.00 mm
  • Absolute Error = |24.97 − 25.00| = 0.03 mm
  • Percent Error = 0.03 / 25.00 × 100%
  • Percent Error = 0.12% — inside the 0.2% tolerance, so the part passes.

Precision manufacturing usually sets tolerance as a signed range; percent error gives the unsigned magnitude for comparison.

Forecasting

How well did your sales forecast match actual revenue?

A finance team forecasts Q3 revenue at $1,200,000. Actual revenue comes in at $1,285,000. What was the forecast error?

  • Measured (forecast) = 1,200,000, Actual = 1,285,000
  • Absolute Error = |1,200,000 − 1,285,000| = 85,000
  • Percent Error = 85,000 / 1,285,000 × 100%
  • Percent Error ≈ 6.61%

Forecasting teams typically use MAPE (mean absolute percent error) across many periods; single-period percent error is one observation of that series.

Variables in the Percent Error Formula

Every term in the formula has a specific role. Here is what each part represents:

Percent Error = |Measured − Actual| / |Actual| × 100%

Where:

The formula is undefined when the actual value is zero, since you cannot divide by zero. In that case, report the absolute error on its own or pick a metric like mean absolute error that tolerates a zero reference.

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