Percent Error Calculator

What is percent error?

Percent error quantifies how far a measured (experimental) value is from a true (accepted) value, expressed as a percentage. It’s widely used in science, engineering, quality control, and education to evaluate measurement accuracy.

Formula

The standard percent error formula is:

Percent error: |measured − true| ÷ |true| × 100

• Absolute error: |measured − true|
• Relative error: |measured − true| ÷ |true|
• Percent error: relative error × 100

Percent error is undefined when the true value is 0. Use percent difference when comparing two experimental values instead.

How to use the percent error calculator

1. Enter measured value: Type your observed result (supports decimals and scientific notation).
2. Enter true value: Type the accepted/reference value (must not be zero for percent error).
3. Choose mode: Stick with Percent error for true vs measured, or switch to Percent difference for two peers.
4. Set decimals: Select preferred precision for outputs.
5. Calculate: Press Calculate to see absolute error, relative error, and percent error instantly.

Worked examples

Example 1: Gravity measurement

Measured: 9.82, True: 9.81

• Absolute error: |9.82 − 9.81| = 0.01
• Relative error: 0.01 ÷ 9.81 ≈ 0.001019
• Percent error: 0.001019 × 100 ≈ 0.10%

Example 2: Chemistry yield

Measured: 24.6 g, True: 25.0 g

• Absolute error: |24.6 − 25.0| = 0.4 g
• Relative error: 0.4 ÷ 25.0 = 0.016
• Percent error: 0.016 × 100 = 1.6%

Best practices and common pitfalls

• Zero true value: If the accepted value is 0, percent error is not defined. Use percent difference.
• Units: Use consistent units across measured and true values.
• Sign vs magnitude: Percent error uses magnitude; it’s always non‑negative by definition.
• Precision: Match output decimals to the precision of your measurement instruments.
• Replicates: For repeated trials, average measured values first, then compute error.

Percent error vs percent difference

Percent error compares a measured value to a known true value. Percent difference compares two measured values when no true value is available, using the average of their magnitudes in the denominator. Use the mode selector in the calculator to switch as needed.

Who uses this calculator?

• Students: Lab reports, physics problems, chemistry yields, and exam prep.
• Professionals: QA/QC, calibration, metrology, analytics, and process improvement.
• Researchers: Method validation, instrument comparison, and reproducibility checks.
• Educators: Teaching error analysis, accuracy vs precision, and measurement reliability.

Frequently asked questions

HOW TO calculate percent error?

Use |measured − true| ÷ |true| × 100. Enter your measured and true values and click Calculate to get the result.

HOW TO handle a true value of zero?

Percent error is undefined when the true value is 0. Use percent difference: |a − b| ÷ ((|a| + |b|)/2) × 100.

HOW TO choose decimals for reporting?

Match the calculator’s decimals to the precision of your instruments or reporting standards for consistency.

HOW TO compare two experimental values?

Select Percent difference mode when there is no accepted “true” value. It uses the average magnitude in the denominator.

HOW TO reduce percent error in experiments?

Calibrate instruments, standardize procedures, control environmental variables, and average multiple trials.

HOW TO enter scientific notation?

Type formats like 3.2e-5 or 6.7E4. The calculator recognizes both uppercase and lowercase “e”.