2026-08-07 9 min

Percent Error Calculator

Calculate the percent error between an observed or measured value and a true or theoretical value. Free online percent error calculator with step-by-step results.

Calculator

Measurement Values

Observed Value

True Value

Allow negative percentage error

Results update automatically

Results update live as you type

Status:Error 8.722%Absolute 5.436Under by 8.722%

Percent Error Summary

Observed56.891

True62.327

Percent Error8.722%

Signed Error-8.722%

Error Breakdown

Metric	Value	Meaning
Absolute Error	5.436	Size of the miss
Relative Error	0.087	Miss ÷ true value
Percent Error	8.722%	Relative × 100
Accuracy	91.278%	100% − error

Results

Normal

Percentage Error

8.722%

|Observed − True| ÷ True × 100%

Absolute Error

5.436

|Observed − True| in original units

Relative Error

0.087

Absolute error ÷ true value (dimensionless)

Signed Error

-8.722%

Underestimate — observed is below true

Accuracy Score

91.278%

100% minus percent error

Direction

Under

Whether the measurement fell short or overshot

Percent error divides by the true value, so results are exact for the inputs given. Keep units consistent, use a non-zero reference, and pair with absolute error for physical context.

Visualizations

Error Magnitudes

5.4Abs Error

0.1Rel Error

8.7Pct Error

Accuracy vs Error Share

Accurate91%

Error9%

Accuracy Meter

Accuracy91.3%

Observed vs True Value

Observed56.9

Formula

Percent error expresses the difference between a measurement and the accepted value as a percentage of the accepted value, making accuracy comparable across scales.

Percent Error = |Observed − True| / True × 100%

Alternative Form

Signed: (Observed − True) / True × 100%; Relative Error = |Observed − True| / True

Variables

Symbol	Name	Unit	Description
E_obs	Observed value	units	The measured or experimental result
E_true	True value	units	The accepted or theoretical reference
E_abs	Absolute error	units	\|Observed − True\|
E_rel	Relative error	ratio	Absolute error ÷ true value
E_%	Percent error	%	Relative error × 100%
s	Signed error	%	Keeps the sign: negative = underestimate
A	Accuracy	%	100% − percent error

Explanation

Dividing by the true value normalizes the error so a 5-unit miss on a 50-unit standard (10%) reads the same regardless of units, while the absolute error keeps the physical size of the miss.

Derivation

Difference = Observed − True. Absolute Error = |Difference|. Relative Error = Absolute Error ÷ True. Percent Error = Relative Error × 100. Signed Error = Difference ÷ True × 100. Accuracy = 100 − Percent Error.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Find the raw difference between observed and true values.

Difference = Observed − True

Observed:56.891

True:62.327

Intermediate: 56.891 − 62.327 = -5.436

Result: Difference = -5.436

Step 2

Take the absolute value to get the absolute error.

Absolute Error = |Difference|

Difference:-5.436

Intermediate: |-5.436|

Result: Absolute error = 5.436

Step 3

Divide by the true value to get the relative error.

Relative Error = Absolute Error ÷ True

Absolute Error:5.436

True:62.327

Intermediate: 5.436 ÷ 62.327

Result: Relative error = 0.087

Step 4

Multiply by 100 to express the error as a percentage.

Percent Error = Relative Error × 100%

Relative Error:0.087

Intermediate: 0.087 × 100

Result: Percent error = 8.722%

Step 5

Check the sign of the raw difference to see the direction of the error.

Signed Error = (Observed − True) ÷ True × 100%

Difference:-5.436

True:62.327

Intermediate: -5.436 ÷ 62.327 × 100

Result: Signed error = -8.722% (underestimate)

Step 6

Convert to an accuracy score by subtracting from 100%.

Accuracy = 100% − Percent Error

Percent Error:8.722%

Intermediate: 100 − 8.722

Result: Accuracy = 91.278%

Final Answer

8.722%

Worked Examples

See how the calculator works with different scenarios.

Scenario

An observed value of 56.891 against a true value of 62.327.

Inputs

Observed:56.891

True:62.327

Calculation

Absolute = |56.891 − 62.327| = 5.436 Relative = 5.436 ÷ 62.327 = 0.087 Percent = 0.087 × 100 = 8.722%

Result

8.722% error — moderate accuracy

Interpretation

A single-digit percent error is acceptable in many teaching labs but would miss a strict 5% tolerance.

Understanding Your Result

Your Result: Percentage Error: 8.722%

Typical range: Under 1% is excellent (analytical chemistry), under 5% is good (physics and engineering), 5–20% is moderate (biology, field work), and over 20% usually signals a broken procedure.

What This Means

Percent error tells you how far a measurement landed from the accepted value in percentage terms, with the absolute error giving the physical size of the miss and the signed error showing its direction.

Why It Matters

It turns raw deviations into a scale-free accuracy score, so a chemistry yield, a machined dimension, and a sensor reading can all be judged against the same 5% or 1% bar.

Professional Interpretation

Report percent error alongside absolute error: the percentage judges fitness for purpose while the absolute value keeps the physical consequence in view.

Recommendations

•Compare against your field tolerance, not a universal cutoff
•Use signed error when the direction of bias matters
•Average repeated trials before computing error
•Keep absolute error in the report for physical context
•Recalibrate when errors skew one-signed across trials
•Never use percent error with a zero reference value

Educational Content

Introduction

Percent error quantifies accuracy: how close a measured value came to the true value. This page computes absolute, relative, signed, and percentage error from any observed/true pair.

Concept Explanation

Subtract to find the gap, divide by the true value to normalize it, and multiply by 100 to speak in percent. The absolute value gives magnitude; dropping it reveals whether you overshot or undershot.

Applications

▸Checking titration and synthesis yields against theory

▸Verifying machined parts against design dimensions

▸Validating sensor readings against reference instruments

▸Grading student lab accuracy in teaching labs

▸Testing medical devices against calibration standards

▸Benchmarking forecasts against realized outcomes

Benefits

•Scale-free: comparable across units and magnitudes
•Separates magnitude (absolute) from direction (signed)
•Maps directly onto tolerance and pass/fail bands
•Simple enough for spreadsheet and mental checks
•Standard metric in scientific reporting and review

Limitations

•Undefined when the true value is zero
•Hides the physical size of large-scale misses
•Single reading says nothing about repeatability
•Asymmetric if the reference itself is uncertain

Best Practices

•Average repeats before computing the final error
•Pair percent error with absolute error in reports
•Use signed error to hunt systematic bias
•Match significant figures to your instruments
•Document which denominator convention you used

Common Misconceptions

Myth: A small percent error means precise measurements.

Truth: Percent error measures accuracy (closeness to truth), not precision (repeatability). Check standard deviation for precision.

Myth: Percent error can never exceed 100%.

Truth: It can: when the miss is bigger than the reference itself, e.g. observing 25 against a true 10 gives 150%.

Myth: Zero percent error proves a perfect experiment.

Truth: An exact match on one trial is usually luck or coarse resolution — repeat the measurement to confirm.

Myth: Negative percent error is a mistake.

Truth: Signed negative error is informative: it means the reading came in below the reference.

Practical Tips

•Average multiple trials before computing error
•Enable signed error to spot systematic bias
•State the denominator when reporting to others
•Use =ABS(A1-B1)/B1*100 for quick spreadsheet checks
•Recalibrate instruments when bias is one-sided
•Control temperature and humidity for sensitive rigs
•Match decimal places to instrument resolution

Common Mistakes

Dividing by the observed value instead of the true value

Always divide by the accepted/true reference so error is measured against the standard.

Using percent error with a zero reference

Switch to absolute error or full-scale error when the true value is zero or near zero.

Confusing percent error with percent difference

Use percent error against a known standard; use percent difference (average denominator) for two peer measurements.

Reporting more digits than the instrument supports

Round the error to the significant figures of your least-precise input.

Judging all fields by the same 5% bar

Apply your discipline tolerance — 1% for assay work, up to 20% for field biology.

Assumptions

This calculator makes the following assumptions to provide estimates:

Known Reference: The true value is treated as an exact, trustworthy standard.

Non-Zero Denominator: The true value must be non-zero for percent error to exist.

Single Comparison: The calculation compares one observed value against one reference.

Consistent Units: Observed and true values are assumed to share the same units.

Independent Reading: The observed value is taken as given; no averaging is performed internally.

Limitations

Be aware of these limitations when using this calculator:

No Precision Info: One reading cannot reveal spread; pair with standard deviation for repeatability.

Zero Reference: Undefined at a true value of zero — absolute error must be used instead.

Reference Uncertainty: If the standard itself is uncertain, the error inherits that doubt.

Scale Blindness: Equal percentages can mean very different physical consequences at different scales.

Frequently Asked Questions

Answers to common questions about this calculator.

What is percent error?

Percent error is a measure of how close an observed or experimental value is to a true or theoretical value, expressed as a percentage. It is calculated by taking the absolute difference between the observed and true values, dividing by the true value, and multiplying by 100%. Percent error is commonly used in science, engineering, and statistics to quantify the accuracy of measurements.

How do you calculate percent error?

To calculate percent error: (1) find the absolute difference between the observed value and the true value, (2) divide that difference by the true value, and (3) multiply by 100%. The formula is: Percent Error = |Observed - True| / True x 100%. If negative percent error is allowed, omit the absolute value: Percent Error = (Observed - True) / True x 100%.

What is the percent error formula?

The standard percent error formula is: Percent Error = |Observed Value - True Value| / |True Value| x 100%. The absolute value ensures the result is always positive, indicating the magnitude of the error without regard to direction. Some applications use the signed version: Percent Error = (Observed - True) / True x 100%, which can be negative.

What is the difference between percent error and percent difference?

Percent error compares a measured value to a known true or accepted value. Percent difference compares two measured values when neither is considered the true value. Percent difference uses the average of the two values in the denominator: |Value1 - Value2| / ((Value1 + Value2)/2) x 100%. Use percent error when you have a reference standard; use percent difference when comparing two experimental results.

What is the difference between percent error and percent change?

Percent error measures accuracy by comparing a measurement to a true value. Percent change measures the relative change between an old value and a new value: (New - Old) / Old x 100%. Percent error is used in experimental science; percent change is used in finance, economics, and trend analysis.

Can percent error be negative?

Percent error can be negative if you omit the absolute value from the formula. A negative percent error indicates the observed value is less than the true value (underestimation). A positive percent error indicates the observed value is greater than the true value (overestimation). By default, most calculators use the absolute value to show only the magnitude of the error.

What does a negative percent error mean?

A negative percent error means the observed or measured value is smaller than the true or accepted value. For example, if you measure 45 mL but the true volume is 50 mL, the percent error is (45 - 50) / 50 x 100% = -10%, indicating a 10% underestimation.

What is a good percent error?

A good percent error depends on the field and context. In physics and engineering, errors under 5% are typically considered good. In chemistry, errors under 1% may be required for quantitative analysis. In biology and social sciences, errors of 10-20% may be acceptable. The key is to understand the tolerances and standards of your specific field.

What is the difference between absolute error and relative error?

Absolute error is the absolute difference between the observed and true values (|Observed - True|), expressed in the same units as the measurement. Relative error is the absolute error divided by the true value, making it a dimensionless ratio. Percent error is relative error multiplied by 100%.

What is the difference between accuracy and precision?

Accuracy refers to how close a measurement is to the true value, which is what percent error measures. Precision refers to how consistent repeated measurements are with each other, which is measured by standard deviation or variance. A measurement can be accurate but not precise, precise but not accurate, both, or neither.

Can percent error be greater than 100%?

Yes, percent error can exceed 100%. This occurs when the absolute difference between the observed and true values is larger than the true value itself. For example, if the true value is 10 and the observed value is 25, the percent error is |25 - 10| / 10 x 100% = 150%.

What is the percent error when the true value is zero?

Percent error is undefined when the true value is zero because division by zero is mathematically undefined. If the true value is zero and the observed value is non-zero, the percent error is infinite (or undefined). In practice, avoid using percent error when the true reference value is zero; use absolute error instead.

How do you reduce percent error in experiments?

To reduce percent error: (1) use calibrated, high-quality instruments, (2) take multiple measurements and use the average, (3) control environmental variables like temperature and humidity, (4) follow standardized procedures carefully, (5) minimize human error through automation or careful technique, and (6) identify and eliminate systematic errors through proper experimental design.

How do you calculate percent error in Excel?

In Excel, calculate percent error using the formula: =ABS(observed - true) / true * 100. For example, if the observed value is in cell A1 and the true value is in cell B1, the formula is =ABS(A1-B1)/B1*100. For signed percent error, omit ABS: =(A1-B1)/B1*100.

Related Calculators

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Related Guides

Deepen your understanding with these educational resources.

Understanding Measurement Accuracy

Accuracy vs precision and error metrics.

Lab Error Analysis Basics

From raw readings to reported error.

Significant Figures Guide

Report only what your instrument earns.

Calibration Best Practices

Keep systematic bias out of your data.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Percent error: |Observed − True| ÷ True × 100%: accuracy as a percentage.
Absolute error: The raw gap |Observed − True| in original units.
Relative error: Absolute error divided by the true value; dimensionless.
Signed error: Error keeping its sign: negative means underestimation.
Accuracy: Closeness of a measurement to the true value.
Precision: Repeatability of measurements, measured by spread.
True value: The accepted or theoretical reference a reading is judged against.
Systematic error: Bias that pushes readings consistently one way.
Random error: Unpredictable variation that averages out over repeats.
Tolerance: The maximum allowable error for a part or process.

Authoritative References

Trusted sources and standards referenced by this calculator.

Wikipedia — Approximation Error Wikipedia — Observational Error Wikipedia — Accuracy and Precision Wikipedia — Relative Change and Difference Britannica — Error Analysis NIST — Accuracy and Precision

Applicable Standards

NIST guidance on accuracy and precision reporting

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Page Information

Last Updated:

2026-08-07

Version:

2.0.0

References:

License:

Free to use for educational and professional purposes.