Percent Error Calculator

Modify the values and click the Calculate button to use

Percent Error: -9.0909%

Percent error: -9.0909%
Absolute error: 1

Percent error compares an observed value with a true or accepted value: (observed − true) ÷ |true| × 100. A negative result means the observation was below the true value.

What this percent error calculator does

Percent error expresses how far an observed or measured value is from a true or accepted value, as a percentage of the true value. It is common in science, engineering, and quality control.

A negative percent error means the observed value is below the true value; a positive value means it is above.

How to use this calculator

Enter the observed value.
Enter the true or accepted value.
Click Calculate.

The default example compares an observed value of 10 with a true value of 11.

Percent error formula

Percent error = (observed − true) / |true| × 100
Absolute error = |observed − true|

The denominator uses the absolute value of the true value so the sign reflects the direction of the observation, not the sign of the true value.

What the results mean

The default example gives a percent error of about −9.0909% and an absolute error of 1. The observed value is about 9.09% below the true value.

A small absolute percent error indicates close agreement; the acceptable threshold depends on the application.

Assumptions and limitations

The true value cannot be zero because the formula divides by it. If the true value is zero, use absolute error or another comparison method.

Percent error is not the same as percent difference. Percent error compares a measurement with a known value; percent difference compares two measurements without a designated true value.

Frequently asked questions

Can percent error be negative?

Yes. A negative result means the observed value is below the true value. Some fields report the absolute value instead.

What is a good percent error?

It depends on the context. A chemistry experiment may accept a few percent, while some engineering measurements require much tighter tolerance.

What if the true value is zero?

The percent error formula is undefined. Use absolute error or a different relative measure.

Is percent error the same as percent difference?

No. Percent error uses a true or accepted value; percent difference usually compares two measured values.

Source

Reference: Wolfram MathWorld — Percent Error.

Disclaimer

This calculator is for educational purposes. Confirm the accepted formula and sign convention for your field.

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