What is the formula for percent error?

Percent Error = (|Vobserved - Vtrue| / Vtrue) * 100%. It measures how far off an observed value is from the accepted true value.

Can percent error be negative?

Yes, if you choose to omit the absolute value calculation. If the observed value is less than the true value, the resulting percent error will be negative (representing underestimation).

Percent Error Calculator — accuracy & deviation solver

Calculate Percent Error

True Value (V_true) The accepted, target, or actual true value (must not be zero).

Observed Value (V_observed) The measured or observed value from experiment.

Error Direction Control whether negative percentage values are allowed when observed < true.

Result

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How to calculate percentage error

The calculation of percentage error compares the difference between an observed value and the accepted true value relative to the true value.

Standard Percentage Error Equations:

Absolute error = |V_observed − V_true|
Relative error = |V_observed − V_true| / V_true
Percentage error = (|V_observed − V_true| / V_true) × 100%

For example, if the observed value is **56.891** and the true value is **62.327**, the calculation is:
|56.891 − 62.327| / 62.327 × 100% = 8.722%

Negative percentage error

When the true value is positive, the percentage error is normally positive due to the absolute value. However, you can choose to calculate **negative percentage error** to see the direction of the error (underestimation).
By omitting the absolute value, if the observed value is smaller than the true value (and the true value is positive), the error is negative:
(V_observed − V_true) / V_true × 100%

For example, given an observed value of **7** and a true value of **9**, the negative percentage error is:
(7 − 9) / 9 × 100% = −22.222%

FAQ

What does a negative percentage error mean?

A negative percentage error indicates that the observed measurement was lower than the accepted true value (underestimation). A positive error indicates it was higher (overestimation).

What if the true value is unknown?

If the true value is completely unknown, percentage error cannot be calculated. Under these situations, standard deviation is typically used to represent error margins.

Disclaimer. RapidRatio is informational only. Verify all calculation steps with experimental protocols or curriculum guidelines.