Percentage Error Calculator

Calculate percentage error between experimental and theoretical values — plus absolute and relative error.

Experimental Value

Theoretical / Accepted

Detailed Metrics

Percentage Error0.101937%

Signed Deviation-0.101937%

Absolute Error0.01

Relative Error0.001019

Deviation from Theoretical Target

-10%-5%0%+5%+10%

Summary Sentence

The experimental value is 0.101937% lower than the theoretical value (Percentage Error: 0.101937%).

Step-by-Step Calculations

1. Absolute Error

Formula: |Experimental - Theoretical|

Substitution: |9.8 - 9.81| = 0.01

2. Relative Error

Formula: Absolute Error / |Theoretical|

Substitution: 0.01 / |9.81| = 0.001019

3. Percentage Error

Formula: Relative Error × 100%

Substitution: 0.001019 × 100 = 0.101937%

Percentage Error Formula & Interpretation

Percentage error measures how far an experimental measurement is from the accepted (theoretical) value: % error = (|E − T| / |T|) × 100.

A positive signed deviation means the experiment over-estimated; negative means under-estimated. Absolute error gives the raw difference, while relative error normalizes it to the scale of the measurement.

Built and maintained by Meet Shah · Last updated 1 August 2026

What this tool is used for

Comparing an experimental result against a theoretical value.
Reporting measurement accuracy in a lab write-up.
Comparing two instruments on the same reference.
Checking whether an error is within a stated tolerance.
Working through a physics or chemistry exercise.

Frequently Asked Questions

What is the formula, exactly?: |experimental − theoretical| ÷ |theoretical| × 100. The accepted value is always the denominator, which is what makes it an error rather than a difference, and both absolute values keep the result positive. The default inputs show the idea: measuring g as 9.8 against the accepted 9.81 is a 0.102% error.
Why does it also show a signed percentage?: Because direction is diagnostic. A magnitude alone cannot distinguish a thermometer reading consistently high from one reading consistently low, and a systematic bias points at a calibration problem while scatter around zero points at random noise. The signed figure keeps the sign of experimental − theoretical.
Why can the theoretical value not be zero?: Because dividing by it is the definition of the measure — relative error is meaningless when the reference is zero, since any deviation is infinitely large in proportion. When the accepted value really is zero, report absolute error in its own units; the tool blocks the case rather than showing Infinity.
How does this differ from percentage difference?: Percentage error has a right answer to compare against and divides by it. Percentage difference compares two measurements of equal standing and divides by their average, which makes it symmetric. Using error where you meant difference silently promotes one of two equally uncertain readings to the status of truth.
What is a good percentage error?: It depends entirely on the field and the instrument. Undergraduate physics labs commonly accept under 5%; an analytical balance should be far inside 0.1%; some biological assays live happily with 20%. The number is only interpretable against the precision of the method that produced it.

Common errors and gotchas

Dividing by the experimental value rather than the accepted one, which is the wrong denominator.
Reporting a signed percentage where the convention is absolute, or the reverse.
Confusing percentage error with percentage difference, which uses the mean as the denominator.
Reporting more figures than the measurement justifies.
Comparing percentage errors when the reference values differ by orders of magnitude.