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Enter an experimental value and a theoretical value to calculate percent error.
How the Percent Error Calculator Works
Enter the value you measured in the lab (experimental) and the value from a textbook or standard reference (theoretical). The calculator returns the absolute percent error — always a positive number — plus the signed percent error, which shows whether you overestimated or underestimated, and a full step-by-step derivation.
The Percent Error Formula
The standard percent error formula compares how far your measurement is from the accepted value, expressed as a percentage of the accepted value:
% Error = ( abs(Experimental - Theoretical) / abs(Theoretical) ) x 100
The formula uses the absolute value of the theoretical value in the denominator. This ensures the result is mathematically correct even when the accepted value is negative — for example, a temperature of −10°C or a charge of −1.6 × 10⁻¹⁹ C. Without the absolute value, a negative denominator would flip the sign of the result unexpectedly.
The absolute value of the numerator (the difference) ensures the result is always a non-negative number. This gives you the magnitude of the error regardless of direction. If you also need to know which direction the error goes, use the signed percent error shown in the results.
How to Calculate Percent Error Step by Step
Using the gravity example — measured 9.75 m/s², accepted value 9.81 m/s²:
- 1
Find the raw difference
Experimental − Theoretical = 9.75 − 9.81 = −0.06
- 2
Take the absolute value of the difference
abs(−0.06) = 0.06 — this is your absolute error.
- 3
Divide by the absolute value of the theoretical value
0.06 / abs(9.81) = 0.06 / 9.81 ≈ 0.006116
- 4
Multiply by 100 to get a percentage
0.006116 × 100 = 0.6116%. Your measurement was 0.6116% lower than the accepted value — an underestimate.
Signed vs Absolute Percent Error
Absolute Percent Error
Always zero or positive. Tells you the magnitude of the error — how far off you were — without indicating direction. This is the standard value used in most lab reports and science courses.
Signed Percent Error
Can be positive or negative. A positive value means your measurement was higher than expected (overestimate). A negative value means it was lower (underestimate). Useful for identifying systematic bias in experimental methods.
When a lab experiment consistently yields a positive signed error, it suggests a systematic overestimate — perhaps from a poorly calibrated instrument or a consistent procedural bias. Knowing the direction helps you correct for the error in future experiments.
Common Percent Error Reference Table
These real-world examples show the percent error you would get for common lab measurements. Try clicking any Quick Load button in the calculator above to see the full step-by-step working.
| Scenario | Experimental | Theoretical | % Error | Direction |
|---|---|---|---|---|
| Gravity (m/s²) | 9.75 | 9.81 | 0.6116% | Underestimate |
| Boiling point (°C) | 99.5 | 100 | 0.5% | Underestimate |
| Mass (g) | 5.2 | 5.0 | 4% | Overestimate |
| Pi approximation | 3.14 | 3.14159 | 0.0506% | Underestimate |
| Density (g/cm³) | 0.98 | 1.00 | 2% | Underestimate |
Percent Error Calculator FAQ
What is the percent error formula?
Percent error = ( abs(Experimental − Theoretical) / abs(Theoretical) ) × 100. The absolute values ensure the denominator is always positive and the final result is always a non-negative number representing magnitude of error.
What does a negative percent error mean?
A negative signed percent error means your measurement was lower than the accepted value — an underestimate. The absolute percent error shown in most lab reports is always positive; the sign only appears in the signed variant, which tells you the direction of the error.
Can percent error be greater than 100%?
Yes. If your experimental value is more than double the theoretical value (or less than zero when the theoretical is positive), the percent error exceeds 100%. This usually signals a fundamental measurement error, a unit conversion mistake, or a flawed experimental setup rather than normal lab variation.
What is the difference between percent error and percent difference?
Percent error compares a measurement to a known theoretical value. Percent difference compares two experimental values when neither is considered the "true" reference — it divides by the average of the two values instead. Use percent error when a standard or accepted value is known, and percent difference when comparing two similar measurements.
Why do we use the absolute value of the theoretical value in the denominator?
Without abs(Theoretical) in the denominator, a negative theoretical value would flip the sign of the result — giving a negative percent error even when the measured value is higher. Taking the absolute value makes the formula consistent: a positive signed error always means overestimate, negative always means underestimate, regardless of the sign of the theoretical value.
What is an acceptable percent error in a lab experiment?
This depends on the field. In most high-school and undergraduate chemistry or physics labs, a percent error under 5% is generally acceptable. Precision analytical chemistry may require below 1%. In engineering contexts, tolerances vary widely by application — sometimes 0.1% is required, other times 10% is fine. Your instructor or the relevant industry standard will specify what counts as acceptable for your experiment.
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